Mathematics and Statistics
Mathematics has always held a central position in the liberal arts, and, over time, it has also come to play an important role in more and more aspects of our lives. Mathematical analysis and modeling are involved in many areas far beyond the traditional association of mathematics with the physical sciences and engineering. This fact is reflected in the diversity of the students who study at least some mathematics during their time at Washington University — students who recognize the importance of quantitative skills in a world that is becoming more and more technological.
Students major in mathematics for many reasons. Some are planning academic careers in mathematics or statistics that involve teaching or research. Others plan to work as actuaries or at other jobs in industry or government. Some plan careers in secondary education. Many majors do not intend to become "mathematicians" at all but simply realize that quantitative training is a valuable asset in many kinds of careers; often, work in mathematics or statistics is meant to complement their study in other areas. Other majors view mathematics as an interesting concentration in their liberal arts education, even though they plan to enter professional fields such as medicine or law.
The Mathematics and Statistics program gives majors and minors a broad introduction to the subject. Majors choose among several tracks to complete their study; these tracks add different emphases to their programs and reflect individual interests or professional goals. Majors are encouraged to complete additional work (perhaps even a minor or a second major) in other related areas.
Contact Info
Phone:  3149356301 
Email:  mathadvising@wustl.edu 
Website:  http://math.wustl.edu 
Chair
John Shareshian
PhD, Rutgers University
Algebraic and topological combinatorics
Directors
José FigueroaLópez
Director of Undergraduate Studies
Professor of Mathematics and Statistics
PhD, Georgia Institute of Technology
Statistics; probability and stochastic processes; mathematical finance
Gregory Knese
Director of Graduate Studies
Associate Professor of Mathematics and Statistics
PhD, Washington University
Complex function theory; operators; harmonic analysis
Endowed Professors
Soumendra Lahiri
Stanley A. Sawyer Professor
PhD, Michigan State University
Mathematical statistics; data science
John E. McCarthy
Spencer T. Olin Professor of Mathematics
PhD, University of California, Berkeley
Analysis; operator theory; one and several complex variables
Rachel Roberts
Elinor Anheuser Professor of Mathematics
PhD, Cornell University
Lowdimensional topology
Professors
QuoShin Chi
PhD, Stanford University
Differential geometry
Renato Feres
PhD, California Institute of Technology
Differential geometry; dynamical systems
José FigueroaLópez
PhD, Georgia Institute of Technology
Statistics; probability and stochastic processes; mathematical finance
Matthew Kerr
PhD, Princeton University
Algebraic geometry; Hodge theory
Steven G. Krantz
PhD, Princeton University
Several complex variables; geometric analysis
Nan Lin
PhD, University of Illinois at Urbana–Champaign
Statistics
Xiang Tang
PhD, University of California, Berkeley
Symplectic geometry; noncommutative geometry; mathematical physics
Brett Wick
PhD, Brown University
Complex analysis; harmonic analysis; operator theory; several complex variables
Mladen Victor Wickerhauser
PhD, Yale University
Harmonic analysis; wavelets; numerical algorithms for data compression
Associate Professors
Roya Beheshti Zavareh
PhD, Massachusetts Institute of Technology
Algebraic geometry
Jimin Ding
PhD, University of California, Davis
Statistics
Gregory Knese
PhD, Washington University
Complex function theory; operators; harmonic analysis
Todd Kuffner
PhD, Imperial College London
Statistics; likelihood; asymptotics; econometrics
Debashis Mondal
