Carnegie Mellon University

Graduate Course Catalog

Graduate courses offered by CMU Biomedical Engineering

42611 | Biomaterials | Prof. Rosalyn Abbott | Spring
This class serves as an overview of the landscape of biomaterial engineering and research. This course will cover the application of materials in biological environments, focusing on structure-processing-property relationships, engineering design principles, and how the biological environment affects the material properties. This course will focus on applications of a variety of materials that interface with biological systems including natural biopolymers, synthetic polymers, metals, and ceramics. Topics include considerations in molecular design of biomaterials, fundamentals of thermodynamic and kinetics relationships, the application of bulk and surface properties in the design of medical devices, and understanding tissue-biomaterials interactions. This course will discuss practical applications of materials in drug delivery, tissue engineering, biosensors, and other biomedical technologies. Students will be assessed with homework assignments and quizzes. At the end of the class, in teams, students will apply the concepts they have learned to write and present a focused review on a biomaterial design/concept that excites them.

42612 | Tissue Engineering | Prof. Adam Feinberg | Fall
This course will train students in advanced cellular and tissue engineering methods that apply physical, mechanical and chemical manipulation of materials in order to direct cell and tissue function. Students will learn the techniques and equipment of bench research including cell culture, immunofluorescent imaging, soft lithography, variable stiffness substrates, application/measurement of forces and other methods. Students will integrate classroom lectures and lab skills by applying the scientific method to develop a unique project while working in a team environment, keeping a detailed lab notebook and meeting mandated milestones. Emphasis will be placed on developing the written and oral communication skills required of the professional scientist. The class will culminate with a poster presentation session based on class projects. Pre-requisite: Knowledge in cell biology and biomaterials, or permission of instructor

42613 | Polymeric Biomaterials | Prof. Adam Feinberg | Spring
This course will cover aspects of polymeric biomaterials in medicine from molecular principles to device scale design and fabrication. Topics include the chemistry, characterization, and processing of synthetic polymeric materials; cell-biomaterials interactions including interfacial phenomena, tissue responses, and biodegradation mechanisms; aspects of polymeric micro-systems design and fabrication for applications in medical devices. Recent advances in these topics will also be discussed.

42615 | Special Topics: Biomaterial Host Interactions in Regenerative Medicine | Prof. Phil Campbell | Spring
Special Topics: This course will provide students with hands-on experience in investigating host responses to synthetic and naturally biomaterials used in regenerative medicine applications. Students will gain experience in the analysis of host responses to these biomaterials as well as strategies to control host interaction. Biomaterial biocompatibility, immune interactions, tissue healing and regeneration will be addressed. Students will integrate classroom lectures with laboratory skills evaluating host-material interactions in a laboratory setting. Laboratory characterization techniques will include cell culture techniques, microscopic, cytochemical, immunocytochemical and histological analyses. Prerequisite: junior or senior standing in Biomedical Engineering or consent of the instructor.

42616 | Bio-nanotechnology: Principles and Applications | Prof. Tzahi Cohen-Karni | Fall
Have you ever wondered what is nanoscience and nanotechnology and their impact on our lives? In this class we will go through the key concepts related to synthesis (including growth methodologies and characterizations techniques) and chemical/physical properties of nanomaterials from zero-dimensional (0D) materials such as nanoparticles or quantum dots (QDs), one-dimensional materials such as nanowires and nanotubes to two-dimensional materials such as graphene. The students will then survey a range of biological applications of nanomaterials through problem-oriented discussions, with the goal of developing design strategies based on basic understanding of nanoscience. Examples include, but are not limited to, biomedical applications such as nanosensors for DNA and protein detection, nanodevices for bioelectrical interfaces, nanomaterials as building blocks in tissue engineering and drug delivery, and nanomaterials in cancer therapy.  This class is open for both undergraduate (junior/senior) and graduate students.

42620 | Engineering Molecular Cell Biology | Prof. Charlie Ren | Fall
Cells are not only basic units of living organisms but also fascinating engineering systems that exhibit amazing functionality, adaptability, and complexity. Applying engineering perspectives and approaches to study molecular mechanisms of cellular processes plays a critical role in the development of contemporary biology. At the same time, understanding the principles that govern biological systems provides critical insights into the development of engineering systems. The goal of this course is to provide basic molecular cell biology for engineering students with little or no background in cell biology, with particular emphasis on integrating engineering concepts throughout the entire learning process of modern molecular and cellular biology. This course will prepare advanced undergraduate or graduate students with the essential knowledge and mindset for future research endeavors involving engineering biological systems at molecular and cellular levels. This course, besides introducing the fundamental biological knowledge, aims to enhance students' comprehension and appreciation of (1) how engineering approaches have led to our current understanding of molecular and cell biology; (2) what the available engineering approaches are that allow manipulation and even creation of biological systems at molecular, cellular and tissue levels; (3) what the current challenges are in molecular and cell biology that could be solved one day by engineering innovation. Course topics include the engineering of cellular components (DNA, RNA, protein, cell membrane, mitochondria, extracellular matrix) and cellular processes (metabolism, proliferation, cell death, tissue formation). Pre-requisites: None. Prior completion of 03-121 Modern Biology is suggested but not required.

42621 | Prof. Elizabeth Wayne | Principles of Immunoengineering and Development of Immunotherapy Drugs | Spring
This course will provide context for the application of engineering principles to modulate the immune system to approach problems in human health. Basic understanding of the components and function of the innate and adaptive immune system. Students will leave with a basic understanding of immunology and of the engineering techniques used to develop and characterize immunotherapy systems. Where appropriate, we will discuss how immunoengineering fits into other disciplines of engineering such as mechanical, chemical, and materials science. Because the purpose of immunoengineering is disease treatment, we will discuss the therapy pipeline, development of clinical trials and the FDA approval process. Immunotherapy will also be assessed within different disease contexts including cancer, infectious disease, allergies, prosthetics and implants, neuro and musculoskeletal disorders.

42624 | Biological Transport and Drug Delivery | Prof. Newell Washburn | Spring
Analysis of transport phenomena in life processes on the  molecular, cellular, organ and organism levels and their application to the  modeling and design of targeted or sustained release drug delivery  technologies. Coupling of mass transfer and reaction processes will be a  consistent theme as they are applied to rates of receptor-mediated solute  uptake in cells, drug transport and biodistribution, and drug release from  delivery vehicles. Design concepts underlying advances in nanomedicine will  be described.

42625 | Surgery for Engineers | Prof. Howard Edington | Spring
This course explores the impact of engineering on surgery. Students will interact with clinical practitioners and investigate the technological challenges that face these practitioners. A number of visits to the medical center are anticipated for hands on experience with a number of technologies utilized by surgeons to demonstrate the result of advances in biomedical engineering. These experiences are expected to include microvascular surgery, robotic surgery, laparoscopic, and endoscopic techniques. Tours of the operating room and shock trauma unit will be arranged. If possible observation of an operative procedure will be arranged (if scheduling permits). Invited surgeons will represent disciplines including cardiovascular surgery, plastic and reconstructive surgery, surgical oncology, trauma surgery, minimally invasive surgery, oral and maxillofacial surgery, bariatric surgery, thoracic surgery, orthopedic surgery, and others.    The Primary Instructor is Howard Edington, M.D., MBA System Chairman of Surgery, Allegheny Health Network. This course meets once a week for 3 hours. Several sessions will be held at the Medical Center, transport provided.  Pre-requisite: Physiology 42-202 and one of the introductory engineering courses, 42-101, 06-100, 12-100. 18-100, 19-101, 24-101, or 27-100  Priority for enrollment is given to BME Graduate students and additional majors, followed by BME minors.

42630 | Introduction to Neural Engineering | Prof. Matt Smith | Spring
Neural engineering sits at the interface between neuroscience and engineering, applying classical engineering approaches and principles to understand the nervous system and its function. Modern neural engineering techniques have been used to measure neural activity using tools based on light, electricity, and magnetism. The same tools for measurement can be redirected to modulate neural activity, and manipulate how an organism perceives, thinks, and acts. The course objectives are to familiarize students with a range of neural engineering approaches to investigating and intervening in the nervous system, emphasizing quantitative understanding and fundamental engineering concepts. The course will pair lectures and discussion with projects involving real neural data (Matlab-based exercises). Example projects could include finding visual responses in EEG data, or determining how groups of individual neurons interact based on spiking data. Overall, the goal is to give the student a deep understanding of select topics in neuroscience and the application of quantitative neural engineering approaches to these topics. This course is intended for advanced undergraduate and entering graduate students. Familiarity with linear algebra, signal processing, and introductory Matlab programming is helpful. This course is suitable for students coming from diverse backgrounds: (1) Students with non-engineering backgrounds seeking quantitative skills, and wanting to learn an engineering approach to neuroscience problems, and (2) students with engineering or other quantitative backgrounds who are seeking ways to apply their skills to scientific questions in neuroscience.

42631 | Neural Data Analysis | Prof. TBD | Fall
The vast majority of behaviorally relevant information is transmitted through the brain by neurons as trains of actions potentials. How can we understand the information being transmitted? This class will cover the basic engineering and statistical tools in common use for analyzing neural spike train data, with an emphasis on hands-on application. Topics may include neural spike train statistics (Poisson processes, interspike intervals, Fano factor analysis), estimation (MLE, MAP), signal detection theory (d-prime, ROC analysis, psychometric curve fitting), information theory, discrete classification, continuous decoding (PVA, OLE), and white-noise analysis. Each topic covered will be linked back to the central ideas from undergraduate probability, and each assignment will involve actual analysis of neural data, either real or simulated, using Matlab. This class is meant for upper-level undergrads or beginning graduate students, and is geared to the engineer who wants to learn the neurophysiologist's toolbox and the neurophysiologist who wants to learn new tools. Those looking for broader neuroscience application (eg, fMRI) or more focus on regression analysis are encouraged to take 36-746. Those looking for more advanced techniques are encouraged to take 18-699. Prerequisites: undergraduate probability (36-225/227, or its equivalent), some familiarity with linear algebra and Matlab programming

42632 | Neural Signal Processing | Prof. Byron Yu | Spring
The brain is among the most complex systems ever studied. Underlying  the brain's ability to process sensory information and drive motor  actions is a network of roughly 10^11 neurons, each making 10^3  connections with other neurons. Modern statistical and machine  learning tools are needed to interpret the plethora of neural data  being collected, both for (1) furthering our understanding of how the  brain works, and (2) designing biomedical devices that interface with  the brain. This course will cover a range of statistical methods and  their application to neural data analysis. The statistical topics  include latent variable models, dynamical systems, point processes,  dimensionality reduction, Bayesian inference, and spectral analysis.  The neuroscience applications include neural decoding, firing rate  estimation, neural system characterization, sensorimotor control,  spike sorting, and field potential analysis. Prerequisites: 18-290;  36-217, or equivalent introductory probability theory and random  variables course; an introductory linear algebra course; senior or  graduate standing. No prior knowledge of neuroscience is needed.

