Statistics

Department website: http://statistics.columbia.edu/

Department of Statistics: 

Department website: https://stat.columbia.edu/

Office location: 1005 SSW (1255 Amsterdam Avenue); 

Office contact: 212-851-2132 

Director of Undergraduate Studies:  

Ronald Neath, 615 Watson (612 West 115th Street), 212-853-1398;

rcn2112@columbia.edu 

Director of Academic Administration:  

Dood Kalicharan, 1003 SSW (1255 Amsterdam), 212-853-1398; dk@stat.columbia.edu 

 

The Study of Statistics

Statistics is the art and science of study design and data analysis.  Probability theory is the mathematical foundation for the study of statistical methods and for the modeling of random phenomena.  The Statistics major builds on a foundation in probability and statistical theory to provide practical training in statistical methods, study design, and data analysis.  The Statistics major is an appropriate background for graduate study in statistics, social science, epidemiology and public health, genetics, and economics; or for professional work in such areas as drug development, health policy, marketing, opinion polling, insurance, banking and finance, and government.  

The Department offers several introductory courses.  

• Students interested in learning statistical concepts, with a goal of being educated consumers of statistics, should take STAT UN1001 INTRO TO STATISTICAL REASONING.  This course is designed for students who have taken a pre-calculus course, and the focus is on general principles.  

• Students seeking an introduction to applied statistics should take STAT UN1101 INTRODUCTION TO STATISTICS.  This course is designed for students who wish to learn to conduct statistical analyses, but do not have a background in calculus; the focus is on the implementation of statistical methods, rather than the underlying theory.  It is recommended for pre-med students, and students considering the applied track of the statistics minor.  

• Students seeking a more mathematically rigorous treatment of the subject should take STAT UN1201 CALC-BASED INTRO TO STATISTICS.  This course is designed for students who have taken a semester of college calculus or the equivalent, and the focus is on preparation for further study in probability and statistical theory and methods.  It is recommended for students considering the statistics major, or the theoretical track of the minor.  

• Students seeking a one-semester calculus-based survey of probability and statistical theory should take STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS.  This course is designed for students who have taken calculus, and is meant as a terminal course.  It provides an abridged version of the material covered in the two-semester sequence STAT GU4203 PROBABILITY THEORY and STAT GU4204 STATISTICAL INFERENCE.  While some mathematically mature students may take the 4203--4204 sequence as an introduction to the field, it is generally recommended that students prepare for it by taking STAT UN1201 CALC-BASED INTRO TO STATISTICS.  

The Department offers a Major in Statistics, a Minor in Statistics, and interdisciplinary majors with Computer Science, Economics, Mathematics, and Political Science.  The major consists of mathematical and computational prerequisites, an introductory course, five core courses in probability and theoretical and applied statistics, plus three electives.  The training provided by the undergraduate major is comparable to a master’s degree in statistics.  The applied track of the minor is suitable for students preparing for academic or professional work in fields where data analysis skills are valued; it can be completed without the mathematical prerequisite required for the major.  Students who are more mathematically inclined can opt for the theoretical track, and complete a minor by taking courses from the core sequence of the statistics major.  

Student Advising 

Statistics Major and Minor Advising:
Ronald Neath, 615 Watson (612 West 115th Street); 212-853-1398; rcn2112@columbia.edu

Data Science Major Advising:
Computer Science: Tim Roughgarden, 410 Mudd; 212-853-8474; tr@cs.columbia.edu
Statistics: Ronald Neath, 615 Watson; 212-853-1398; rcn2112@columbia.edu

Economics - Statistics Major Advising:
Economics: Susan Elmes, 1006 IAB; 212-854-9124; se5@columbia.edu
Statistics: Ronald Neath, 615 Watson; 212-853-1398; rcn2112@columbia.edu

Mathematics - Statistics Major Advising:
Mathematics: Julien Dubedat, 601 Mathematics; 212-854-8806; jd2653@columbia.edu
Statistics: Ronald Neath, 615 Watson; 212-853-1398; rcn2112@columbia.edu

Political Science - Statistic Major Advising:
Political Science: Andrew Gelman, 1016 SSW (1255 Amsterdam); gelman@stat.columbia.edu
Statistics: Ronald Neath, 615 Watson; 212-853-1398; rcn2112@columbia.edu

Enrolling in Classes 

Students may wish to consult the following guidelines when undertaking course planning.  