PhD, University of Washington
Statistics
Ari Stern
PhD, California Institute of Technology
Geometric numerical analysis; computational mathematics
Assistant Professors
Aliakbar Daemi
PhD, Harvard University
Gauge theory; lowdimensional topology; symplectic geometry
Laura Escobar Vega
PhD, Cornell University
Combinatorics; algebraic geometry
Steven Frankel
PhD, University of Cambridge
Geometric topology; dynamics
Wanlin Li
PhD, University of Wisconsin–Madison
Number theory; arithmetic geometry
Robert Lunde
PhD, Carnegie Mellon University
Statistical network analysis; time series; resampling methods; highdimensional statistics
Martha Precup
PhD, University of Notre Dame
Applications of Lie theory to algebraic geometry and the related combinatorics
Donsub Rim
PhD, University of Washington
Applied mathematics
Yanli Song
PhD, Pennsylvania State University
Noncommutative geometry; symplectic geometry; representation theory
Professors Emeriti
Lawrence Conlon
PhD, Harvard University
Differential topology
Ron Freiwald
PhD, University of Rochester
General topology
Gary R. Jensen
PhD, University of California, Berkeley
Differential geometry
N. Mohan Kumar
PhD, Bombay University
Algebraic geometry; commutative algebra
Robert McDowell
PhD, Purdue University
General topology
Richard Rochberg
PhD, Harvard University
Complex analysis; interpolation theory
Jack Shapiro
PhD, City University of New York
Algebraic Ktheory
Edward Spitznagel
PhD, University of Chicago
Statistics; statistical computation; application of statistics to medicine
Edward N. Wilson
PhD, Washington University
Harmonic analysis; differential geometry
David Wright
PhD, Columbia University
Affine algebraic geometry; polynomial automorphisms
William Chauvenet Postdoctoral Lecturers
Nilanjan Chakraborty
PhD, Michigan State University
High dimensional inference; time series; bootstrap
Michael Landry
PhD, Yale University
Lowdimensional geometry; topology
Andrew Walton Green
PhD, Clemson University
Harmonic analysis; partial differential equations
Ben Wormleighton
PhD, University of California, Berkeley
Algebraic and symplectic geometry
Postdoctoral Lecturers
Chetkar Jha
PhD, University of Missouri–Columbia
Hierarchical Bayesian methods; highdimensional data analysis; network analysis with applications to biomedical datasets such as singlecell RNA sequencing datasets; SNP genotyping datasets
Minh Nguyen
PhD, University of Arkansas
Gauge theory; low dimensional topology
Rudy Rodsphon
PhD, Vanderbilt University
Noncommutative geometry
Angel Roman
PhD, Pennsylvania State University
Representation theory; operator algebras
Jesus Sanchez
PhD, Pennsylvania State University
Noncommutative index theory; cyclic cohomology; spin Riemannian geometry, high dimensional gauge theory
Joel Villatoro
PhD, University of Illinois at Urbana–Champaign
Differential geometry; Poisson geometry; singular spaces
Bowen Xie
PhD, Iowa State University
Queueing theory; stochastic control problems; mathematical finance
Senior Lecturer
Abigail Jager
PhD, University of Chicago
Statistics; causal inference
Lecturers
Silas Johnson
PhD, University of WisconsinMadison
Algebraic number theory; arithmetic statistics
Karl Schaefer
PhD, University of Chicago
Algebraic number theory
Associate Director of Undergraduate Studies
Blake Thornton
PhD, University of Utah
Geometric topology
On this page:
Requirements for All Majors  Major in Mathematical Sciences  Major in Mathematics  Major in Applied Mathematics  Major in Statistics  Major in Mathematics and Computer Science  Major in Mathematics and Economics  Bachelor of Science in Data Science  Notes to All Majors in Mathematics and Statistics  Additional Information
Requirements for All Majors
Total units required: 3642
Required common units: 12 units
 The threecourse calculus sequence (9 units)* and an introductory computer science course (3 units)**:
Code  Title  Units 