42640 | Image-Based Computational Modeling and Analysis | Prof. Jessica Zhang | Fall
Biomedical modeling and visualization play an important role in mathematical modeling and computer simulation of real/artificial life for improved medical diagnosis and treatment. This course integrates mechanical engineering, biomedical engineering, computer science, and mathematics together. Topics to be studied include medical imaging, image processing, geometric modeling, visualization, computational mechanics, and biomedical applications. The techniques introduced are applied to examples of multi-scale biomodeling and simulations at the molecular, cellular, tissue, and organ level scales.

42641 | Rehabilitation Engineering | Prof. Edmund Lopresti | Fall 2024
Rehabilitation engineering is the systematic application of engineering sciences to design, develop, adapt, test, evaluate, apply, and distribute technological solutions to problems confronted by individuals with disabilities. This course focuses on assistive technologies - technologies designed for use in the everyday lives of people with disabilities to assist in the performance of activities of daily living. The course surveys assistive technologies designed for a variety of functional limitations - including mobility, communication, hearing, vision, and cognition - as they apply to activities associated with employment, independent living, education, and integration into the community. This course considers not only technical issues in device development, but also the psychosocial factors and market forces that influence device acceptance by individuals and the marketplace.  Pre-req:  Junior or senior standing

42645 | Cellular Biomechanics |  every other year
This course discusses how mechanical quantities and processes such as force, motion, and deformation influence cell behavior and function, with a focus on the connection between mechanics and biochemistry. Specific topics include: (1) the role of stresses in the cytoskeleton dynamics as related to cell growth, spreading, motility, and adhesion; (2) the generation of force and motion by moot molecules; (3) stretch-activated ion channels; (4) protein and DNA deformation; (5) mechanochemical coupling in signal transduction. If time permits, we will also cover protein trafficking and secretion and the effects of mechanical forces on gene expression. Emphasis is placed on the biomechanics issues at the cellular and molecular levels; their clinical and engineering implications are elucidated. 

42648 | Cardiovascular Mechanics | Prof. Jason Szafron | Spring
The primary objective of the course is to learn to model blood flow and mechanical forces in the cardiovascular system. After a brief review of cardiovascular physiology and fluid mechanics, the students will progress from modeling blood flow in a.) small-scale steady flow applications to b.) small-scale pulsatile applications to c.) large-scale or complex pulsatile flow applications. The students will also learn how to calculate mechanical forces on cardiovascular tissue (blood vessels, the heart) and cardiovascular cells (endothelial cells, platelets, red and white blood cells), and the effects of those forces. Lastly, the students will learn various methods for modeling cardiac function.  When applicable, students will apply these concepts to the design and function of selected medical devices (heart valves, ventricular assist devices, artificial lungs).

42649 | Introduction to Biomechanics | Prof. Axel Moore | Fall
The purpose of this course is to achieve a broad overview of the application of mechanics to the human body.  This includes solid, fluid, and viscoelastic mechanics applied to single cells, the cardiovascular system, lungs, muscles, bones, and human movement. The physiology of each system will be reviewed as background prior to discussing mechanics applications within that system.  There are no firm prerequisites, but statics, fluid mechanics, and biology are helpful.

42650 | Introduction to Biomedical Imaging | Prof. Jana Kainerstorfer | Spring
The field of medical imaging describes methods of seeing the interior of the human body, as well as visual representation of tissue and organ function. The materials covered in this course will give an overview of existing medical imaging devices used in a clinical and pre-clinical setting. The course presents the principles of medical imaging technologies, explaining the mathematical and physical principles, as well as describing the fundamental aspects of instrumentation design. Students will gain a thorough understanding of how these methods are used to image morphological and physiological features. Imaging methods will include Ultrasound, X-ray, computed tomography (CT), and magnetic resonance imaging (MRI), as well as optical methods. For each method, the fundamental imaging principles will be discussed, and examples of clinical applications will be presented. No prior knowledge of imaging methods is required.

42652 | Nano-Bio-Photonics | Prof. Maysam Chamanzar | Spring
Light can penetrate biological tissues non-invasively. Most of the available bio-optic tools are bulky. With the advent of novel nanotechnologies, building on-chip integrated photonic devices for applications such as sensing, imaging, neural stimulation, and monitoring is now a possibility. These devices can be embedded in portable electronic devices such as cell phones for point of care diagnostics. This course is designed to convey the concepts of nano-bio-photonics in a practical way to prepare students to engage in emerging photonic technologies. The course starts with a review of electrodynamics of lightwaves. The appropriate choice of wavelength and material platform is the next topic. Then optical waveguides and resonators are discussed. Resonance-based sensing is introduced followed by a discussion of the Figure of Merits (FOMs) used to design on-chip sensors. Silicon photonics is introduced as an example of a CMOS-compatible platform. On-chip spectroscopy is the next topic. The second part covers nano-plasmonics for bio-detection and therapy. The design methods are discussed, followed by an overview of nanofabrication and chemical synthesis, and then a discussion of applications. The last part of this course will be dedicated to a review of recent applications such as Optogenetic neural stimulation, Calcium imaging, Cancer Imaging and Therapy. Senior or graduate standing required. This course is cross-listed with 18416. Although students in 18-616 and 18-416 will share the same lectures and recitations, students in 18-616 will receive distinct course projects. Students in 18-416 and 18-616 will be graded on separate curves.

42655 | Biostatistics | Prof. Patjanaporn Chalacheva | Spring
This course introduces statistical methods for making inferences in engineering, biology and medicine. Students will learn how to select the most appropriate methods, how to apply these methods to actual data, and how to read and interpret computer output from a commonly used statistical package. The topics covered are descriptive statistics; elementary probability; discrete and continuous random variables and their distributions; hypothesis testing involving interval (continuous and discrete) and categorical (nominal and ordinal) variables, for two and three or more treatments; simple and multiple linear regression; time-series analysis; clustering and classification; and time-to-event (survival) analysis. Students will also learn how to write the statistical component of a "Results" section for a scientific paper and learn about the limitations of the statistical analyses.  Basic familiarity with probability and probability distribution preferred but not required.

42656 | Introduction to Machine Learning for Biomedical Engineers | Prof. Parjanaporn Chalacheva | Fall
This course introduces fundamental concepts, methods and applications in machine learning and datamining. We will cover topics such as parametric and non-parametric learning algorithms, support vector machines, neural networks, clustering, clustering and principal components analysis.   The emphasis will be on learning high-level concepts behind machine learning algorithms, and applying them to biomedical-related problems. This course is intended for advanced undergraduate and graduate students in Biomedical Engineering or related disciplines. Students should have experience with high-level programming language such as Matlab, basic familiarity with probability, statistics and linear algebra, and should be comfortable with manipulating vectors and matrices.

42660 | Bioinstrumentation | Prof. Yu-li Wang | Spring
This course aims to build concepts and skills in electronics for the design and construction of instruments for biomedical applications.   The course uses a flipped, fast-paced format to cover a range of electronic components and circuits, including resistors, capacitors, transistors, sensors, actuators, amplifiers, signal filters, and microcontrollers, through lectures, tutorials, weekly lab projects, and term projects.   Students, with or without a background in electronics, will gain hands-on skills to build functional instruments for physiological measurements such as temperature, gas concentration, blood pressure, and EKG signals.

42665 | Brain-Computer Interface: Principles and Applications | Prof. Bin He | Spring
This course provides an introduction and comprehensive review of the concepts, principles and methods of Brain-computer interface (BCI) technology. BCIs have emerged as a novel technology that bridges the brain with external devices. BCIs have been developed to decode human intention, leading to direct brain control of a computer or device, bypassing the neuromuscular pathway. Bi-directional brain-computer interfaces not only allows device control, but also opens the door for modulating the central nervous system through neural interfacing. Using various recorded brain signals that reflect the "intention" of the brain, BCI systems have shown the capability to control external devices, such as computers and robots. Neural stimulation using electrical, magnetic, optical and acoustic energy has shown capability to better understanding of the brain functions and intervene with central nervous systems. This course teaches the fundamentals how a BCI system works and various building blocks of BCIs, from signal acquisition, signal processing, feature extraction, feature translation, neurostimulation, to device control, and various applications. Examples of noninvasive BCIs are discussed to provide an in-depth understanding of the noninvasive BCI technology. Open to seniors or graduate students in engineering or science programs, or upon instructor's approval (for exceptional juniors, e.g.).

42666 | Neuroengineering Practicum | Prof. Bin He | Fall
This course will examine topics and issues related to ethics, professional conduct, conflicts, plagiarism, copyright, authorship, research design considerations, IRB, IACUC, intellectual properties, review process, regulatory science and FDA process, professional presentations, and technical writing in neuroengineering. Students will discuss neuro-ethical implications of neural technologies and learn about the process of bringing such technologies to market, including intellectual property and FDA approval considerations. Students will also discuss essential career development skills for a neuroengineering R & D career in academia and industry. Students will also have the opportunity to tour neuroengineering research and/or clinical laboratories. An important component of the course is to develop students' communications skills including developing an effective research proposal and an effective technical report, as well as effective oral presentations of the ideas developed in the proposal and technical report. The essentials for successful proposal writing will be discussed in case studies. Each student will be required to develop a research proposal based upon students' own research or an emerging research topic in neuroengineering. Each student will also be required to develop a technical report on an neuroengineering topic. It is expected that students will improve her/his writing skills for proposal/report development with case studies, group discussions, and individualized feedbacks on students' own writing and presentation. This course will help students to develop practical skills addressing real world problems in neuroengineering.

42667 | Biofabrication and Bioprinting | Prof. Rachelle Palchesko | Spring
Description: This laboratory course is designed to introduce students to and give them hands-on experience using methods that are used to fabricate scaffolds that are often used in tissue engineering, drug delivery, and some medical devices. Methods that will be taught include plastic FDM (filament deposition methods) to 3d print thermoplastic materials and molds for casting soft hydrogel materials, as well as 3d Bioprinting of soft hydrogel materials into a support bath material. This course will include a lecture component to introduce students to the concepts needed to design and fabricate the scaffolds. Lecture topics will include (but are not limited to): chemical and physical properties of biomaterials, CAD, and post-processing methods. There are no pre-requisite courses; however prior introductory lab experience is suggested.

42668 | "Fun"-damentals of MRI and Neuroimaging Analysis| Prof. Sossena Wood | Fall
Description: Neuroimaging gives us many ways to learn how the brain operates through various functions and disease states without having to perform any invasive surgery. This course will cover the methodology and analysis of structural magnetic resonance imaging (MRI) and functional MRI in humans and animals. Through lecture, discussion and analysis of sample data, students will understand the (A) history of MRI, (B) physics of MRI, (C) utilization with MRI and other devices used to interpret biological tissue, (D) how to design an fMRI experiment, and (E) analysis techniques in MRI. At the end of the course, students will have strong fundamental MRI and fMRI skillset and gain programming skills in MATLAB and learn other tools like SPM to process MRI and fMRI datasets in appropriate software packaging.

42669 | Energy Applications in Biology and Medicine | Prof. Yoed Rabin | Spring
Description: This course covers a wide range of energy-based applications in biology and medicine, such as cancer treatments by cryosurgery (freezing), thermal ablation (heating), photodynamic therapy (light-activated drugs), and irreversible electroporation (a non-thermal electrical application). This course also covers thermal regulation in humans and other mammals, as well as cryopreservation (low-temperature preservation) of tissues and organs for the benefit of organ banking and transplant medicine. The course combines lectures and individual assignments relating to the underlying principles of engineering, with teamwork on open-ended projects relating to concurrent challenges at the convergence of engineering and medical sciences. The course plan assumes a mastery of the fundamentals of heat transfer at the undergraduate level.