• It is advisable to take STAT UN1101 INTRODUCTION TO STATISTICS and STAT UN2102 Applied Statistical Computing before taking any of the more advanced minor courses:  STAT UN2103 APPLIED LINEAR REG ANALYSIS, STAT UN2104 APPL CATEGORICAL DATA ANALYSIS, STAT UN3104 Applied Bayesian Analysis, STAT UN3105 APPLIED STATISTICAL METHODS, and STAT UN3106 APPLIED MACHINE LEARNING.  

• It is advisable to take STAT UN1201 CALC-BASED INTRO TO STATISTICS, STAT GU4203 PROBABILITY THEORY, STAT GU4204 STATISTICAL INFERENCE, and STAT GU4205 LINEAR REGRESSION MODELS in sequence.  

• Courses in stochastic analysis should be preceded by STAT GU4203 PROBABILITY THEORY, and for many students, it is advisable to take STAT GU4207 ELEMENTARY STOCHASTIC PROCESS before embarking on STAT GU4262 Stochastic Processes for Finance, STAT GU4264 STOCHASTC PROCSSES-APPLICTNS I, or STAT GU4265 STOCHASTIC METHODS IN FINANCE.  

• Most of the statistics courses numbered from 4221 to 4234 are best preceded by STAT GU4205 LINEAR REGRESSION MODELS.  

• The data science courses STAT GU4206 STAT COMP ＆ INTRO DATA SCIENCE, STAT GU4241 STATISTICAL MACHINE LEARNING, and STAT GU4242 Advanced Machine Learning should be taken in sequence. 

Preparing for Graduate Study 

The BA/MA option allows current Columbia undergraduate students (Columbia College, SEAS, the School of General Studies, and Barnard) the opportunity to complete both the bachelor’s degree and the master’s degree (BA/MA) in a shorter period of time, thus providing an option that is financially advantageous.  The BA/MA in Statistics is open to students from all majors.  

Coursework Taken Outside of Columbia

Coursework in fulfillment of a major or minor must be taken at Columbia University unless explicitly noted here and/or expressly permitted by the Director of Undergraduate Studies.  Exceptions or substitutions permitted by the Director of Undergraduate Studies should be confirmed in writing by email to the student. 

Advanced Placement 

Columbia College and the School of General Studies award 3 points of credit for a score of 5 on the AP statistics exam.  Students who are required to take STAT UN1101 for their major should check with their major advisor to determine whether this credit provides exemption from their requirement.  

Students pursuing a major that requires STAT UN1201 should plan to take that course at Columbia, even if they scored a 5 on the AP statistics exam.  AP credit cannot be used to satisfy a requirement for STAT UN1201.  

Transfer Courses 

When students transfer to Columbia from other institutions, their coursework at their previous institution must first be considered by their school in order to be evaluated for degree credit (e.g., to confirm that the courses will count toward the 124 points of credit that every student is required to complete for the B.A. degree).  Only after that degree credit is confirmed, departments may consider whether those courses can also be used to fulfill specific degree requirements toward a major or minor.  

No more than two DUS-approved STAT courses toward a Statistics major may be fulfilled with transfer credit.  

Not more than one DUS-approved STAT course toward a Statistics joint major or a Statistics minor may be fulfilled with transfer credit.  

Study Abroad Courses

Classes taken abroad through Columbia-led programs (i.e., those administered by Columbia’s Center for Undergraduate Global Engagement and taught by Columbia instructors) are treated as Columbia courses, equivalent to those taken on the Morningside Heights campus.  If they are not explicitly listed by the department as fulfilling requirements in the major or minor, the DUS will need to confirm that they can be used toward requirements in the major/minor.  