Math 131  Calculus I  3 
Math 132  Calculus II  3 
Math 233  Calculus III  3 
CSE 131  Introduction to Computer Science  3 
Total Units  12 
 *
AP credit can be applied, and students who have completed Math 203 Honors Mathematics I and Math 204 Honors Mathematics II will have this requirement waived.
 **
This course may be waived after consultation with the director of undergraduate studies of the Department of Computer Science & Engineering.
The Major in Mathematical Sciences
Total units required: 24 units of upperlevel courses, including the following:
Code  Title  Units 

Math 309  Matrix Algebra  3 
Math 310  Foundations for Higher Mathematics  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
 One of the following fullyear 400level sequences*:
Code  Title  Units 

Math 4111 & Math 4121  Introduction to Analysis and Introduction to Lebesgue Integration  6 
Math 4171 & Math 4181  Topology I and Topology II  6 
Math 429 & Math 430  Linear Algebra and Modern Algebra  6 
Math 449 & Math 450  Numerical Applied Mathematics and Topics in Applied Mathematics  6 
Math 494 & Math 439  Mathematical Statistics and Linear Statistical Models  6 
 *
Students whose primary major is secondary education may fulfill this requirement by taking Math 302 Elementary Geometry from an Advanced Point of View and Math 331 Algebraic Systems.
 At least one course from the following list (that has not already been used to fulfill any of the previous requirements listed):
Code  Title  Units 

Math 370  Introduction to Combinatorics  3 
Math 371  Graph Theory  3 
Math 410  Introduction to Fourier Series and Integrals  3 
Math 4111  Introduction to Analysis  3 
Math 415  Partial Differential Equations  3 
Math 416  Complex Variables  3 
Math 4171  Topology I  3 
Math 429  Linear Algebra  3 
Math 434  Survival Analysis  3 
Math 4351  Number Theory and Cryptography  3 
Math 439  Linear Statistical Models  3 
Math 449  Numerical Applied Mathematics  3 
The Major in Mathematics
Total units required: 30 units of upperlevel courses, including the following:
Code  Title  Units 

Math 310  Foundations for Higher Mathematics  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
Math 4111  Introduction to Analysis  3 
Math 4121  Introduction to Lebesgue Integration  3 
Math 429  Linear Algebra  3 
Math 430  Modern Algebra  3 
Math 416  Complex Variables  3 
Math 4171  Topology I  3 
At least one of the following:  
Math 407  An Introduction to Differential Geometry  3 
Math 415  Partial Differential Equations  3 
Math 4181  Topology II  3 
Math 4351  Number Theory and Cryptography  3 
The Major in Applied Mathematics
Total units required: 30 units of upperlevel courses, including the following:
Code  Title  Units 

Math 310  Foundations for Higher Mathematics  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
Math 4111  Introduction to Analysis  3 
Math 4121  Introduction to Lebesgue Integration  3 
Math 429  Linear Algebra  3 
Math 449  Numerical Applied Mathematics  3 
Math 450  Topics in Applied Mathematics  3 
At least two of the following:  
Math 410  Introduction to Fourier Series and Integrals  3 
Math 415  Partial Differential Equations  3 
Math 416  Complex Variables  3 
Math 4351  Number Theory and Cryptography  3 
The Major in Statistics
Total units required: 30 units of upperlevel courses, including the following:
Code  Title  Units 

Math 309  Matrix Algebra  3 
Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
Math 493  Probability  3 
Math 494  Mathematical Statistics  3 
Math 439  Linear Statistical Models  3 
Math 459  Bayesian Statistics  3 
or Math 475  Statistical Computation 
 At least two probability or statistics courses at the 400 level or above
The Major in Mathematics and Computer Science
The McKelvey School of Engineering and the College of Arts & Sciences developed a new major that efficiently captures the intersection of the complementary studies of computer science and math.
McKelvey Engineering students who declare this major must fulfill the core course requirements listed below and all other requirements for the Applied Science degree in the McKelvey School of Engineering. They must also complete Engr 310 Technical Writing and 8 units of courses designated as NSM (Natural Sciences & Math) from Anthropology (L48 Anthro), Biology and Biomedical Sciences (L41 Biol), Chemisty (L07 Chem), Earth, Environmental, and Planetary Sciences (L19 EPSc), Physics (L31 Physics) or Environmental Studies (L82 EnSt).
Arts & Sciences students who declare this major must fulfill the distribution requirements and all other requirements for an AB degree in addition to the specific requirements listed below.
Core Course Requirements*
Code  Title  Units 