42675 | Fundamentals of Computational Biomedical Engineering | Prof. Yu-li Wang | Fall
This goal of this course is to enable students with little or no programming background to use computational methods to solve basic biomedical engineering problems.  Students will use MATLAB to solve linear systems of equations, model fit using least squares techniques (linear and nonlinear), interpolate data, perform numerical integration and differentiation, solve differential equations, and visualize data. Specific examples for each topic will be drawn from different areas of biomedical engineering, such as bioimaging and signal processing, biomechanics, biomaterials, and cellular and biomolecular technology.

42678 | Medical Device Innovation and Realization | Prof. Denver Faulk | Spring
The increasing pace of medical discoveries and emerging technologies presents a unique and exciting time for medical devices. Medical devices range from biomaterials that stimulate the body to repair itself to drug eluting stints to robotic surgical systems. Because they seek to improve and prolong human health, there are unique requirements and challenges for medical device development compared to most other industries. This class will look at how medical device innovation is currently practiced as well as the drivers which govern it, such as the FDA, intellectual property, reimbursement, and funding. By the end of this course, students should be able to: (1) obtain a broad understanding of medical devices; (2) identify new product opportunities; (3) understand the drivers that affect medical device development; and (4) develop strategies to address those drivers within the overall medical device development plan.

42687 | AI Applications in BME  | Prof. Patjanaporn Chalacheva | Spring
Description: This course provides hands-on experience in applying the fundamentals of artificial intelligence/machine learning (AI/ML) to problems in a variety of biomedical research areas and applications. Students will work in teams to design, develop, and evaluate an AI/ML system to achieve one or more of the following goals: identifying patterns in the data, modeling the input-output relationships and/or classifying data into distinct categories. The datasets for this course will be drawn from different BME-related areas provided by biomedical researchers, clinicians, and other publicly available sources. In addition to the project work, the course will discuss issues that are specific to the development and implementation of AI algorithms in medical settings. This includes FDA approval, human clinical trials, the Health Insurance Portability and Accountability Act, and medical ethics. This computational project-based course is available to any student who has completed Introduction to Machine Learning course.

42691 | Biomechanics of Human Movement  | Prof. Eni Halilaj | Fall
This course provides an overview of the mechanical principles underlying human movement biomechanics and the experimental and modeling techniques used to study it. Specific topics will include locomotion, motion capture systems, force plates, muscle mechanics, musculoskeletal modeling, three dimensional kinematics, inverse dynamics, forward dynamic simulations, and imaging-based biomechanics. Homework and final class projects will emphasize applications of movement biomechanics in orthopedics, rehabilitation, and sports.

42692 | Special Topics: Nanoscale Manufacturing Using Structural DNA Nanotechnology | Prof. TBD | Fall
This course provides an introduction to modern nanoscale manufacturing using structural DNAnanotechnology. This DNA-based approach to manufacturing has much in common with other fabrication methods in micro- and nano-engineering: computer aided design tools are necessary for device design and resulting structures can only be seen using advanced microscopy. However, instead of machining larger materials down to micro- and nanostructures, DNA origami is fabricated using a "bottom up" approach for self-assembling individual oligonucleotides into 2D and 3D nanostructures. Resulting structures can be designed to have novel mechanical and electrical properties and have applications as broad-ranging as medicine, biological computing, and energy systems. The course will include lectures, hands-on physical modeling, homework problems, 3D modeling of DNA origami using caDNAno and CANDO software, and student team projects and presentations.

42693 | Special Topics in Integrated systems Technology: Micro/Nano Biomedical Devices  | Prof. Siyang Zheng | Fall
Biomedical devices constantly call for innovations. Micro/nano fabrication not only miniaturizes devices and instruments, but also can enable new biomedical devices and significantly boost device performance. This course introduces fundamental micro/nano fabrication technologies and related materials of biomedical devices. The biomedical background and design principles of various biomedical devices will be presented. Both diagnostic and therapeutic devices will be discussed, including point-of-care diagnostic devices, biosensors, DNA sequencers, medical implants, prosthetic devices, drug delivery systems, medical robots, etc.

42694 |  Engineering Principles of Medical Devices | Prof. Siyang Zheng | Spring
Medical devices are apparatuses widely used in diagnosis, treatment and prevention of human diseases. The invention and adoption of medical devices is one of the major driving forces for the revolution in modern healthcare. This course takes a systematic and quantitative approach for the design and implementation of medical devices. We will mainly focus on three major medical device categories: bioelectrical devices, biomechanical devices, and medical devices enabled by emerging technologies. For each category, domain knowledge and fundamental principles will be introduced, and detailed design, implementation, and performance analysis will be studied. Analytical equations and simulation tools will be used when appropriate. The course will prepare students with a solid foundation to further study, research, and work in medical device related fields. Pre-requisite or Co-requisite: 42-202 and (21-120 or 21-122 or 21-259) and (33-141 or 33-142) or permission of instructor

42695 | Special Topics: Engineering Protein Therapeutics | Prof. TBD |  Spring

42696 |  Special Topics: Wearable Health Technologies | Prof. Eni Halilaj | Spring
This course will provide an overview of emerging wearable health technologies and give students hands-on experience in solving ongoing technical challenges. The wearable sensing field is experiencing explosive growth, with exciting applications in medicine. New lightweight devices will make it easier to monitor health conditions in real time, automatically import data into health informatics systems, and provide haptic feedback with humans in the loop. We will review several aspects of these technologies, including hardware, software, user experience, communication networks, applications, and big data analytics. Students will be paired with a company for a semester-long project that tackles timely computational challenges. Programming experience, in any language, is a pre-requisite.
42697 | Special Topics: Orthopaedic Tissue Mechanics | Prof. Axel Moore | Spring
In this course we will assess the composition, structure, function, failure, and repair of orthopaedic tissues, such as bone, cartilage, intervertebral disc, ligament, tendon, and meniscus. We will pay special attention to the analysis of composite materials, derivation of relevant analytical models, fitting of experimental data, and underlying assumptions. Students will have the opportunity to work in teams to assess seminal papers and explore unmet challenges in the field of orthopaedics. This course will prepare students who are interested in pursuing topics in the field of orthopaedics, rehabilitation, design of prosthetics, and tissue engineering. There are no prerequisites, but statics, dynamics, mechanics of materials, fluid mechanics, biomechanics, and biology are helpful.

42702 | Advanced Physiology  | Prof. Phil Campbell | Fall
This course is an introduction to human physiology and includes units on all major organ systems.  Particular emphasis is given to the musculoskeletal, cardiovascular, respiratory, digestive, excretory, and endocrine systems.  Modules on molecular physiology tissue engineering and physiological modeling are also included.  Due to the close interrelationship between structure and function in biological systems, each functional topic will be introduced through a brief exploration of anatomical structure.  Basic physical laws and principles will be explored as they relate to physiologic function.  Prerequisite:  03-121 Modern Biology, or permission of instructor.

42737 | Biomedical Optical Imaging | Prof. Jana Kainerstorfer | Fall (every other year)
Biophotonics, or biomedical optics, is a field dealing with the application of optical science and imaging technology to biomedical problems, including clinical applications. The course introduces basic concepts in electromagnetism and light tissue interactions, including optical properties of tissue, absorption, fluorescence, and light scattering. Imaging methods will be described, including fluorescence imaging, Raman spectroscopy, optical coherence tomography, diffuse optical spectroscopy, and photoacoustic tomography. The basic physics and engineering of each imaging technique are emphasized. Their relevance to human disease diagnostic and clinical applications will be included, such as breast cancer imaging and monitoring, 3D retinal imaging, ways of non-invasive tumor detection, as well as functional brain imaging in infants.

42744 | Medical Devices  | Prof. Boyle Cheng | Fall
This survey course is an introduction to the engineering, clinical, legal, regulatory and business aspects of medical device performance and failure. Topics covered include a broad range of successful medical devices in clinical use, as well as historical case studies of devices that were withdrawn from the market as a consequence of noted failures. In-depth study of specific medical devices will include cardiovascular, orthopedic, and neurological disciplines. We will study best practices employed in the clinical setting, principles governing the design processes, and modes of failure as a risk to the patient population. Additional lectures will provide fundamental topics concerning biomaterials used for implantable medical devices (metals, polymers, ceramics), biocompatibility, imaging, patient risks and mechanisms of failure (wear, corrosion, fatigue, fretting, etc.). The level of technical content will require junior standing for MCS and CIT students, a degree in science or engineering for non-MCS or non-CIT graduate students, or permission of the instructor for all other students.  42-744 should only be taken for graduate credit.

42781 | Professional Issues in Biomedical Engineering | Prof. Keith Cook | Spring | Prof. Bin He | Fall
This course exposes students to many of the issues that biomedical engineers face.  It provides an overview of professional topics including bioethics, regulatory issues, communication skills, teamwork, and other contemporary issues.  Outside speakers and case studies will describe real world problems and professional issues in biotechnology and bioengineering, and progress toward their solution.  A term paper describing on how the topics in class are applicable to a specific biomedical industry is required as well.

42782 | Biomedical Engineering Systems Modeling and Analysis | Prof. Sossena Wood | Spring | Prof. Patjanaporn Chalacheva | Fall
This course will prepare students to develop mathematical models for biological systems and for biomedical engineering systems, devices, components, and processes and to use models for data reduction and for system performance analysis, prediction and optimization. Models considered will be drawn from a broad range of applications and will be based on algebraic equations, ordinary differential equations and partial differential equations. The tools of advanced engineering mathematics comprising analytical, computational and statistical approaches will be introduced and used for model manipulation. There will be an extra project.

42783 | Neural Engineering laboratory | Prof. Matt Smith | Fall
Neural engineering applies classic engineering approaches and principles to understand the nervous system and its function. The measurement of neural activity involves a number of basic tools that have evolved over decades to sense the activity of neurons (individual neurons, populations of neurons and nerve fibers) or activity that is related to neurons (such as the oxygenation of blood in the brain). To intervene in the nervous system, a comparable set of tools have evolved to change neural activity locally or globally, on short and long time scales. The successful application of these methods to measure and manipulate neural activity requires both a basic science and engineering understanding of the principles behind their action, along with practical experience in applying them in real-world settings. This laboratory course will pair lectures with laboratory exercises to gain a deep understanding of the tools we use to measure and manipulate neural activity, as well as the analytic approaches to this data. It will involve both building and diagnosing recording hardware, experimental data collection, data analysis in Matlab or Python, and scientific writing. Overall, the goal is to provide students with a deep understanding of the methods for acquiring experimental data in neuroscience. Familiarity with signal processing and introductory Matlab or Python programming is helpful. This course is suitable for students from diverse backgrounds: (1) Students with experimental backgrounds seeking a range of hands-on experience in different experimental settings and a deeper understanding of different experimental methods, and (2) students with engineering and other quantitative backgrounds seeking exposure to experimental data collection methods and practices.