Classes taken abroad through other institutions and programs are treated as transfer credit to Columbia, and are subject to the same policies as other transfer courses, including limits on the number of approved STAT course that can be applied to the major/minor.  

Summer Courses

Summer courses at Columbia are offered through the School of Professional Studies.  Courses taken in a Summer Term may be used toward requirements for the Statistics major or minor.  

More general policies about Summer coursework can be found in the Academic Regulations section of this Bulletin. 

Undergraduate Research 

Matriculated students who will be undergraduates at Columbia College, Barnard College, the School of General Studies, or the School of Engineering and Applied Sciences may apply to the Department’s summer internship program.  Students work under the supervision of Statistics Department faculty mentors.  The internship provides a summer housing allowance and a stipend.  Applicants should send a brief statement of interest and a copy of their transcript to the Statistics DUS by the end of March to be considered.  If summer project descriptions are posted on the Department’s website, please indicate your preferred project(s) in your statement of interest.  

Students seeking research opportunities with Statistics Department faculty during the academic year are advised to be entrepreneurial and proactive: identify congenial faculty whose research is appealing, request an opportunity to meet, and provide some indication of previous coursework when asking for a project.  

Department Honors 

Students are considered for department honors on the basis of GPA and the comprehensiveness and difficulty of their coursework in Statistics and related disciplines.  Generally, no more than 10% of graduating majors receive departmental honors in a given academic year.  

Professors

• David Blei (with Computer Science)
• John Cunningham
• Richard R. Davis
• Victor H. de la Peña
• Andrew Gelman (with Political Science)
• Ioannis Karatzas (with Mathematics)
• Jingchen Liu
• Shaw-Hwa Lo
• Marcel Nutz (with Mathematics)
• Liam Paninski
• Philip Protter
• Daniel Rabinowitz
• Bodhisattva Sen
• Michael Sobel
• Simon Tavaré (with Biological Sciences)
• Zhiliang Ying
• Ming Yuan
• Tian Zheng (Chair)
•  

Associate Professors

• Samory Kpotufe
• Arian Maleki
• Sumit Mukherjee
•  

Assistant Professors

• Marco Avella
• Yuqi Gu
• Cynthia Rush
• Anne van Delft
•  

Term Assistant Professors

• Carsten Chong
• Gokce Dayanikli
• Yongchen Kwon
• Johannes Wiesel
• Chenyang Zhong
•  

Adjunct Faculty

• Demissie Alemayehu
• Mark Brown
• Guy Cohen
• Regina Dolgoarshinnykh
• Hammou El Barmi
• Tat Sang Fung
• Xiaofu He
• Ying Liu
• Ka-Yi Ng
• Ha Nguyen
• Cristian Pasarica
• Kamiar Rahnama Rad
• Ori Shental
• Haiyuan Wang
• Rongning Wu
•  

Lecturers in Discipline

• Banu Baydil
• Anthony Donoghue
• Wayne Lee
• Dobrin Marchev
• Ronald Neath
• Alex Pijyan
• David Rios
• Joyce Robbins
• Gabriel Young
•  

Guidance for Undergraduate Students in the Department

Program Planning for all Students 

Selecting a first course in Statistics: 

• Students interested in learning statistical concepts, with a goal of being educated consumers of statistics, should take STAT UN1001 INTRO TO STATISTICAL REASONING.  This course is designed for students who have taken a pre-calculus course, and the focus is on general principles.  

• Students seeking an introduction to applied statistics should take STAT UN1101 INTRODUCTION TO STATISTICS.  This course is designed for students who wish to learn to conduct statistical analyses, but do not have a background in calculus; the focus is on the implementation of statistical methods, rather than the underlying theory.  It is recommended for pre-med students, and students considering the applied track of the statistics minor.  

• Students seeking a more mathematically rigorous treatment of the subject should take STAT UN1201 CALC-BASED INTRO TO STATISTICS.  This course is designed for students who have taken a semester of college calculus or the equivalent, and the focus is on preparation for further study in probability and statistical theory and methods.  It is recommended for students considering the statistics major, or the theoretical track of the minor.  