CSE 131  Introduction to Computer Science  3 
CSE 247  Data Structures and Algorithms  3 
Math 131  Calculus I (AP credit may satisfy this requirement)  3 
Math 132  Calculus II (AP credit may satisfy this requirement)  3 
Math 233  Calculus III  3 
Math 310  Foundations for Higher Mathematics  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
or CSE 240  Logic and Discrete Mathematics  
Math 309  Matrix Algebra  3 
Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
or ESE 326  Probability and Statistics for Engineering  
or Math 3211  Statistics for Data Science I  
CSE 347  Analysis of Algorithms  3 
Total Units  27 
 *
Each of these core courses must be passed with a C or better.
Electives
Eight upperlevel courses from Math or Computer Science & Engineering can be chosen from the approved list, with the following caveats:
 At least three courses must be taken from CSE and at least three course must be taken from Math.
 Up to two preapproved courses from outside both departments can be selected.
 CSE 400 Independent Study or CSE 400E Independent Study may be taken for a maximum of 3 units and must be approved by a CS+Math review committee.
List of Approved Electives
Computer Science & Engineering
Code  Title  Units 

CSE 217A  Introduction to Data Science  3 
CSE 341T  Parallel and Sequential Algorithms  3 
CSE 411A  AI and Society  3 
CSE 412A  Introduction to Artificial Intelligence  3 
CSE 416A  Analysis of Network Data  3 
CSE 417T  Introduction to Machine Learning  3 
CSE 427S  Cloud Computing with Big Data Applications  3 
CSE 442T  Introduction to Cryptography  3 
CSE 447T  Introduction to Formal Languages and Automata  3 
CSE 468T  Introduction to Quantum Computing  3 
CSE 513T  Theory of Artificial Intelligence and Machine Learning  3 
CSE 514A  Data Mining  3 
CSE 515T  Bayesian Methods in Machine Learning  3 
CSE 516A  MultiAgent Systems  3 
CSE 517A  Machine Learning  3 
CSE 518A  HumanintheLoop Computation  3 
CSE 533T  Coding and Information Theory for Data Science  3 
CSE 534A  LargeScale Optimization for Data Science  3 
CSE 541T  Advanced Algorithms  3 
CSE 543T  Algorithms for Nonlinear Optimization  3 
CSE 544T  Special Topics in Computer Science Theory  3 
CSE 546T  Computational Geometry  3 
CSE 554A  Geometric Computing for Biomedicine  3 
CSE 555T  Adversarial AI  3 
CSE 559A  Computer Vision  3 
CSE 581T  Approximation Algorithms  3 
CSE 584A  Algorithms for Biosequence Comparison  3 
CSE 587A  Algorithms for Computational Biology  3 
Mathematics and Statistics
Code  Title  Units 

Math 350  Topics in Applied Mathematics  3 
Math 370  Introduction to Combinatorics  3 
Math 371  Graph Theory  3 
Math 407  An Introduction to Differential Geometry  3 
Math 4111  Introduction to Analysis  3 
Math 4121  Introduction to Lebesgue Integration  3 
Math 4171  Topology I  3 
Math 420  Experimental Design  3 
Math 429  Linear Algebra  3 
Math 430  Modern Algebra  3 
Math 434  Survival Analysis  3 
Math 4351  Number Theory and Cryptography  3 
Math 439  Linear Statistical Models  3 
Math 444  The Mathematics of Quantum Theory  3 
Math 449  Numerical Applied Mathematics  3 
Math 450  Topics in Applied Mathematics  3 
Math 456  Topics in Financial Mathematics  3 
Math 459  Bayesian Statistics  3 
Math 460  Multivariate Statistical Analysis  3 
Math 4601  Statistical Learning  3 
Math 461  Time Series Analysis  3 
Math 462  Mathematical Foundations of Big Data  3 
Math 470  Analytic Combinatorics  3 
Math 475  Statistical Computation  3 
Math 493  Probability  3 
Math 494  Mathematical Statistics  3 
Math 495  Stochastic Processes  3 
Electrical & Systems Engineering
Code  Title  Units 

ESE 4031  Optimization for Engineered Planning, Decisions and Operations  3 
ESE 415  Optimization  3 
ESE 417  Introduction to Machine Learning and Pattern Classification  3 
ESE 427  Financial Mathematics  3 
ESE 429  Basic Principles of Quantum Optics and Quantum Information  3 
ESE 520  Probability and Stochastic Processes  3 
Economics
Code  Title  Units 

Econ 4151  Applied Econometrics  3 
Econ 467  Game Theory  3 
Linguistics
Code  Title  Units 