42790 | Practicum in Biomedical Engineering | Prof. Patjanaporn Chalacheva | Fall, Spring, Summer
Students will work with a faculty member, local biomedically-oriented company or local clinical researcher on a technical research, development or outreach project.  A faculty member affiliated with the Department of Biomedical Engineering will either serve as the advisor for an internal project or as a liaison for an external industrial/clinical project.  The project will culminate in an oral presentation and an internally-archived written report which documents the project and its results.  The presentation and report will be reviewed by the faculty advisor/liaison; this review will serve as the basis for the assignment of the course grade. Pre-requisite:  Graduate standing and consent of faculty advisor/liaison.  Variable units.

42792 | Internship in Biomedical Engineering | Prof. Patjanaporn Chalacheva | Summer
A summer internship at an industrial or clinical setting will offer a unique training opportunity for our MS students to gain knowledge and skills to practice biomedical engineering in a real-world setting. The internship will improve team working skills, communication skills, and problem-solving skills. These skills will be practiced in a real-world setting to prepare students who seek industrial employment post-MS study. After the internship, the student will dedicate time to reflect on the internship and summarize their experience in the form of a written report to be submitted to the department.  Pre-requisite: Graduate standing, require special arrangement through the advisor and approval of the department, and approval of the Office of International Education for foreign students.

42799 | Directed Study | Fall, Spring, Summer
This course is intended for directed study only with permission of the Associate Department Head.

42801/42701 | Biomedical Engineering Seminar | Prof. Rosalyn Abbott | Fall, Spring
The Biomedical Engineering Seminar is required each semester for all BME graduate students in residence. It provides opportunities to learn about research in various and related fields being conducted at other universities, industry, and hospitals. All graduate students must register for this course during each semester of full-time study. Attendance is mandatory. Students may register for either 0 unit as 42-701 Biomedical Engineering Seminar or 3 units as Biomedical Engineering Seminar with Self-Study.  Students registering for 42-701 receive a pass/fail grade based on the submission of notes taken at the seminars. Students registering for 42-801 receive a letter grade based on both notes taken at the seminar and reports from 2 hours of self-study following each seminar.

42890 | M.S. Research | Fall, Spring, Summer
This course can be taken by students in the MS programs who conduct directed research with a BME faculty member or other research mentor approved by BME department. The student must notify the department before starting a research project. Students should register for 42-890 only after formal assignment of an advisor and each semester thereafter if the project continues.

42990 | Ph.D. Thesis Research | Fall, Spring, Summer
This course is designed to give students enrolled in the Ph.D. program an opportunity to conduct extensive research over the course of their studies culminating in a Ph.D. thesis.

Graduate courses offered by other CMU departments

The courses listed below are offered by other departments but have been preapproved as meeting BME course requirements. Descriptions of these courses may be found in the University Course Catalog. Students are urged to contact the instructor if they are uncertain about the background required. Additional courses may be approved as electives upon petition, which must be submitted before taking the course. Regardless of the approval of individual courses, the overall course selection must reflect a clear theme in biomedical engineering.

02601 | Programming for Scientists
Provides a practical introduction to programming for students with little previous programming experience who are interested in science. Fundamental scientific algorithms will be introduced, and extensive programming assignments will be based on analytical tasks that might be faced by scientists, such as parsing, simulation, and optimization. Principles of good software engineering will also be stressed. The course will introduce students to the Go programming language, an industry-supported, modern programming language, the syntax of which will be covered in depth. Other assignments may be given in other programming languages to highlight the commonalities and differences between languages. No biology background is needed. Analytical skills, an understanding of programming basics, and mathematical maturity are required.

02604 | Fundamentals of Bioinformatics
How do we find potentially harmful mutations in your genome? How can we reconstruct the Tree of Life? How do we compare similar genes from different species? These are just three of the many central questions of modern biology that can only be answered using computational approaches. This 12-unit course will delve into some of the fundamental computational ideas used in biology and let students apply existing resources that are used in practice every day by thousands of biologists. The course offers an opportunity for students who possess an introductory programming background to become more experienced coders within a biological setting. As such, it presents a natural next course for students who have completed 02-601.

02680 | Essential Mathematics and Statistics for Scientists
This course rigorously introduces fundamental topics in mathematics and statistics to first-year master's students as preparation for more advanced computational coursework. Topics are sampled from information theory, graph theory, proof techniques, phylogenetics, combinatorics, set theory, linear algebra, neural networks, probability distributions and densities, multivariate probability distributions, maximum likelihood estimation, statistical inference, hypothesis testing, Bayesian inference, and stochastic processes.  Students completing this course will obtain a broad skillset of mathematical techniques and statistical inference as well as a deep understanding of mathematical proof. They will have the quantitative foundation to immediately step into an introductory master's level machine learning or automation course. This background will also serve students well in advanced courses that apply concepts in machine learning to scientific datasets, such as 02-710 (Computational Genomics) or 02-750 (Automation of Biological Research). The course grade will be computed as the result of homework assignments, midterm tests, and class participation.

02710 | Computational Genomics
Dramatic advances in experimental technology and computational analysis are fundamentally transforming the basic nature and goal of biological research. The emergence of new frontiers in biology, such as evolutionary genomics and systems biology is demanding new methodologies that can confront quantitative issues of substantial computational and mathematical sophistication.  From the computational side this course focuses on modern machine learning methodologies for computational problems in molecular biology and genetics, including probabilistic modeling, inference and learning algorithms, data integration, time series analysis, active learning, etc. This course counts as a CSD Applications elective

02712 | Computational Methods for Biological Modeling and Simulation | Fall
This course covers a variety of computational methods important for modeling and simulation of biological systems. It is intended for graduates and advanced undergraduates with either biological or computational backgrounds who are interested in developing computer models and simulations of biological systems. The course will emphasize practical algorithms and algorithm design methods drawn from various disciplines of computer science and applied mathematics that are useful in biological applications. The general topics covered will be models for optimization problems, simulation and sampling, and parameter tuning. Course work will include problem sets with significant programming components and independent or group final projects.

02718 | Computational Medicine
Modern medical research increasingly relies on the analysis of large patient datasets to enhance our understanding of human diseases. This course will focus on the computational problems that arise from studies of human diseases and the translation of research to the bedside to improve human health. The topics to be covered include computational strategies for advancing personalized medicine, pharmacogenomics for predicting individual drug responses, metagenomics for learning the role of the microbiome in human health, mining electronic medical records to identify disease phenotypes, and case studies in complex human diseases such as cancer and asthma. We will discuss how machine learning methodologies such as regression, classification,  clustering, semi-supervised learning, probabilistic modeling, and time-series modeling are being used to analyze a variety of datasets collected by clinicians. Class sessions will consist of lectures, discussions of papers from the literature, and guest presentations by clinicians and other domain experts. Grading will be based on homework assignments and a project.  02-250 is a suggested pre-requisite.

02730 | Cell and Systems Modeling
This course will introduce students to the theory and practice of modeling biological systems from the molecular to the organism level with an emphasis on intracellular processes. Topics covered include kinetic and equilibrium descriptions of biological processes, systematic approaches to model building and parameter estimation, analysis of biochemical circuits modeled as differential equations, modeling the effects of noise using stochastic methods, modeling spatial effects, and modeling at higher levels of abstraction or scale using logical or agent-based approaches. A range of biological models and applications will be considered including gene regulatory networks, cell signaling, and cell cycle regulation. Weekly lab sessions will provide students hands-on experience with methods and models presented in class. Course requirements include regular class participation, bi-weekly homework assignments, a take-home exam, and a final project. The course is designed for graduate and upper-level undergraduate students with a wide variety of backgrounds.  The course is intended to be self-contained but students may need to do some additional work to gain fluency in core concepts.  Students should have a basic knowledge of calculus, differential equations, and chemistry as well as some previous exposure to molecular biology and biochemistry.  Experience with programming and numerical computation is useful but not mandatory.  Laboratory exercises will use MATLAB as the primary modeling and computational tool augmented by additional software as needed. *THIS COURSE WILL BE AT PITT

02750 | Automation of Scientific Research
Automated scientific instruments are used widely in research and engineering. Robots dramatically increase the reproducibility of scientific experiments, and are often cheaper and faster than humans, but are most often used to execute brute-force sweeps over experimental conditions. The result is that many experiments are "wasted" on conditions where the effect could have been predicted. Thus, there is a need for computational techniques capable of selecting the most informative experiments.  This course will introduce students to techniques from Artificial Intelligence and Machine Learning for automatically selecting experiments to accelerate the pace of discovery and to reduce the overall cost of research. Real-world applications from Biology, Bioengineering, and Medicine will be studied. Grading will be based on homeworks and two exams. The course is intended to be self-contained, but students should have a basic knowledge of biology, programming, statistics, and machine learning.

03534 | Biological Imaging and Fluorescence Spectroscopy
This laboratory is designed to teach concepts and experimental methods in cell and developmental biology. Students work with a variety of organisms to examine how cells traverse development from rapidly dividing, undifferentiated cells, through cell commitment and the establishment of spatial and temporal patterns of gene expression, to the specific characteristics and responses of terminally differentiated cells. The course makes extensive use of video microscopy with phase contrast, DIC and fluorescence microscopes. Biochemical, immunological and molecular biological techniques are used to probe the molecules and processes of cells undergoing development. Experimentation using living organisms and/or their tissues, cells or molecules is an essential component of this course.

03620 | Techniques in Electron Microscopy
This laboratory course is designed to provide students with the ability to make measurements on and interpret data from living systems. The experimental modules reinforce concepts from 42-101 Introduction to Biomedical Engineering and expose students to four areas of biomedical engineering: biomedical signal and image processing, biomaterials, biomechanics, and cellular and molecular biotechnology. Several cross-cutting modules are included as well. The course includes weekly lectures to complement the experimental component. Priority for enrollment will be given to students who have declared the Additional Major in Biomedical Engineering. Notes: This course number is reserved for students who are CIT majors and registered with the HPP program. 

03712 | Computational Methods for Biological Modeling and Simulation | Spring
This course covers a variety of computational methods important for modeling and simulation of biological systems. It is intended for graduates and advanced undergraduates with either biological or computational backgrounds who are interested in developing computer models and simulations of biological systems. The course will emphasize practical algorithms and algorithm design methods drawn from various disciplines of computer science and applied mathematics that are useful in biological applications. The general topics covered will be models for optimization problems, simulation and sampling, and parameter tuning. Course work will include problem sets with significant programming components and independent or group final projects.

03730 | Advanced Genetics
This course considers selected current topics in molecular genetics at an advanced level. Emphasis is on classroom discussion of research papers. Topics are subject to change yearly. Examples of past topics include: nucleocytoplasmic trafficking of RNA in yeast, genome imprinting in mammals, molecular genetics of learning and memory in Drosophila, viral genomics, using yeast as a model system to study the molecular basis of human neurodegenerative diseases, and CRISPR/Cas9 genome editing.

