Carnegie Mellon University

# Majors/Minor

## Statistics consists of two intertwined threads of inquiry: Statistical Theory and Data Analysis.

The former uses probability theory to build and analyze mathematical models of data in order to devise methods for making effective predictions and decisions in the face of uncertainty. The latter involves techniques for extracting insights from complicated data, designs for accurate measurement and comparison, and methods for checking the validity of theoretical assumptions. Statistical Theory informs Data Analysis and vice versa. The Statistics Department curriculum follows both of these threads and helps the student develop the complementary skills required.

Explore the requirements for each of the majors and the minor that we provide in our department:

Our core major builds a strong foundation in methods, theory, computation, and practice.

We emphasize modern methods, strong communication skills, and hands-on experience analyzing real data. This is an ideal choice for any student interested in statistical thinking and data science and is tremendous preparation for a career that requires data skills.

## Major Requirements

### Theory Requirements

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Multivariate Calc/Analysis 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325 or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259

### Data-Analysis Requirements

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9 various
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9 36-202, 36-208, 36-290, or 36-309
Special Topics 36-46x and 36-47x  9 various
Modern Regression 36-401  9 C or higher in 36-226, 36-236, or 36-326 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401
Concentration Area

This can be fulfilled by four courses or an approved Minor or Additional Major, in another department, that compliment Statistics & Data Science.

Examples of Common Concentrations

• Computer Science
• Humanities Analytics Minor
• Computational Finance
• Computational Biology
• Psychology
• Social and Decision Sciences
• Integrative Design, Arts, and Technology

*This is not an exhaustive list

### Computing Requirements

Course Topic/Title Course Number Units Prerequisites
Statistical Computing 36-350  9 (36-202, 36-208, 36-290, 36-309 or 70-208, or equivalent), 36-225 and 36-235
Fundamentals of Programming
*Beginning with EY2023-2024
15-110/112 12

This joint major develops the critical ideas and skills underlying statistical machine learning — the creation and study of algorithms that enable systems to automatically learn and improve with experience.

It is ideal for students interested in statistical computation, data science, or “Big Data” problems, including those planning to pursue a related Ph.D. or a job in the tech industry.

## Major Requirements

### Theory Requirements*21-122 is not required for students entering in 2024 or later.

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Multivariate Calc/Analysis 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Concepts of Mathematics 21-127 12
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325, or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259

### Data-Analysis Requirements (Option 1)

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9 various
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9 various
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9 various
Modern Regression 36-401  9 C or higher in 36-226, 36-235, or 36-326 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401

### Data-Analysis Requirements (Option 2)

Course Topic/Title Course Number Units Prerequisites
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9 various
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-47x, 36-490, 36-493 or 36-497  9
Modern Regression 36-401  9 C or higher in 36-226, 36-235, or 36-326 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401

### Computing Requirements

Course Topic/Title Course Number Units Prerequisites
Statistical Computing 36-350 or 36-650  9 (36-202, 36-208, 36-290, 36-309, 70-208, or equivalent) and 36-225 or 36-235
Fundamentals of Programming 15-112 12
Principles of Iterative Computation 15-122 10 C or higher in 15-112
Machine Learning 10-301/315/701 12 C or higher in (15-122 or 15-123) and (15-151 or 21-127)
Algorithms and Advanced Data Structures 15-351 12 15-111, 15-123, 15-121, or 15-122
Machine Learning Elective See StatML audit in Stellic for current list  9 vary by elective

This joint major focuses on the skills needed to apply statistical modeling and methodology to the empirical analysis of economic data.

It is ideal for students who plan to pursue an advanced degree in statistics, economics, or management or a career in government, industry, finance, education, or public policy.

## Major Requirements

### Theory Requirements

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Multivariate Calc/Analysis 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325, or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259

### Data-Analysis Requirements

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-490, 36-493 or 36-497  9 36-202, 36-208, 36-290, or 36-309
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-46x, 36-490, 36-493 or 36-497  9
Modern Regression 36-401  9 C or higher in 36-226, 36-326, or 36-625 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401

### Computing Requirements

Course Topic/Title Course Number Units Prerequisites
Statistical Computing 36-350  9 (36-202, 36-208, 36-290, 36-309 or 70-208, or equivalent) and 36-225
Fundamentals of Programming
*Beginning with EY2023-2024
15-110 or 15-112 12

### Economics Requirements

Course Topic/Title Course Number Units Prerequisites
Principles of Microeconomics 73-102 or 73-104  9
Principles of Macroeconomics 73-103  9 73-102
Intermediate Microeconomics 73-230  9 (21256 or 21259 or 21269 or 21268) and (73102 or 73100)
Intermediate Macroeconomics 73-240  9 (21259 or 21269 or 21268 or 21256) and (73103 or 73100) and (73230)
Writing for Economists 73-270  9 (76101) and (73230) and (73240)
Economics and Data Science 73-265  9 (21120) and (36200 or 36201) and (73100 or 73102)
Econometrics I 73-274  9 (21256 or 21259 or 21268 or 21269) and (36225) and (73230)
Advanced Quantitative Analysis 73-374, 73-423, 70-467  9 various
Two advanced electives 73-300 through 73-495, excluding 73-374 18 various

This track focuses on the fundamental mathematical theory underlying statistical inference and prediction.