Ling 317  Introduction to Computational Linguistics  3 
Ling 427  Computation and Learnability in Linguistic Theory  3 
Biology and Biomedical Sciences
Code  Title  Units 

Biol 5657  Biological Neural Computation  3 
Biomedical Engineering
Code  Title  Units 

BME 470  Mathematics of Imaging Science  3 
The Major in Mathematics and Economics
Total units required: 57
Required courses:
Code  Title  Units 

CSE 131  Introduction to Computer Science  3 
Econ 1011  Introduction to Microeconomics  3 
Econ 1021  Introduction to Macroeconomics  3 
Econ 4011  Intermediate Microeconomic Theory  3 
Econ 4021  Intermediate Macroeconomic Theory  3 
Econ 413  Introduction to Econometrics  3 
or Econ 413W  Introduction to Econometrics with Writing  
Math 131  Calculus I  3 
Math 132  Calculus II  3 
Math 233  Calculus III  3 
Math 309  Matrix Algebra  3 
Math 310  Foundations for Higher Mathematics  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
or Math 3211  Statistics for Data Science I  
or Math 493  Probability 
Elective courses:
Majors must complete seven electives, with three in each discipline and one from either department.
In Economics:
One of the three electives can be any Economics course with Econ 4011 or Econ 4021 as a prerequisite, including from an approved study abroad program. The other two economics electives must come from the following list:
Code  Title  Units 

Econ 404  Behavioral Economics and Experimental Economics  3 
Econ 407  Market Design  3 
Econ 410  Macroeconomics of Inequality  3 
Econ 4151  Applied Econometrics  3 
Econ 435  Open Economy Macroeconomics  3 
Econ 437  The Economics of Financial Intermediation  3 
Econ 445  Public Finance  3 
Econ 452  Industrial Organization  3 
Econ 4567  Auction Theory and Practice  3 
Econ 460  Urban Economics  3 
Econ 467  Game Theory  3 
Econ 471  Development Economics  3 
Econ 477  Topics in Financial Economics  3 
Econ 480  Labor Economics  3 
Econ 484  Computational Macroeconomics  3 
 With instructor permission, students may use any of the following for Economics elective credit: Econ 501, Econ 502, Econ 503, Econ 504, Econ 511, or Econ 513.
 Econ 413 may be taken from an approved study abroad program. Consult with Academic Coordinator Dorothy Petersen in the Department of Economics for more information.
In Mathematics:
For Mathematics, the electives can come from the following list:
Code  Title  Units 

Math 410  Introduction to Fourier Series and Integrals  3 
Math 4111  Introduction to Analysis  3 
Math 4121  Introduction to Lebesgue Integration  3 
Math 415  Partial Differential Equations  3 
Math 416  Complex Variables  3 
Math 420  Experimental Design  3 
Math 429  Linear Algebra  3 
Math 439  Linear Statistical Models  3 
Math 4392  Advanced Linear Statistical Models  3 
Math 449  Numerical Applied Mathematics  3 
Math 450  Topics in Applied Mathematics  3 
Math 456  Topics in Financial Mathematics  3 
Math 459  Bayesian Statistics  3 
Math 460  Multivariate Statistical Analysis  3 
Math 461  Time Series Analysis  3 
Math 462  Mathematical Foundations of Big Data  3 
Math 475  Statistical Computation  3 
Math 493  Probability  3 
Math 494  Mathematical Statistics  3 
Math 495  Stochastic Processes  3 
Advising, Questions, and Further Considerations:
 Students may declare a prime or a second major in Math + Economics via L24 (Math) or L11 (Econ), which will determine their major advisor.
 It is possible to earn the Certificate in Financial Economics in conjunction with this major (prime or second).
 It is possible to graduate with Latin Honors or with “English” honors. Students should refer to the departments’ websites or consult with either Professor Blake Thornton in the Department of Mathematics and Statistics or Academic Coordinator Dorothy Petersen in the Department of Economics for more information.
 Substitutions for Mathematics courses and study abroad approval for Mathematics courses will be determined by the Department of Mathematics and Statistics.
 Substitutions for Economics courses and study abroad approval will be determined by Academic Coordinator Dorothy Petersen in the Department of Economics.
 Substitutions for CSE 131 are subject to approval by the McKelvey School of Engineering.
The Bachelor of Science in Data Science
The McKelvey School of Engineering and the College of Arts & Sciences developed a new major that efficiently captures the intersection of mathematics and statistics with computer science for data science. The Bachelor of Science in Data Science (BSDS) will give students the formal foundation needed to understand the applicability and consequences of the various approaches to analyzing data with a focus on statistical modeling and machine learning.
McKelvey Engineering students who declare this major must fulfill the core course requirements listed below and all other requirements for the Applied Science degree in the McKelvey School of Engineering. They must also complete Engr 310 Technical Writing and 8 units of courses designated as NSM (Natural Sciences & Math) from Anthropology (L48 Anthro), Biology and Biomedical Sciences (L41 Biol), Chemistry (L07 Chem), Earth and Planetary Sciences (L19 EPSc), Physics (L31 Physics) or Environmental Studies (L82 EnSt).
Arts & Sciences students who declare this major must fulfill the distribution requirements and all other requirements for an AB degree in addition to the specific requirements listed below.
Data Science Core Requirements (CR)*
Code  Title  Units 