03741 | Advanced Cell Biology
This course covers fourteen topics in which significant recent advances or controversies have been reported. For each topic there is a background lecture by the instructor, student presentations of the relevant primary research articles and a general class discussion. Example topics are: extracellular matrix control of normal and cancer cell cycles, force generating mechanisms in trans-membrane protein translocation, signal transduction control of cell motility, and a molecular mechanism for membrane fusion.

03742 | Advanced Molecular Biology
The structure and expression of eukaryotic genes are discussed, focusing on model systems from a variety of organisms including yeast, flies, worms, mice, humans, and plants. Topics discussed include (1) genomics, proteomics, and functional proteomics and (2) control of gene expression at the level of transcription of mRNA from DNA, splicing of pre-mRNA, export of spliced mRNA from the nucleus to the cytoplasm, and translation of mRNA.

03751 | Advanced Developmental Biology and Human Health
This course will examine current research in developmental biology, focusing on areas that have important biomedical implications. The course will examine stem cell biology, cellular reprogramming, cell signaling pathways, tissue morphogenesis, and genetic/developmental mechanisms of birth defects and human diseases. Emphasis will be placed on the critical reading of recent, original research papers and classroom discussion, with supporting lectures by faculty.

03757 (Section B) | Graduate Cellular Neuroscience
Graduate Cellular Neuroscience: Modern neuroscience is an interdisciplinary field that seeks to understand the function of the brain and nervous system. This course provides a comprehensive survey of cellular and molecular neuroscience ranging from molecules to simple neural circuits. Topics covered will include the properties of biological membranes, the electrical properties of neurons, neural communication and synaptic transmission, mechanisms of brain plasticity and the analysis of simple neural circuits. In addition to providing information the lectures will describe how discoveries were made and will develop students' abilities to design experiments and interpret data.

03762 | Advanced Cellular Neuroscience
This course is an introductory graduate course in cellular neuroscience.  As such it will assume little or no background but will rapidly progress to discussions of papers from the primarily literature.  The structure of the course will be about half lectures and half discussions of new and classic papers from the primary literature.  These discussions will be substantially led by students in the course.  Topics covered will include ion channels and excitability, synaptic transmission and plasticity, molecular understanding of brain disease and cell biology of neurons.  Assessment will be based on class participation, including performance on in-class presentations and a writing assignment.

03763 | Advanced Systems Neuroscience
This course is a graduate version of 03-363.  Students will attend the same lectures as the students in 03-363, plus an additional once weekly meeting.  In this meeting, topics covered in the lectures will be addressed in greater depth, often through discussions of papers from the primary literature.  Students will read and be expected to have an in depth understanding of several classic papers from the literature as well as current papers that illustrate cutting edge approaches to systems neuroscience or important new concepts.  Use of animals as research model systems will also be discussed.  Performance in this portion of the class will be assessed by supplemental exam questions as well as by additional homework assignments. 

Students should have taken the equivalent of the undergraduate version of the course before getting into 03-763. If students don’t have an adequate background they’re encouraged to take the undergraduate version of the course.

03871 | Structural Biophysics
This course (MB-1) is the first-semester core course for the joint CMU-Pitt graduate program in Molecular Biophysics and Structural Biology (MBSB). The physical properties of biological macromolecules and the methods used to analyze their structure and function are discussed in in-depth lectures. Topics covered include: protein architecture and folding; nucleic acid structures and energetics; structure determination by X-ray crystallography and NMR; optical spectroscopy with emphasis on absorption and fluorescence, NMR spectroscopic methods; other methods to characterize proteins and protein-ligand interactions, such as mass spectrometry, calorimetry, single-molecule manipulation and measurements, and surface plasmon resonance. Sufficient detail is given to allow the student to critically evaluate the current literature.

06462 | Optimization Modeling and Algorithms
Formulation and solution of mathematical optimization problems with  and without constraints. Objective functions are based on economics  or functional specifications. Both discrete and continuous variables  are considered.

06607 | Physical Chemistry of Colloids and Surfaces
Thermodynamics of surfaces; adsorption at gas, liquid, and solid interfaces; capillarity; wetting, spreading, lubrication and adhesion; properties of monolayers and thin films; preparation and characterization of colloids; colloidal stability, flocculation kinetics, micelles, electrokinetic phenomena and emulsions.

06609 | Physical Chemistry of Macromolecules
This course develops fundamental principles of polymer science. Emphasis is placed on physio-chemical concepts associated with the macromolecular nature of polymeric materials. Engineering aspects of the physical, mechanical and chemical properties of these materials are discussed in relation to molecular structure. Topics include an introduction to polymer science and a general discussion of commercially important polymers; molecular weight; condensation and addition synthesis mechanisms with emphasis on molecular weight distribution; solution thermodynamics and molecular conformation; rubber elasticity; and the rheological and mechanical properties of polymeric systems.  Students not having the prerequisite listed may seek permission of the instructor.

06610 | Rheology and Structure of Complex Fluids
This course will cover the basic concepts of rheology and mechanical behavior of fluid systems.  Both the experimental and theoretical aspects of rheology will be discussed.  The basic forces influencing complex fluid rheology and rheology will be outlined and discussed; including excluded volume, van der Waals, electrostatic and other interactions.  Methods of characterizing structure will be covered including scattering techniques, optical polarimetry and microscopy. Examples will focus on several types of complex fluids including polymer solutions and melts, gelling systems, suspensions and self-assembling fluids.

06663 | Analysis and Modeling of Transport Phenomena
Students will learn the basic differential equations and boundary conditions governing momentum, heat, and mass transfer. Students will learn how to think about these equations in dimensionless terms and will apply them to model physical and chemical processes.  The primary mode for solving them will be numerical. Analytical results for classical problems of high symmetry also will be presented to serve as a basis for comparison and validation.  Software: A finite element and computational transport tool.

06804 | Drug Delivery Systems
The body is remarkable in its ability to sequester and clear foreign entities - whether they be "bad" (e.g. pathogens) or "good" (e.g. therapeutic drugs). This course will explore the design principles being used to engineer modern drug delivery systems capable of overcoming the body's innate defenses to achieve therapeutic effect. Specifically, we will study the chemistry, formulation, and mechanisms of systems designed to deliver DNA, siRNA, chemotherapeutics, and proteins across a variety of physiological barriers. This is a graduate level course that is also open to undergraduate seniors.

09707 | Nanoparticles
This course discusses the chemistry, physics, and biology aspects of several major types of nanoparticles, including metal, semiconductor, magnetic, carbon, and polymer nanostructures. For each type of nanoparticles, we select pedagogical examples (e.g. Au, Ag, CdSe, etc.) and introduce their synthetic methods, physical and chemical properties, self assembly, and various applications. Apart from the nanoparticle materials, other topics to be briefly covered include microscopy and spectroscopy techniques for nanoparticle characterization, and nanolithography techniques for fabricating nano-arrays. The course is primarily descriptive with a focus on understanding major concepts (such as plasmon, exciton, polaron, etc.). The lectures are power point presentation style with sufficient graphical materials to aid students to better understand the course materials. Overall, this course is intended to provide an introduction to the new frontiers of nanoscience and nanotechnology. Students will gain an understanding of the important concepts and research themes of nanoscience and nanotechnology, and develop their abilities to pursue highly disciplinary nanoscience research. 3 hrs. lec.

09719 | Bioorganic Chemistry: Peptides, Proteins and Combinatorial Chemistry
This course will introduce students to new developments in chemistry and biology, with emphasis on the synthesis, structural and functional aspects of peptides, proteins and small molecules. Basic concepts of bioorganic chemistry will be presented in the context of the current literature and students will have the opportunity to learn about the experimental methods used in various research labs. An introduction to combinatorial chemistry in the context of drug design and drug discovery will also be presented. Students will be required to keep abreast of the current literature. Homeworks and team projects will be assigned on a regular basis. The homework assignments will require data interpretation and experimental design; and team projects will give students the opportunity to work in teams to tackle contemporary problems at the interface of chemistry and biology. Students enrolled in the graduate level course (09-719) will be required to turn in an original research proposal at the end of the course, in addition to the homework assignments, midterm, and final exam that are required for the undergraduate course.

09741 | Organic Chemistry of Polymers
A study of the synthesis and reactions of high polymers. Emphasis is on practical polymer preparation and on the fundamental kinetics and mechanisms of polymerization reactions. Topics include: relationship of synthesis and structure, step-growth polymerization, chain-growth polymerization via  radical, ionic and coordination intermediates, copolymerization, discussions of specialty polymers and reactions of polymers. Students in 09-741 will take the same lectures and the same exams as those enrolled in 09-502 but, in addition, will prepare a term paper on the topic of advanced polymeric materials, to be approved by the instructor. 09-509 or 09-715, Physical Chemistry of Macromolecules, is excellent preparation for this course but is not required. 3-6 hrs. lec.

09801 | Special Topics in Physical Chemistry: Computational Tools for Molecular Science
The objective of this course is to equip the students with modern computational tools essential for productive and creative pursuits in the area of molecular science and nanoscience. This goal will be accomplished through a sequence of hands-on computational exploration segments covering the key areas such as: data visualization and manipulation, elements of linear algebra and its practical applications, Fourier analysis, ordinary and partial differential equations, elements of computational quantum chemistry, and practical introduction to machine learning. As a primary computing tool, the course will use Mathematica, which allows for seamless mixing of symbolic and numerical calculations aided by vast libraries of high performance algorithms. Direct linking of Mathematica and MATLAB will be also covered. Choice of these tools makes it possible to shift the emphasis from computer programming to computational explorations, problem solving and discovery. It also makes the course open to the students with no prior experience in technical computing.

10701 | Introduction to Machine Learning for Ph.D
Machine learning studies the question "How can we build computer programs that automatically improve their performance through experience?"   This includes learning to perform many types of tasks based on many types of experience.  For example, it includes robots learning to better navigate based on experience gained by roaming their environments, medical decision aids that learn to predict which therapies work best for which diseases based on data mining of historical health records, and speech recognition systems that learn to better understand your speech based on experience listening to you.  This course is designed to give PhD students a thorough grounding in the methods, mathematics and algorithms needed to do research in and apply machine learning. Students entering the class with a pre-existing working knowledge of probability, statistics and algorithms will be at an advantage, but the class has been designed so that anyone with a strong mathematical and computer science  background can catch up and fully participate. If you are interested in this topic, but are not a PhD student, or are a PhD student not specializing in machine learning, you might consider the master's level course on Machine Learning, 10-601."  This class may be appropriate for MS and undergrad students who are interested in the theory and algorithms behind ML.    ML course comparison:

10702 | Statistical Machine Learning
Machine learning studies the question "How can we build computer programs that automatically improve their performance through experience?"   This includes learning to perform many types of tasks based on many types of experience.  For example, it includes robots learning to better navigate based on experience gained by roaming their environments, medical decision aids that learn to predict which therapies work best for which diseases based on data mining of historical health records, and speech recognition systems that learn to better understand your speech based on experience listening to you.  This course is designed to give PhD students a thorough grounding in the methods, mathematics and algorithms needed to do research in and apply machine learning. Students entering the class with a pre-existing working knowledge of probability, statistics and algorithms will be at an advantage, but the class has been designed so that anyone with a strong mathematical and computer science  background can catch up and fully participate. If you are interested in this topic, but are not a PhD student, or are a PhD student not specializing in machine learning, you might consider the master's level course on Machine Learning, 10-601."  This class may be appropriate for MS and undergrad students who are interested in the theory and algorithms behind ML.    ML course comparison:

10708 | Probabilistic Graphical Models
Many of the problems in artificial intelligence, statistics, computer systems, computer vision, natural language processing, and computational biology, among many other fields, can be viewed as the search for a coherent global conclusion from local information. The probabilistic graphical models' framework provides a unified view for this wide range of problems, enabling efficient inference, decision-making, and learning in problems with a very large number of attributes and huge datasets. This graduate-level course will provide you with a strong foundation for both applying graphical models to complex problems and for addressing core research topics in graphical models.  The class will cover classical families of undirected and directed graphical models (i.e. Markov Random Fields and Bayesian Networks), modern deep generative models, as well as topics in causal inference. It will also cover the necessary algorithmic toolkit, including variational inference and Markov Chain Monte Carlo methods.  Students entering the class should have a pre-existing working knowledge of probability, statistics, and algorithms, though the class has been designed to allow students with a strong mathematical background to catch up and fully participate. Students are required to have successfully completed an introductory course to ML (for example 10715, 10701, or 10601) or an equivalent class.