It is ideal for students who are interested in pursuing a Ph.D. in Statistics, an advanced degree in a related field requiring strong mathematical preparation, or a career in which a strong background in statistical theory is valuable.

## Major Requirements

### Theory Requirements

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Integration and Approximation 21-122 10 21-112 or 21-120
Multivariate Calc/Analysis 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Concepts of Mathematics 21-127 12
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325, or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259
Principles of Real Analysis 21-355  9 21-127 and 21-122
Intro to Probability Modeling 36-410  9 36-235, 36-225, 36-218, 36-219, or 36-625
Two of the following:
Probability and Math
Intermediate Statistics
Discrete Math
Optimization
Combinatorics
Real Analysis II
36-700
21-228
21-257 or 21-292
21-301
21-356
12
9
9
9
9
21-127 or 15-151
21-127 or 15-151
21-240, 21-241, 21-242, 21-256, 06-262, or 18-202
21-122 and (15-251 or 21-228)
(21-259,21-268,or 21-269) and 21-241/2 and 21-355

### Data-Analysis Requirements

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9 various
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-47x, 36-46x, or 36-490, 36-493 or 36-497  9 36-202, 36-208, 36-290, or 36-309
Special Topics 36-46x or 36-47x  9 various
General Elective various  9 various
Modern Regression 36-401  9 C or higher in 36-226, 36-326, or 36-625 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401

### Computing Requirements

Course Topic/Title Course Number Units Prerequisites
Statistical Computing 36-350, 15-110 or 15-112  9 36-235/219 and 36-225
Fundamentals of Programming
*Beginning with EY2023-2024
15-110 or 15-112 12

New technologies for measuring the brain are revolutionizing our understanding of the brain, and the revolution is data-driven.

This track focuses on the statistical problems in neuroscience, including neural data analysis and neuroimaging. It is ideal for students interested in data science with an emphasis on brain and behavior or in neuroscience with an emphasis on data analysis.

## Major Requirements

### Theory Requirements

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Multivariate 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325, or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259

### Data-Analysis Requirements

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9
Advanced Elective 36-303, 36-311, 36-315, 36-318, 36-47x, 36-46x, or 36-490, 36-493 or 36-497  9 various
Special Topics 36-46x or 36-47x  9 various
Modern Regression 36-401  9 C or higher in 36-226, 36-326, or 36-625 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402  9 C or higher in 36-401
Computing Requirements
Course Topic/Title Course Number Units Prerequisites
Statistical Computing 36-350  9 36-235 and 36-225
Fundamentals of Programming
*Beginning with EY2023-2024
15-110 or 15-112 12

### Neuroscience Requirements

Course Topic/Title Course Number Units Prerequisites
Cognitive Psychology 85-211  9
Biological Foundations of Behavior 85-219  9
Three Neuroscience Electives

With at least one selected from each list
(A) Methodology and Analysis and
(B) Neuroscientific Background.

27

### List of Approved Neuroscience Electives A: Methodology and Analysis

Course Topic/Title Course Number Units Prerequisites
Probability and Mathematical Statistics or Intermediate Statistics 36-700 12
Machine Learning 10-301, 10-315 or 10-701 12 15-122 and (15-151 or 21-127)
Signals and Systems 18-290 12
Cognitive Science Research Methods 85-314 12 36-309, 85-211 or 85-219
Neural Data Analysis 86-631 or 42-631 12

### List of Approved Neuroscience Electives B: Neuroscientific Background

Course Topic/Title Course Number Units Prerequisites
Cellular Neuroscience 03-362  9 85-219, 42-202, 03-161, or 03-240
Systems Neuroscience 03-363  9 85-219, 42-202, 03-161, or 03-240
Neural Computation 15-386  9 21-122 and 15-122
Cognitive Neuropsychology 85-414  9 85-219 or 85-211
Intro to Parallel Distributed Processing 85-419  9 85-213 or 85-211

In order to declare the minor, students need to complete this form.

## Minor Requirements

### Theory Requirements

Course Topic/Title Course Number Units Prerequisites
Calculus 21-111 and 112, or 21-120 20 or 10
Multivariate Calc/Analysis 21-256, 21-259, or 21-268  9–10 21-112 or 21-120
Linear/Matrix Algebra 21-240, 21-241, or 21-242 10–11
Probability 36-235, 36-225, 36-218, 36-219, 21-325, or 15-259  9 various
Statistical Inference 36-236, 36-226, or 36-326  9 C or higher in 36-235, 36-225, 36-219, 36-218, 21-325 or 15-259

### Data-Analysis Requirements

Course Topic/Title Course Number Units Prerequisites
Beginning Data Analysis 36-200  9
Intermediate Data Analysis 36-202, 36-208, 36-290, or 36-309  9 various
Modern Regression 36-401  9 C or higher in 36-236, 36-226, 36-326, or 36-625 and pass (21-240 or 21-241)
Advanced Methods for Data Analysis 36-402, 36-410, 36-47x, 36-46x, 36-490, 36-493, 36-497  9 C or higher in 36-401

Note: We recommend that you use the information provided as a general guideline, and then schedule a meeting with a Statistics Undergraduate Advisor to discuss the requirements in more detail, and build a program that is tailored to your strengths and interests.

For more detailed information on each major or minor, please see our Undergraduate Catalog.