• Students seeking a one-semester calculus-based survey of probability and statistical theory should take STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS.  This course is designed for students who have taken calculus, and is meant as a terminal course.  It provides an abridged version of the material covered in the two-semester sequence STAT GU4203 PROBABILITY THEORY and STAT GU4204 STATISTICAL INFERENCE.  While some mathematically mature students may take the 4203--4204 sequence as an introduction to the field, it is generally recommended that students prepare for it by taking STAT UN1201 CALC-BASED INTRO TO STATISTICS.  

Course Numbering Structure

The 1000-level courses (STAT UN1001, STAT UN1101 and STAT UN1201) are introductory courses.  Most students will begin their study of statistics with one of these three courses.  

The 2000-level courses (STAT UN2102, STAT UN2103 and STAT UN2104) are courses in computational and applied statistics, with STAT UN1101 or STAT UN1201 as a prerequisite.  These are important courses in the minor program; students pursuing a statistics major will learn this material by studying the more mathematical treatment given in the 4000-level courses.  

The 3000-level courses (STAT UN3104, STAT UN3105 and STAT UN3106) introduce more specialized statistical methods which build on the material introduced in STAT UN2102 and STAT UN2103.  While the statistical methods covered in these courses can be quite advanced, the mathematical level remains modest.  Again, these courses are part of the minor curriculum, and students completing a statistics major will learn this material elsewhere in the statistics curriculum.  

STAT GU4001 is a one-semester calculus-based course in probability and statistics, intended for students who seek a mathematically rigorous course, but do not intend to major or minor in statistics (for most, this will be a terminal course).  

The 4200-level courses are intended for students majoring in statistics and related disciplines. 

Courses numbered 4203 through 4207 introduce fundamental material in probability theory, statistical inference, data analysis, and statistical computing; these courses comprise the core of the statistics major.  

Courses numbered 4221 through 4234 cover specialized statistical data analysis techniques, and are possible electives for students in the statistics major.  

Courses numbered 4241 through 4243 introduce modern tools in machine learning and data science.  

Courses numbered between 4261 and 4265 cover statistical and probabilistic theory and methods in modern finance.  

Undergraduate Programs of Study

Major in Statistics

The major should be planned with the director of undergraduate studies. Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major. The major requires 14 courses, as follows:

Course List

Code	Title	Points
Mathematics Prerequisite (four courses)
MATH UN1101	CALCULUS I
MATH UN1102	CALCULUS II
MATH UN1201	CALCULUS III
MATH UN2010	LINEAR ALGEBRA
Computer Science Requirement (one course). Choose one of the following
COMS W1004	Introduction to Computer Science and Programming in Java
ENGI E1006	INTRO TO COMP FOR ENG/APP SCI
STAT UN2102	Applied Statistical Computing
Statistical prerequisite (one course)
STAT UN1201	CALC-BASED INTRO TO STATISTICS
Core courses in probability and statistics (five courses):
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
STAT GU4206	STAT COMP ＆ INTRO DATA SCIENCE
STAT GU4207	ELEMENTARY STOCHASTIC PROCESS
Electives (three courses):
An approved selection of three advanced courses in mathematics, statistics, applied mathematics, industrial engineering and operations research, computer science, or an advanced quantitative course in a social science. At least one elective must be a Statistics Department course numbered between 4221 and 4291

• The mathematics prerequisite can also be satisfied by taking the Honors Mathematics A and B sequence, MATH UN1207 and MATH UN1208.
• Students preparing for graduate study in statistics are encouraged to replace two electives with MATH GU4061 INTRO MODERN ANALYSIS I and  MATH GU4062 INTRO MODERN ANALYSIS II .

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Major in Data Science

In response to the ever increasing importance of “big data” in scientific and policy endeavors, the last few years have seen an explosive growth in theory, methods, and applications of AI and machine learning.  The Department of Computer Science and the Department of Statistics jointly offer a Data Science major that emphasizes the interface between the two disciplines.  