10725 | Convex Optimization
Nearly every problem in machine learning can be formulated as the optimization of some function, possibly under some set of constraints. This universal reduction may seem to suggest that such optimization tasks are intractable. Fortunately, many real world problems have special structure, such as convexity, smoothness, separability, etc., which allow us to formulate optimization problems that can often be solved efficiently. This course is designed to give a graduate-level student a thorough grounding in the formulation of optimization problems that exploit such structure, and in efficient solution methods for these problems. The main focus is on the formulation and solution of convex optimization problems, though we will discuss some recent advances in nonconvex optimization. These general concepts will also be illustrated through applications in machine learning and statistics. Students entering the class should have a pre-existing working knowledge of algorithms, though the class has been designed to allow students with a strong numerate background to catch up and fully participate. Though not required, having taken 10-701 or an equivalent machine learning or statistical modeling class is strongly encouraged, as we will use applications in machine learning and statistics to demonstrate the concepts we cover in class. Students will work on an extensive optimization-based project throughout the semester.

11785 | Introduction to Deep Learning
Neural networks have increasingly taken over various AI tasks, and currently produce the state of the art in many AI tasks ranging from computer vision and planning for self-driving cars to playing computer games. Basic knowledge of NNs, known currently in the popular literature as "deep learning", familiarity with various formalisms, and knowledge of tools, is now an essential requirement for any researcher or developer in most AI and NLP fields. This course is a broad introduction to the field of neural networks and their "deep" learning formalisms. The course traces some of the development of neural network theory and design through time, leading quickly to a discussion of various network formalisms, including simple feedforward, convolutional, recurrent, and probabilistic formalisms, the rationale behind their development, and challenges behind learning such networks and various proposed solutions. We subsequently cover various extensions and models that enable their application to various tasks such as computer vision, speech recognition, machine translation and playing games. Instruction Unlike prior editions of 11-785, the instruction will primarily be through instructor lectures, and the occasional guest lecture. Evaluation Students will be evaluated based on weekly continuous-evaluation tests, and their performance in assignments and a final course project. There will be six hands-on assignments, requiring both low-level coding and toolkit-based implementation of neural networks, covering basic MLP, convolutional and recurrent formalisms, as well as one or more advanced tasks, in addition to the final project.

12659 | Special Topics: Matlab
This mini course is designed to be a practical introduction to engineering scientific computation. The topics of this class will include basic  matrix computation, solving ordinary and partial differential equations,  solving systems of linear equations, computing eigenvalues and eigenvectors, and basic signal processing and neural network techniques. Throughout the  course, these scientific computation tools will be demonstrated using  interactive scientific software called MATLAB.

15686 | Neural Computation
Computational neuroscience is an interdisciplinary science that seeks to understand how the brain computes  to achieve  natural intelligence.  It seeks to understand the computational principles and mechanisms of intelligent behaviors and mental abilities -- such as perception, language, motor control, and learning -- by building artificial systems and computational models with the same capabilities. This course explores how neurons encode and process information, adapt and learn, communicate, cooperate, compete and compute at the individual level as well as at the levels of networks and systems. It will introduce basic concepts in computational modeling, information theory, signal processing, system analysis, statistical and probabilistic inference. Concrete examples will be drawn from the visual system and the motor systems,  and studied from computational, psychological and biological perspectives. Students will learn to perform computational experiments using Matlab and quantitative studies of neurons and neuronal networks.

15853 | Algorithms in the Real World
No description. Please contact the department.

15883 | Computational Models of Neural Systems
This course is an in-depth study of information processing in real neural systems from a computer science perspective. We will examine several brain areas, such as the hippocampus and cerebellum, where processing is sufficiently well understood that it can be discussed in terms of specific representations and algorithms. We will focus primarily on computer models of these systems, after establishing the necessary anatomical, physiological, and psychophysical context. There will be some neuroscience tutorial lectures for those with no prior background in this area.     Please refer to for the most recent schedule updates.

16711 | Kinematics, Dynamic Systems and Control
Kinematics, Dynamic Systems, and Control is a graduate level introduction to robotics. The course covers fundamental concepts and methods to analyze, model and control robotic mechanisms which move in the physical world and manipulate it. Main topics include the fundamentals of kinematics, dynamics and control applied to the kinematics, dynamics and control of rigid body chains. Additional topics include state estimation and dynamic parameter identification.

16720 | Computer Vision
This course introduces the fundamental techniques used in computer vision, that is, the analysis of patterns in visual images to reconstruct and understand the objects and scenes that generated them. Topics covered include image formation and representation, camera geometry, and calibration, computational imaging, multi-view geometry, stereo, 3D reconstruction from images, motion analysis, physics-based vision, image segmentation and object recognition. The material is based on graduate-level texts augmented with research papers, as appropriate. Evaluation is based on homeworks and a final project. The homeworks involve considerable Matlab programming exercises.  Texts recommended but not required:  Title: "Computer Vision Algorithms and Applications" Author: Richard Szeliski Series: Texts in Computer Science Publisher: Springer ISBN: 978-1-84882-934-3  Title: "Computer Vision: A Modern Approach" Authors: David Forsyth and Jean Ponce Publisher: Prentice Hall ISBN: 0-13-085198-1

16722 | Sensing and Sensors
The principles and practices of quantitative perception (sensing) illustrated by the devices and algorithms (sensors) that implement them.  Learn to critically examine the sensing requirements of robotics applications, to specify the required sensor characteristics, to analyze whether these specifications can be realized even in principle, to compare what can be realized in principle to what can actually be purchased or built, to understand the engineering factors that account for the discrepancies, and to design transducing, digitizing, and computing systems that come tolerably close to realizing the actual capabilities of available sensors.   Grading will be based on homework assignments, class participation, and a final exam.  Three or four of the homework assignments will be hands-on "take-home labs" done with an Arduino kit that students will purchase in lieu of purchasing a textbook.  Top-level course modules will cover (1) sensors, signals, and measurement science, (2) origins, nature, and amelioration of noise, (3) end-to-end sensing systems, (4) cameras and other imaging sensors and systems, (5) range sensing and imaging, (6) navigation sensors and systems, (7) other topics of interest to the class (as time allows).

16725 | (Bio)Medical Image Analysis
Students will gain theoretical and practical skills in 2D, 3D, and 4D biomedical image analysis, including skills relevant to general image analysis. The fundamentals of computational medical image analysis will be explored, leading to current research in applying geometry and statistics to segmentation, registration, visualization, and image understanding.  Additional and related covered topics include de-noising/restoration, morphology, level sets, and shape/feature analysis.  Students will develop practical experience through projects using the latest version of the National Library of Medicine Insight Toolkit ( ITK ) and SimpleITK, a popular open-source software library developed by a consortium of institutions including Carnegie Mellon University and the University of Pittsburgh. In addition to image analysis, the course will include interaction with radiologists and pathologist(s). *** Lectures are at CMU and students will visit clinicians at UPMC.  Some or all of the class lectures may also be videoed for public distribution, but students may request to be excluded from distributed video. 16-725 is a graduate class, and 16-425 is a cross-listed undergraduate section.  16-425 is new this year, and has substantially reduced requirements for the final project and for the larger homework assignments, nor does it require shadowing the clinicians. Prerequisites:  Knowledge of vector calculus, basic probability, and either C++ or python, including basic command-line familiarity and how to pass arguments to your own command-line programs.  Extensive expertise with C++ and templates is not necessary, but some students may find it helpful.

16824 | Visual Learning and Recognition
A graduate seminar course in Computer Vision with emphasis on representation and reasoning for large amounts of data (images, videos and associated tags, text, gps-locations etc) toward the ultimate goal of Image Understanding. We will be reading an eclectic mix of classic and recent papers on topics including: Theories of Perception, Mid-level Vision (Grouping, Segmentation, Poselets), Object and Scene Recognition, 3D Scene Understanding, Action Recognition, Contextual Reasoning, Image Parsing, Joint Language and Vision Models, etc. We will be covering a wide range of supervised, semi-supervised and unsupervised approaches for each of the topics above.

16868 | Biomechanics and Motor Control
The course provides an introduction into the mechanics and control of legged locomotion with a focus on the human system. The main topics covered include fundamental concepts, muscle-skeleton mechanics, and neural control. Examples of bio-inspiration in robots and rehabilitation devices are highlighted.  By the end of the course, you will have the basic knowledge to build your own dynamic control models of animal and human motions. The course develops the material in parallel with an introduction into Matlab's Simulink and SimMechanics environments for modeling nonlinear dynamic systems. Assignments and team projects will let you apply your knowledge to problems of animal and human motion in theory and computer simulations.

16879 | Medical Robotics
This course presents an overview of medical robotics intended for graduate students and advanced undergraduates.  Topics include robot kinematics, registration, navigation, tracking, treatment planning, and technical and medical aspects of specific applications.  The course will include guest lectures from robotics researchers and surgeons, as well as observation of surgical cases.  The course is open to non-majors who have the requisite background.

18491 | Fundamentals of Signal Processing
This course addresses the mathematics, implementation, design and application of the digital signal processing algorithms widely used in areas such as multimedia telecommunications and speech and image processing. Topics include discrete-time signals and systems, discrete-time Fourier transforms and Z-transforms, discrete Fourier transforms and fast Fourier transforms, digital filter design and implementation, and multi-rate signal processing. The course will include introductory discussions of 2-dimensional signal processing, linear prediction, adaptive filtering, and selected application areas. Classroom lectures are supplemented with implementation exercises using MATLAB.  Students in 18491 and 18691 will share the same lectures and recitations.  Nevertheless, students receiving credit for 18691 will be required to complete an additional capstone project at the end of the semester.  Students in 18691 may have additional homework problems on a weekly basis.

18612 | Neural Technology: Sensing and Stimulation
This course gives engineering insight into the operation of excitable cells, as well as circuitry for sensing and stimulation nerves. Initial background topics include diffusion, osmosis, drift, and mediated transport, culminating in the Nernst equation of cell potential. We will then explore models of the nerve, including electrical circuit models and the Hodgkin-Huxley mathematical model. Finally, we will explore aspects of inducing a nerve to fire artificially, and cover circuit topologies for sensing action potentials and for stimulating nerves.