Math 131  Calculus I  3 
Math 132  Calculus II  3 
Math 233  Calculus III  3 
Math 309  Matrix Algebra  3 
Math 3211  Statistics for Data Science I  3 
Math 4211  Statistics for Data Science II  3 
Math 439  Linear Statistical Models  3 
CSE 131  Introduction to Computer Science  3 
CSE 247  Data Structures and Algorithms  3 
CSE 217A  Introduction to Data Science  3 
CSE 314A  Data Manipulation and Management  3 
CSE 417T  Introduction to Machine Learning (or Math 4601 Statistical Learning)  3 
Total Units  36 
 *
Each of these core courses must be passed with a grade of C or better.
Data Science Technical Electives
Four courses from Mathematics & Statistics or Computer Science & Engineering can be chosen from an approved list, with the following caveats:
 At least one course from Mathematics & Statistics (at the 400 level or above)
 At least one course from CSE (ending in S, T, M, or A)
 At most one course at the 200 level
List of Approved Data Science Technical Electives
Computer Science and Engineering
Code  Title  Units 

CSE 237S  Programming Tools and Techniques  3 
CSE 256A  Introduction to HumanCentered Design  3 
CSE 311A  Introduction to Intelligent Agents Using Science Fiction  3 
CSE 347  Analysis of Algorithms  3 
CSE 359A  Signals, Data and Equity (Cannot be doublecounted in EPR)  3 
CSE 411A  AI and Society (Cannot be doublecounted in EPR)  3 
CSE 412A  Introduction to Artificial Intelligence  3 
CSE 416A  Analysis of Network Data  3 
CSE 417T  Introduction to Machine Learning (Cannot be doublecounted in CR)  3 
CSE 427S  Cloud Computing with Big Data Applications  3 
CSE 435S  Database Management Systems  3 
CSE 457A  Introduction to Visualization  3 
CSE 514A  Data Mining  3 
CSE 515T  Bayesian Methods in Machine Learning  3 
CSE 517A  Machine Learning  3 
CSE 518A  HumanintheLoop Computation  3 
CSE 534A  LargeScale Optimization for Data Science  3 
CSE 543T  Algorithms for Nonlinear Optimization  3 
CSE 559A  Computer Vision  3 
Mathematics and Statistics
Code  Title  Units 

Math 322  Biostatistics  3 
Math 420  Experimental Design  3 
Math 434  Survival Analysis  3 
Math 4392  Advanced Linear Statistical Models  3 
Math 449  Numerical Applied Mathematics  3 
Math 450  Topics in Applied Mathematics  3 
Math 456  Topics in Financial Mathematics  3 
Math 459  Bayesian Statistics  3 
Math 460  Multivariate Statistical Analysis  3 
Math 461  Time Series Analysis  3 
Math 4601  Statistical Learning (Cannot be doublecounted in CR)  3 
Math 462  Mathematical Foundations of Big Data  3 
Math 475  Statistical Computation  3 
Math 493  Probability  3 
Math 494  Mathematical Statistics  3 
Math 495  Stochastic Processes  3 
Math 5047  Geometry/Topology III: Differential Geometry  3 
Math 5061  Theory of Statistics I  3 
Math 5062  Theory of Statistics II  3 
Math 5071  Linear Statistical Models Grad  3 
Math 5072  Advanced Linear Models II  3 
Electrical and Systems Engineering
Code  Title  Units 