The major requires 18 courses, as follows.  (Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major.)

Notes:

The mathematics prerequisite can also be satisfied by taking the Honors Mathematics A and B sequence, MATH UN1207 and MATH UN1208.

Course List

Code	Title	Points
Mathematical Prerequisites
MATH UN1101	CALCULUS I
MATH UN1102	CALCULUS II
MATH UN1201	CALCULUS III
or MATH UN1205	ACCELERATED MULTIVARIABLE CALC
MATH UN2010	LINEAR ALGEBRA
Statistics Required Courses
STAT UN1201	CALC-BASED INTRO TO STATISTICS
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
STAT GU4241	STATISTICAL MACHINE LEARNING
or COMS W4771	MACHINE LEARNING
Statistics Electives
Select two of the following courses:
STAT UN3106	APPLIED MACHINE LEARNING
STAT GU4206	STAT COMP ＆ INTRO DATA SCIENCE
STAT GU4243	APPLIED DATA SCIENCE
STAT GU4224	BAYESIAN STATISTICS
STAT GU4242	Advanced Machine Learning
Computer Science Introductory Courses
Select one of the following courses:
COMS W1004	Introduction to Computer Science and Programming in Java
COMS W1005	Introduction to Computer Science and Programming in MATLAB
ENGI E1006	INTRO TO COMP FOR ENG/APP SCI
COMS W1007
And select one of the following courses:
COMS W3134	Data Structures in Java
COMS W3136	ESSENTIAL DATA STRUCTURES
COMS W3137	HONORS DATA STRUCTURES ＆ ALGOL
Computer Science Required Courses
COMS W3203	DISCRETE MATHEMATICS
CSOR W4231	ANALYSIS OF ALGORITHMS I
Computer Science Electives
Select three of the following courses:
COMS W3261	COMPUTER SCIENCE THEORY
COMS W4236	INTRO-COMPUTATIONAL COMPLEXITY
COMS W4252	INTRO-COMPUTATIONAL LEARN THRY
COMS W4111	INTRODUCTION TO DATABASES
COMS W4130
Any COMS W47xx course EXCEPT W4771

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Major in Economics-Statistics

Please read Requirements for all Economics Majors, Concentrators, and Interdepartmental Majors in the Economics section of this Bulletin.

The major in Economics-Statistics provides students with a grounding in economic theory comparable to that of the general economics major, but also exposes students to a more rigorous and extensive statistics training. This program is recommended for students with strong quantitative skills and for those contemplating graduate studies in economics.

Two advisers are assigned for the interdepartmental major, one in the Department of Economics and one in the Department of Statistics. The economics adviser can only advise on economics requirements and the statistics adviser can only advise on statistics requirements.

Students should be aware of the rules regarding the use of the Pass/D/Fail option. Courses in which a grade of D has been received do not count toward the major requirements.

The economics-statistics major requires 18 courses, as follows:

Course List

Code	Title	Points
Economics Core Courses
Complete the Economics core courses.
Economics Electives
Select three electives at the 3000-level or above, of which no more than one may be a Barnard course.
Mathematics
Select one of the following sequences:
MATH UN1101  - MATH UN1102  - MATH UN1201  - MATH UN2010	CALCULUS I and CALCULUS II and CALCULUS III and LINEAR ALGEBRA
MATH UN1101  - MATH UN1102  - MATH UN1205  - MATH UN2010	CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA
MATH UN1207  - MATH UN1208	HONORS MATHEMATICS A and HONORS MATHEMATICS B
Statistics
STAT UN1201	CALC-BASED INTRO TO STATISTICS
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
One elective from among courses numbered STAT GU4206 through GU4266.
Computer Science
Select one of the following courses:
COMS W1004	Introduction to Computer Science and Programming in Java
COMS W1005	Introduction to Computer Science and Programming in MATLAB
COMS W1007
ENGI E1006	INTRO TO COMP FOR ENG/APP SCI
STAT UN2102	Applied Statistical Computing
Seminar
ECON GU4918	SEMINAR IN ECONOMETRICS

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Major in Mathematics-Statistics

This major program is designed to prepare students for: (1) a career in industries, such as finance and insurance, that require a high level of mathematical sophistication and a substantial knowledge of probability and statistics; and (2) graduate study in quantitative disciplines. 