18614 | Microelectromechanical Systems
This course introduces fabrication and design fundamentals for Microelectromechanical Systems (MEMS): on-chip sensor and actuator systems having micron-scale dimensions. Basic principles covered include microstructure fabrication, mechanics of silicon and thin-film materials, electrostatic force, capacitive motion detection, fluidic damping, piezoelectricity, piezoresistivity, and thermal micromechanics.   Applications covered include pressure sensors, micromirror displays, accelerometers, and gas microsensors. Grades are based on exams and homework assignments.    4 hrs. lec.

18751 | Applied Stochastic Process
Basic probability concepts : Probability space, simple and compound events, statistical independence, and Bayes Rule. Total Probability Concept; Bernoulli trials; Poisson Law. De Moivre-Laplace Theorem. Definition of a Random Variable (RV); Probability distribution of an RV: cumulative distribution function (CDF) and probability density function (PDF). Two Random Variables; several Random Variables. Functions of RV?s; conditional distributions; conditional expectations; joint distributions. Moments, generating functions, and characteristic functions of RVs. Chebyshev inequality. Estimation; linear estimation; minimum mean square estimation; and orthogonality principle. Limit theorems; Central Limit Theorem; Law of Large Numbers (both strong LLN and Weak LLN). Definition of a Random Process (RP). Different notions of stationarity. Poisson and Gaussian processes. Autocorrelation and Power Spectral Density (PSD) of an RP. Processing of random (stochastic) processes by linear systems. Ergodicity. Spectral analysis. Matched Filtering. Selected applications from telecommunications, data networking (queuing), Kalman filtering.

18752 | Estimation, Detection and Learning
This course discusses estimation, detection, identification and machine learning, covering a variety of methods, from classical to modern.  In detection, the topics covered include hypothesis testing, Neyman-Pearson detection, Bayesian classification and methods to combine classifiers.  In estimation, the topics include maximum-likelihood and Bayesian estimation, regression, prediction and filtering, Monte Carlo methods and compressed sensing.  In identification and machine learning, topics include Gaussian and low-dimensional models, learning with kernels, support vector machines, neural networks, deep learning, Markov models and graphical models.

18771 | Linear Systems
A modern approach to the analysis and engineering applications of linear systems. Modeling and linearization of multi-input-- multi-output dynamic physical systems. State-variable and transfer function matrices. Emphasis on linear and matrix algebra. Numerical matrix algebra and computational issues in solving systems of linear algebraic equations, singular value decomposition, eigenvalue-eigenvector and least-squares problems. Analytical and numerical solutions of systems of differential and difference equations. Structural properties of linear dynamic physical systems, including controllability, observability and stability. Canonical realizations, linear state-variable feedback controller and asymptotic observer design. Design and computer applications to electronic circuits, control engineering, dynamics and signal processing. 4 hrs. lec.     Pre-Reqs:  18-470 or 18-474 and Graduate standing in CIT or MCS.

18792 | Advanced Digital Signal Processing
This course will examine a number of advanced topics and applications in one-dimensional digital signal processing, with emphasis on optimal signal processing techniques. Topics will include modern spectral estimation, linear prediction, short-time Fourier analysis, adaptive filtering, plus selected topics in array processing and homomorphic signal processing, with applications in speech and music processing.     4 hrs. lec.

18793 | Image and Video Processing
This course covers signal processing techniques specialized for handling 2D (images) and 3D (videos) signals. It builds upon 1D signal processing techniques developed in 18-290 and 18-491 and specializes them for the case of images and videos. In this class, you will learn fundamental tools and techniques for processing images and videos, and will learn to apply them to a range of practical applications.   This course provides the fundamentals for studying images and videos. We will develop signal models specific to images and videos, develop associated optimization techniques for solving restoration problems like denoising, inpainting, study specialized compression algorithms. Specific focus will be on transform-domain, PDE and sparsity-based models and associated optimization techniques. These formal techniques will be enriched via applications in mobile devices, medical image processing, and compressive sensing.

18794 | Pattern Recognition Theory
Decision theory, parameter estimation, density estimation, non-parametric techniques, supervised learning, linear discriminant functions, clustering, unsupervised learning, artificial neural networks, feature extraction, support vector machines, and pattern recognition applications (e.g., face recognition, fingerprint recognition, automatic target recognition, etc.).     4 hrs. lec.     Prerequisites: 36-217, or equivalent introductory probability theory and random variables course and an introductory linear algebra course and senior or graduate standing.

18799 | K Special Topics in Signal Processing: Advanced Machine Learning
Please go to the ECE Website to view "Special Topics in Signal Processing" course descriptions.

21690 | Methods of Optimization
An introduction to the theory and algorithms of linear and nonlinear programming with an emphasis on modern computational considerations.  The simplex method and its variants, duality theory and sensitivity analysis.  Large-scale linear programming.  Optimality conditions for unconstrained nonlinear optimization.  Newton's method, line searches, trust regions and convergence rates.  Constrained problems, feasible-point methods, penalty and barrier methods, interior-point methods.  (Three 50 minute lectures)

24614 | Microelectromechanical Systems
This course introduces fabrication and design fundamentals for Microelectromechanical Systems (MEMS): on-chip sensor and actuator systems having micron-scale dimensions.  Basic principles covered include microstructure fabrication, mechanics of silicon and thin-film materials, electrostatic force, capacitive motion detection, fluidic damping, piezoelectricity, piezoresistivity, and thermal micromechanics.  Applications covered include pressure sensors, micromirror displays, accelerometers, and gas microsensors.  Grades are based on exams and homework assignments.

24618 | Computational Analysis of Transport Phenomena
In this course, students will develop basic understanding and skill sets to perform simulations of transport phenomena (mass, momentum, and energy transport) for engineering applications using a CAE tool, learn to analyze and compare simulation results with theory or available data, and develop ability to relate numerical predictions to behavior of governing equations and the underlying physical system. First 8 weeks of the course will include lectures and simulation-based homework assignments. During last 7 weeks, teams of students will work on self-proposed projects related to computational analysis of transport phenomena. In the project, students will learn to approach loosely defined problems through design of adequate computational mesh, choice of appropriate numerical scheme and boundary conditions, selection of suitable physical models, efficient utilization of available computational resources etc. Each team will communicate results of their project through multiple oral presentations and a final written report. Detailed syllabus of the course is provided on the URL given below.

24623 | Molecular Simulation of Materials
The purpose of this course is to expose engineering students to the theory and implementation of numerical techniques for modeling atomic-level behavior. The main focus is on molecular dynamics and Monte Carlo simulations. Students will write their own simulation computer codes, and learn how to perform calculations in different thermodynamic ensembles. Consideration will be given to heat transfer, mass transfer, fluid mechanics, mechanics, and materials science applications.  The course assumes some knowledge of thermodynamics and computer programming. 4 hrs lec.

24673 | Soft Robots: Mechanics, Design and Modeling
Soft, elastically-deformable machines and electronics will dramatically improve the functionality, versatility, and biological compatibility of future robotic systems.  In contrast to conventional robots and machines, these ?soft robots? will be composed of elastomers, gels, fluids, gas, and other non-rigid matter.  We will explore emerging paradigms in soft robotics and study their design principles using classical theories in solid mechanics, thermodynamics, and electrostatics.  Specific topics include artificial muscles, peristaltic robotics, soft pneumatic robotics, fluid-embedded elastomers, and particle jamming.  This course will include a final project in which students may work individually or as a team.  For the project, students are expected to design and simulate and/or build all or part (eg. sensors, actuators, grippers, etc.) of a soft robot. Prerequisites:  Statics and Stress Analysis or equivalents.

24674 | Design of Biomechatronic Systems for Humans
This course introduces fabrication and design fundamentals for Microelectromechanical Systems (MEMS): on-chip sensor and actuator systems having micron-scale dimensions.  Basic principles covered include microstructure fabrication, mechanics of silicon and thin-film materials, electrostatic force, capacitive motion detection, fluidic damping, piezoelectricity, piezoresistivity, and thermal micromechanics.  Applications covered include pressure sensors, micromirror displays, accelerometers, and gas microsensors.  Grades are based on exams and homework assignments.

24688 | Introduction to CAD and CAE Tools
This course offers the hands-on training on how to apply modern CAD and CAE software tools to engineering design, analysis and manufacturing. In the first section, students will learn through 7 hands-on projects how to model complex free-form 3D objects using commercial CAD tools. In the second section, students will learn through 7 hands-on projects how to simulate complex multi-physics phenomena using commercial CAE tools.  Units: 12 Format: 2 hrs. Lec., 2 hrs. computer lab

24703 | Numerical Methods in Engineering
This course emphasizes numerical methods to solve differential equations that are important in engineering. Procedures will be presented for solving systems of ordinary differential equations and boundary value problems in partial differential equations. Students will be required to develop computer algorithms and employ them in a variety of engineering applications. Comparison with analytical results from 24-701 will be made whenever possible. 4 hrs. lec. Prerequisite: some programming experience is required.

24718 | Computational Fluid Dynamics
This course focuses on numerical techniques for solving partial differential equations including the full incompressible Navier-Stokes equations. Several spatial-temporal discretization methods will be taught, namely the finite difference method, finite volume method and briefly, the finite element method. Explicit and implicit approaches, in addition to methods to solve linear equations are employed to study fluid flows. A review of various finite difference methods which will be used to analyze elliptic, hyperbolic, and parabolic partial differential equations and the concepts of stability, consistency and convergence are presented at the beginning of the course to familiarize the students with general numerical methods.  Detailed syllabus of the course is provided on the URL given below.  4 hr. lec

24755 | Finite Elements in Mechanics I
The basic theory and applications of the finite element method in mechanics are presented.  Development of the FEM as a Galerkin method for numerical solution of boundary value problems.  Applications to second-order steady problems, including heat conduction, elasticity, convective transport, viscous flow and others.  Introduction to advanced topics, including fourth-order equations, time dependence and nonlinear problems.   12 Units  Prerequisite(s):  Graduate standing or consent of instructor

24778 | Mechatronic Design
Mechatronics is the synergistic integration of mechanical mechanisms, electronics, and computer control to achieve a functional system. Because of the emphasis upon integration, this course will center around laboratory projects in which small teams of students will configure, design, and implement mechatronic systems. Lectures will complement the laboratory experience with operational principles and system design issues associated with the spectrum of mechanical, electrical, and microcontroller components. Class lectures will cover selected topics including mechatronic design methodologies, system modeling, mechanical components, sensor and I/O interfacing, motor control, and microcontroller basics.

24780 | Engineering Computation
This course covers the practical programming and computational skills necessary for engineers.  These include: (1) programming in C++, (2) visualization using OpenGL, (3) basic data structures, and (4) basic algorithms.  The course covers computational techniques required for solving common engineering problems and background algorithms and data structures used in modern Computer-Aided Design, Computer-Aided Manufacturing, and Computer-Aided Engineering tools.  The course also offers intensive hands-on computational assignments for practice of common applications.