ESE 4031  Optimization for Engineered Planning, Decisions and Operations  3 
ESE 415  Optimization  3 
ESE 427  Financial Mathematics  3 
Energy, Environmental & Chemical Engineering
Code  Title  Units 

EECE 202  Computational Modeling in Energy, Environmental and Chemical Engineering  3 
Linguistics
Code  Title  Units 

Ling 317  Introduction to Computational Linguistics  3 
Ethics and Professional Responsibility Requirement (EPR)
 3 units of courses from the following list:
List of EPR Course Options
Code  Title  Units 

Engr 4501  Engineering Ethics and Sustainability  1 
Engr 4502  Engineering Leadership and Team Building  1 
Engr 4503  Conflict Management and Negotiation  1 
Engr 450F  Engineers in the Community (Engineering Ethics, Leadership and Conflict Management)  3 
Engr 520P  Presentation Skills for Scientists and Engineers  2 
CSE 359A  Signals, Data and Equity (Cannot be doublecounted as an Elective)  3 
CSE 411A  AI and Society (Cannot be doublecounted as an Elective)  3 
MSB 512  Ethics in Biostatistics and Data Science  2 
Practicum Requirement
 3 units of an approved comprehensive data science project or experience. A practicum must be approved by the committee of data science faculty.
 The practicum experience should be completed during the nexttolast semester of study (i.e., the first semester of senior year). It is important that practicum plans be submitted for review prior to starting the project or course work to ensure the proposed work is sufficient for the objectives of the practicum. Afterthefact approvals are possible but not guaranteed.
 Appropriate practicum work is possible via Independent Study (CSE 400E or Math 400) or via projectfocused classes, including (but not limited to) CSE 437S Software Engineering Workshop and CSE 454A Software Engineering for External Clients. Students should contact course instructors in advance to identify the degree of agency the student will have over project selection and requirements.
 Contact the CSE undergraduate coordinator in the CSE department office or the Math department office to initiate the approval process.
Notes to All Majors in Mathematics and Statistics
 Upperlevel mathematics courses have course numbers that begin with a "3" or higher (e.g., Math 3200 Elementary to Intermediate Statistics and Data Analysis). Lowerlevel courses do not count toward upperlevel mathematics requirements, even if they are crosslisted as an upperlevel course in another department or program. For example, if Math 2200 Elementary Probability and Statistics was crosslisted by another department as 3XXX, registering for that 3XXX course would not satisfy an upperlevel mathematics requirement.
 Certain approved substitutions are found on the Department of Mathematics and Statistics webpage. However, in all cases, at most, only one substitution can be used that involves a course not homebased in the department.
Additional Information
Additional Requirements
 All mathematics majors must take Math 131 Calculus I, Math 132 Calculus II, and Math 233 Calculus III. There are other ways to fulfill this requirement, including AP credit and Math 203 Honors Mathematics IMath 204 Honors Mathematics II. Some students may obtain a waiver if they took similar courses before coming to Washington University.
 Math 318 Introduction to Calculus of Several Variables and Math 308 Mathematics for the Physical Sciences cannot both be used to fulfill major requirements.
 All required courses (both lower and upperlevel courses) must be completed with a letter grade of C or better.
 Courses transferred from other accredited colleges and universities can be counted, with the following caveats, if they receive department approval:
 Courses transferred from a twoyear college (e.g., a community college) cannot be used to satisfy upperlevel requirements.
 At least half of the upperlevel units required in a mathematics major or minor program must be fulfilled by Department of Mathematics and Statistics courses taken at Washington University or in Washington Universityapproved overseas study programs.
 Courses from the School of Continuing & Professional Studies cannot be used to fulfill major requirements.
 No upperlevel course used to satisfy a major requirement can be counted toward the requirements of any other major or minor (i.e., no doublecounting of courses).
 At most, 3 units of independent study or research work can count toward the major requirements.
 At most, 3 units from a different department at Washington University can count toward the major requirements.