The major requires 14 courses, as follows.  (Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major.):

Course List

Code	Title	Points
Mathematics
Select one of the following sequences:
MATH UN1101	CALCULUS I
MATH UN1102	CALCULUS II
MATH UN1201	CALCULUS III
MATH UN2010	LINEAR ALGEBRA
MATH UN2500	ANALYSIS AND OPTIMIZATION
OR
MATH UN1101	CALCULUS I
MATH UN1102	CALCULUS II
MATH UN1205	ACCELERATED MULTIVARIABLE CALC
MATH UN2010	LINEAR ALGEBRA
MATH UN2500	ANALYSIS AND OPTIMIZATION
OR
MATH UN1207	HONORS MATHEMATICS A
MATH UN1208	HONORS MATHEMATICS B
MATH UN2500	ANALYSIS AND OPTIMIZATION
Statistics required courses
STAT UN1201	CALC-BASED INTRO TO STATISTICS
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
And select one of the following courses:
STAT GU4207	ELEMENTARY STOCHASTIC PROCESS
STAT GU4262	Stochastic Processes for Finance
STAT GU4264	STOCHASTC PROCSSES-APPLICTNS I
STAT GU4265	STOCHASTIC METHODS IN FINANCE
Computer Science
Select one of the following courses:
COMS W1004	Introduction to Computer Science and Programming in Java
COMS W1005	Introduction to Computer Science and Programming in MATLAB
ENGI E1006	INTRO TO COMP FOR ENG/APP SCI
COMS W1007
or an advanced Computer Science offering in programming
Electives
An approved selection of three advanced courses in mathematics, statistics, applied mathematics, industrial engineering and operations research, computer science, or approved mathematical methods courses in a quantitative discipline. At least one elective must be a Mathematics Department course numbered 3000 or above.

• Notes:

• The mathematics prerequisite can also be satisfied by taking the Honors Mathematics A and B sequence, MATH UN1207 and MATH UN1208.  

• Students preparing for doctoral study in mathematics or statistics are encouraged to take MATH GU4061 INTRO MODERN ANALYSIS I and MATH GU4062 INTRO MODERN ANALYSIS II.

Major in Political Science–Statistics

The interdepartmental major of political science–statistics is designed for students who desire an understanding of political science to pursue advanced study in this field and who also wish to have at their command a broad range of sophisticated statistical tools to analyze data related to social science and public policy research.

Students should be aware of the rules regarding the use of the Pass/D/Fail option. Courses in which a grade of D has been received do not count toward the major requirements.

The political science-statistics major requires a minimum of 6 courses in political science, and 7 or 8 courses in statistics & mathematics, to be distributed as follows:

Course List

Code	Title	Points
Political Science
Students must choose a primary subfield to study. Within the subfield, students must take a minimum of three courses, including the subfield's introductory course. The subfields and their corresponding introductory courses are as follows:
American Politics:
POLS UN1201	INTRO TO AMERICAN POLITICS
Comparative Politics:
POLS UN1501	INTRO TO COMPARATIVE POLITICS
International Relations:
POLS UN1601	INTERNATIONAL POLITICS
Political Theory:
POLS UN1101	POLITICAL THEORY I
Additionally, students must take a 4-point seminar in their primary subfield.
Research Methods
Students must take the following two research methods courses:
POLS GU4710	PRINC OF QUANT POL RESEARCH 1
or POLS UN3704	RESEARCH DESIGN: DATA ANALYSIS
POLS GU4712	PRINC OF QUANT POL RESEARCH 2
Statistics
Select one of the following two sequences.
Sequence recommended for students preparing for graduate study in statistics.
MATH UN1101	CALCULUS I
MATH UN1102	CALCULUS II
MATH UN2010	LINEAR ALGEBRA
STAT UN1201	CALC-BASED INTRO TO STATISTICS
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
STAT GU4206	STAT COMP ＆ INTRO DATA SCIENCE
Students taking the first track may replace the Mathematics prerequisites with both of MATH UN1207 and MATH UN1208
or
Sequence recommend for students preparing to apply statistical methods in the social sciences.
STAT UN1101	INTRODUCTION TO STATISTICS
STAT UN2102	Applied Statistical Computing
STAT UN2103	APPLIED LINEAR REG ANALYSIS
STAT UN2104	APPL CATEGORICAL DATA ANALYSIS
STAT UN3105	APPLIED STATISTICAL METHODS
STAT UN3106	APPLIED MACHINE LEARNING
Statistics elective:
Students must take an approved elective in a statistics or a quantitatively oriented course in a social science.