24783 | Advanced Engineering Computation
This course covers the advanced programming and computational skills necessary for solving engineering problems.  These include (1) efficient data structures and algorithms for modeling and processing real-world data sets such as trees, hash tables, searching, priority queues, etc. (2) techniques for simulation and visualization such as numerically solving ODEs and PDEs, viewing control, programmable shader, etc., (4) tools for version controlling, scripting, and code building including sub-version, git, and cmake.  Students will experience practical training in the above knowledge and programming skills through bi-weekly assignments and a final team project.  Prerequisites- 24-780 Engineering Computation or equivalent C++ and OpenGL programming experience

24787 | Machine Learning and Artificial Intelligence for Engineers
This course introduces fundamental machine learning and artificial intelligence techniques useful for engineers working on data-intensive problems. Topics include: Probability and Bayesian learning, generative and discriminative classification methods, supervised and unsupervised learning, neural networks, support vector machines, clustering, dimensionality reduction, regression, optimization, evolutionary computation, and search.  The lectures emphasize the theoretical foundations and the mathematical modeling of the introduced techniques, while bi-weekly homework assignments focus on the implementation and testing of the learned techniques in software. The assignments require knowledge of Python including text and image input/output, vector and matrix operations, simple loops, and data visualization. Students must have undergraduate level experience with linear algebra and vector calculus.

27410 | Computational Techniques in Engineering
This course develops the methods to formulate basic engineering problems in a way that makes them amenable to computational/numerical analysis. The course will consist of three main modules: basic programming skills, discretization of ordinary and partial differential equations, and numerical methods. These modules are followed by two modules taken from a larger list: Monte Carlo-based methods, molecular dynamics methods, image analysis methods, and so on. Students will learn how to work with numerical libraries and how to compile and execute scientific code written in Fortran-90 and C++. Students will be required to work on a course project in which aspects from at least two course modules must be integrated.

27565 | Nanostructured Materials
This course is an introduction to nanostructured materials or nanomaterials. Nanomaterials are objects with sizes larger than the atomic or molecular length scales but smaller than microstructures with at least one dimension in the range of 1-100 nm. The physical and chemical properties of these materials are often distinctively different from bulk materials. For example, gold nanoparticles with diameters ~15 nm are red and ~40 nm gold nanoparticles are purple whereas bulk gold has a golden color.  The course starts with a discussion of top-down and bottom-up fabrication methods for making nanostructures as well as how to image and characterize nanomaterials including scanning probe microscopies. Emerging nanomaterials such as fullerenes, graphene, carbon nanotubes, quantum dots and nanocomposites are also discussed. The course then focuses on applications of nanomaterials to microelectronics, particularly nanoscale devices and the emerging field of molecular-scale electronics. The miniaturization of integrated systems that sense mechanical or chemical changes and produce as electrical signal is presented. The principles and applications of the quantum confinement effects on optical properties are discussed, mainly as sensors. The last part of the course is a discussion of nanoscale mechanisms in biomimetic systems and how these phenomena are applied in new technologies including molecular motors.

27734 | Methods of Computational Materials Science
This course introduces students to the theory and practice of computational materials science  from the electronic to the microstructural scale. Both the underlying physical models and their  implementation as computational algorithms will be discussed. Topics will include:  Density functional theory Molecular dynamics Monte Carlo methods Phase field models Cellular automata Data science  Examples and homework problems will be taken from all areas of materials science. Coursework  will utilize both software packages and purpose-built computer codes. Students should be comfortable  writing, compiling, and running simple computer programs in MatLab, Python, or comparable environment.

33441 | Introduction to BioPhysics
Biological physics, or the physics of living systems, is an exciting interdisciplinary frontier of physics that aims to understand the phenomenon of life using concepts and tools from Physics. This intermediate level course will introduce the general concepts and principles underpinning the physical behavior of living systems, from the dynamics of proteins and molecules to collective behavior of living cells and organisms. The course will develop key physics concepts that are most vital to biological processes, including energy conversion, information transfer, mechanics of movement, statistical phenomena, and fluid flow. We will apply these physics concepts to demonstrate how biological systems function, build simplified mathematical models to predict behavior, and use experimental data to inform and test models. The integration of biological phenomena, physical concepts, mathematical modeling, and analysis of experimental data represents an entirely new mode of learning, based on strategies adopted in research. These strategies will break traditional disciplinary barriers between physics and biology. The students will be expected to gain an intuitive grasp of ways to: frame the physical problem, identify appropriate theoretical frameworks, analyze experimental data, and ways to generalize and to understand the dependence of biophysical phenomenon on time and length scales. No prior knowledge of biology is expected.  This class is offered in Fall of even years (e.g. Fall '22, 24, etc.)

33767 | Biophysics: From Basic Concepts to Current Research
This course mixes lectures and student presentations on advanced topis in Biological Physics. In the course, students will gain a deep appreciation of the fact that very basic physical and chemical principles underly many central life processes. Life is not only compatible with the laws of physics and chemistry, rather, it exploits them in ingenious ways. After taking the course, students should be able to name examples of such situations for which they can provide a coherent line of reasoning that outlines these connections. They will be able to explain key experiments by which these connections either have been found or are nowadays routinely established, and outline simple back-of-the-envelope estimates by which one can convince oneself of either the validity or inapplicability of certain popular models and ideas. They should also have become sufficiently familiar with the key terminology frequently encountered in biology, such that they can start to further educate themselves by consulting biological and biophysical literature. The course uses Physical Biology of the Cell  by Rob Phillips et al. (Garland Science, New York, NY, 2013, ISBN 978-0-8153-4450-6).

36700 | Probability and Mathematical Statistics
This is a one-semester course covering the basics of statistics. We will first provide a quick introduction to probability theory, and then cover fundamental topics in mathematical statistics such as point estimation, hypothesis testing, asymptotic theory, and Bayesian inference. If time permits, we will also cover more advanced and useful topics including nonparametric inference, regression and classification. Prerequisites: one- and two-variable calculus and matrix algebra.  Graduate students in degree-seeking programs are given priority.

36705 | Intermediate Statistics
This course covers the fundamentals of theoretical statistics. Topics include: probability inequalities, point and interval estimation, minimax theory, hypothesis testing, data reduction, convergence concepts, Bayesian inference, nonparametric statistics, bootstrap resampling, VC dimension, prediction and model selection. This course is primarily for PhD students in Statistics & Data Science, Machine Learning, and Computer Science; it requires an appropriate background for entering those programs.

36759 | Statistical Models of the Brain
This new course is intended for CNBC students, as an additional  option for fulfilling the computational core course requirement,  but it will also be open to Statistics and Machine Learning  students. It should be of interest to anyone wishing to see the  way statistical ideas play out within the brain sciences, and it  will provide a series of case studies on the role of stochastic  models in scientific investigation.  Statistical ideas have been part of neurophysiology and the brainsciences since the first stochastic description of spike trains, and the quantal hypothesis of neurotransmitter release, more than 50 years ago. Many contemporary theories of neural system behavior are built  with statistical models. For example, integrate-and-fire neurons are  usually assumed to be driven in part by stochastic noise; the role of  spike timing involves the distinction between Poisson and non-Poisson  neurons; and oscillations are characterized by decomposing variation  into frequency-based components.  In the visual system, V1 simple  cells are often described using linear-nonlinear Poisson models; in  the motor system, neural response may involve direction tuning; and  CA1 hippocampal receptive field plasticity has been characterized  using dynamic place models.  It has also been proposed that  perceptions, decisions, and actions result from optimal (Bayesian)  combination of sensory input with previously-learned regularities; and  some investigators report new insights from viewing whole-brain  pattern responses as analogous to statistical classifiers.  Throughout the field of statistics, models incorporating random ``noise'' components are used as an effective vehicle for data analysis. In neuroscience, however, the models also help form a conceptual framework for understanding neural function.  This course will examine some of the most important methods and  claims that have come from applying statistical thinking

45906 | The Business of Healthcare Innovation
Entrepreneurial Alternatives will examine paths of entrepreneurship outside of high-growth, new venture creation.  In particular, the course will focus on tactical elements of business acquisition and franchise purchase including target evaluation, financial analysis of targets, business valuation, deal structuring, financing of purchases, and post-purchase operations and integration.  In addition to its focus on business acquisition and franchise purchase, this course will explore other alternative entrepreneurial paths including social entrepreneurship and corporate entrepreneurship.

76795 | Science Writing
You will learn how to write clear, well-organized, compelling articles about science, technology and health topics for a general audience. You will learn how to carry out research on scientific topics using primary and secondary sources, how to conduct interviews, and how to organize that information in a logical fashion for presentation. For writing majors, the course will increase their understanding of scientific research and how to describe it accurately and in a compelling manner to a general audience. For science majors, this course will teach them how to craft fluid, powerful prose so that they can bring their disciplines to life. The course is not intended just for those who want to become science writers, but for anyone who may have the need to explain science, medicine, or technology to a general audience, whether it is an engineer describing a green building project at a public hearing or a computer programmer describing new software to a firm's marketing staff. Scientists and educators today are increasingly concerned about the public's lack of understanding about scientific principles and practices, and this course is one step toward remedying that deficit. You will get a chance to read several examples of high-quality science writing and interview researchers, but the primary emphasis will be on writing a series of articles, and rewriting them after they've been edited. Your assignments will range from profiles of scientists to explanations of how something works. In particular, this year's class will focus on how science and society interact, whether that means the way that science writers write about public health and the COVID pandemic or climate change. The class will be run partly as a writing workshop where students will be organized in teams where they will discuss ideas, as well as edit and critique each other's work in class, in a process similar to what journalists routinely go through.

85765 | Cognitive Neuroscience
This course will cover fundamental findings and approaches in cognitive neuroscience, with the goal of providing an overview of the field at an advanced level.  Topics will include high-level vison, spatial cognition, working memory, long-term memory, learning, language, executive control, and emotion.  Each topic will be approached from a variety of methodological directions, for example, computational modeling, cognitive assessment in brain-damaged humans, non-invasive brain monitoring in humans, and single-neuron recording in animals.  Lectures will alternate with sessions in seminar format. Prerequisites: Graduate standing or two upper-level psychology courses from the areas of developmental psychology, cognitive psychology, computational modeling of intelligence,  neuropsychology or neuroscience.

86675 | Computational Perception
In this course, we will first cover the biological and psychological foundational knowledge of biological perceptual systems, and then apply computational thinking to investigate the principles and mechanisms underlying natural perception. The course will focus on vision this year, but will also touch upon other sensory modalities.  You will learn how to reason scientifically and computationally about problems and issues in perception, how to extract the essential computational properties of those abstract ideas, and finally how to convert these into explicit mathematical models and computational algorithms.  Topics include perceptual representation and inference, perceptual organization, perceptual constancy, object recognition, learning and scene analysis. Prerequisites: First year college calculus, some basic knowledge of linear algebra and probability and some programming experience are desirable.

Pitt BIOE 2330 | Biomedical Imaging
Biomedical imaging introduces the major imaging modalities (x-ray, cat-scan, MRI, ultrasound) used in clinical medicine and biomedical research, as well as the fundamentals of images, from a signals and systems standpoint.