Minor in Statistics

The minor requires five courses, distributed as follows.  

Students should select one of the following two tracks.  

The requirements for the Applied track of the statistics minor are:   

Introduction to statistics (one course):  Choose one of the following 

STAT UN1101 INTRODUCION TO STATISTICS

STAT UN1201 CALC-BASED INTRO TO STATISTICS 

Applied statistics core (two courses):  Take both of the following 

STAT UN2102 Applied Statistical Computing 

STAT UN2103 APPLIED LINEAR REG ANALYSIS

Statistics electives (two courses):  Choose any two of the following 

STAT UN2104 APPL CATEGORICAL DATA ANALYSIS 

STAT UN3104 Applied Bayesian Analysis 

STAT UN3105 APPLIED STATISTICAL METHODS 

STAT UN3106 APPLIED MACHINE LEARNING 

The requirements for the Theoretical track are:  

Introduction to Statistics (one course) 

STAT UN1201 CALC-BASED INTRO TO STATISTICS 

Probability and statistics core (three courses) 

STAT GU4203 PROBABILITY THEORY 

STAT GU4204 STATISTICAL INFERENCE 

STAT GU4205 LINEAR REGRESSION MODELS 

Elective (one course)  

One additional STAT course numbered 4206 through 4261

For students who entered Columbia in or before the 2023-24 academic year

Concentrations are available to students who entered Columbia in or before the 2023-2024 academic year.  The requirements for the Bachelor of Arts degree, and the role of the concentration in those requirements, can be found in the Academic Requirements section of the Bulletin dated the academic year when the student matriculated at Columbia and the Bulletin dated the academic year when the student was a sophomore and declared programs of study. 

Concentrations are not available to students who entered Columbia in or after Fall 2024. 

Concentration in Statistics

The concentration requires 6 courses in statistics, as follows. 

Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count towards the concentration.  

STAT UN1101 INTRODUCTION TO STATISTICS 

STAT UN2102 Applied Statistical Computing

STAT UN2103 APPLIED LINEAR REG ANALYSIS 

STAT UN2104 APPL CATEGORICAL DATA ANALYSIS 

STAT UN3105 APPLIED STATISTICAL METHODS 

STAT UN3106 APPLIED MACHINE LEARNING

(Students may replace courses nominally required for the concentration by approved Statistics Department courses.)

Introductory Courses

Students interested in statistical concepts, but who do not anticipate undertaking statistical analyses, should take STAT UN1001 Introduction to Statistical Reasoning. Students seeking an introduction to applied statistics or preparing for the concentration should take STAT UN1101 Introduction to Statistics (without calculus). Students seeking a foundation for further study of probability theory and statistical theory and methods should take STAT UN1201 Calculus-based Introduction to Statistics. Students seeking a one-semester calculus-based survey should take STAT GU4001 Introduction to Probability and Statistics. The undergraduate seminar STAT UN1202 features faculty lectures prepared with undergraduates in mind; students may attend without registering.

Applied Statistics Concentration Courses

The applied statistics sequence, together with an introductory course, forms the concentration in applied statistics. STAT UN2102 Applied statistical computing may be used to satisfy the computing requirement for the major, and the other concentration courses may be used to satisfy the elective requirements for the major. (Students who sat STAT GU4205 Linear Regression for the major would find that they have covered essentially all of the material in STAT UN2103 Applied Linear Regression Analysis.

Foundation Courses

The calculus-based foundation courses for the core of the statistics major. These courses are GU4203 Probability Theory, GU4204 Statistical Inference, GU4205 Linear Regression, GU4206 Statistical Computing and Introduction to Data Science, and GU4207 Elementary Stochastic processes. Ideally, students would take Probability theory or the equivalent before taking either Statistical Inference or Elementary Stochastic Processes, and would have taken Statistical Inference before, or at least concurrently with taking Linear Regression Analysis, and would have taken Linear Regression analysis before, or at least concurrently, with taking the computing and data science course. A semester of calculus should be taken before Probability, additional semesters of calculus are recommended before Statistical Inference, and a course in linear algebra before Linear Regression is strongly recommended. For the more advanced electives in stochastic processes, Probability Theory is an essential prerequisite, and many students would benefit from taking Elementary Stochastic Processes, too. Linear Regression and the computing and data science course should be taken before the advanced electives in machine learning and data science. Linear Regression is a strongly recommended prerequisite, or at least co-requisite, for the remaining advanced statistical electives.

Course List

Code	Title	Points
STAT GU4203	PROBABILITY THEORY
STAT GU4204	STATISTICAL INFERENCE
STAT GU4205	LINEAR REGRESSION MODELS
STAT GU4206	STAT COMP ＆ INTRO DATA SCIENCE
STAT GU4207	ELEMENTARY STOCHASTIC PROCESS

Advanced Statistics Courses

Advanced statistics courses combine theory with methods and practical experience in data analysis. Undergraduates enrolling in advanced statistics courses would be well-advised to have completed STAT GU4203 (Probability Theory), GU4204 (Statistical Inference), and GU4205 (Linear Regression).

Actuarial Sciences Courses

Only students preparing for a career in actuarial sciences should consider the courses in this section. Such students may also be interested in courses offered through the School of Professional Studies M.S. Program in Actuarial Science, but must check with the academic advisors in their schools to know whether they are allowed to register for those courses. Students majoring in statistics and preparing for a career in actuarial science may take STAT GU4282 (Regression and Time Series Analysis) in place of the major requirement STAT GU4205 (Linear Regression Analysis).

Course List

Code	Title	Points
STAT GU4281	Theory of Interest
STAT GU4282	Linear Regression and Time Series Methods

Advanced Data Science Courses

In response to the ever growing importance of ``big data” in scientific and policy endeavors, the last few years have seen an explosive growth in theory, methods, and applications at the interface between computer science and statistics. The Department offers a sequence that begins with the core course STAT GU4206 (Statistical Computing and Introduction to Data Science) and continues with the advanced electives GU4241 (Statistical Machine Learning) and GU4242 (Advanced Machine Learning), and also the advanced elective STAT GU4243 (Applied Data Science). Undergraduate students without experience in programming would likely benefit from taking the statistical computing and data science course before attempting GU4241, GU4242, or GU4243.

Course List

Code	Title	Points
STAT GU4241	STATISTICAL MACHINE LEARNING
STAT GU4242	Advanced Machine Learning
STAT GU4243	APPLIED DATA SCIENCE
STAT GU4702	Exploratory Data Analysis and Visualization

Advanced Stochastic Processes Courses

The stochastic processes electives in this section have STAT GU4203 (Probability Theory) or the equivalent as prerequisites Most students would also benefit from taking STAT GU4207 (Elementary Stochastic Processes) before embarking on the more advanced stochastic processes electives.

Course List

Code	Title	Points
STAT GU4262	Stochastic Processes for Finance
STAT GU4264	STOCHASTC PROCSSES-APPLICTNS I
STAT GU4265	STOCHASTIC METHODS IN FINANCE

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