 A student cannot declare more than one major or minor in the department. This restriction includes joint majors such as Mathematics and Economics, Mathematics and Computer Science, and Data Science. These majors are considered "in the department" even if they are declared in another department.
Course Substitutions
At most, one approved substitution can be made using a course not homebased in the Department of Mathematics and Statistics. Please note the policy that, at most, one course from a different department at Washington University can count toward a major or minor.
 ESE 326 can be taken in place of Math 3200. ESE 326 Probability and Statistics for Engineering and Math 3200 Elementary to Intermediate Statistics and Data Analysis cannot both count toward a major or minor.
 Any course from another department that is crosslisted as a mathematics L24 course can count as an upperlevel elective. Examples include Math 501C Theoretical Physics, L24 440C, and L24 403C. Such L24 courses always end with a "C."
 The following courses can count as upperlevel mathematics electives:
Courses in Probability and Statistics
The major and minor in statistics require electives in probability and statistics. Below is the list of these allowed courses:
 Math 3200 Elementary to Intermediate Statistics and Data Analysis*
 Math 3211 Statistics for Data Science I*
 Math 322 Biostatistics
 Math 420 Experimental Design
 Math 434 Survival Analysis
 Math 439 Linear Statistical Models
 Math 4392 Advanced Linear Statistical Models
 Math 459 Bayesian Statistics
 Math 460 Multivariate Statistical Analysis
 Math 461 Time Series Analysis
 Math 462 Mathematical Foundations of Big Data
 Math 475 Statistical Computation
 Math 493 Probability
 Math 494 Mathematical Statistics
 Math 495 Stochastic Processes
 Math 496 Topics in Statistics: Topics In Statistics
Distinctions in Mathematical Sciences, Mathematics, Applied Mathematics and Statistics
Distinction
 Complete at least 33 units of upperlevel mathematics and/or statistics courses.
 The GPA for these 33 upperlevel units must be at least 3.7. If more than 33 units are taken for a letter grade, the courses with the lowest grades can be omitted when computing the GPA for this purpose.
 Complete at least five courses, each with a B or better, at level 400+.
 All of these courses must be classroom courses (not independent study or study for honors), and they must all be taken for a letter grade.
High Distinction
 Complete all requirements for Distinction.
 Complete an honors thesis.
Highest Distinction
 Complete all requirements for High Distinction.
 Complete at least five courses, each with a grade of B+ or better, at the 400 level or higher. These courses can be the same five courses used for the Distinction requirement, but the grades must be B+ or better.
 Complete one of the two paths described below:
 Graduate Qualifier Path: Graduate qualifier courses in mathematics and statistics are twosemester sequences that start in the fall. In mathematics, a twosemester graduate qualifier sequence has a qualifier exam at the end of each semester. In statistics, a twosemester sequence has a qualifier exam only at the end of the sequence in spring.
Students must complete and pass one of the following:
 Two semesters of qualifier courses* and their corresponding exams in mathematics (These courses can involve a single yearlong sequence or be the first semesters of two different sequences.)
 One fullyear qualifier course sequence* and its corresponding exam in statistics
 Course Work Path:
 Graduate Qualifier Path: Graduate qualifier courses in mathematics and statistics are twosemester sequences that start in the fall. In mathematics, a twosemester graduate qualifier sequence has a qualifier exam at the end of each semester. In statistics, a twosemester sequence has a qualifier exam only at the end of the sequence in spring.
 Complete at least 42 units of upperlevel mathematics and/or statistics courses. The GPA for these 42 upperlevel units must be at least 3.7. If more than 42 units are taken for a letter grade, the courses with the lowest grades can be omitted when computing the GPA for this purpose.
 Complete at least nine total courses at the 400 level or above, all with a B+ or better. These courses can include the five courses taken for distinction. All of these courses must be classroom courses (not independent study or study for honors), and they must all be taken for a letter grade.
 *
These qualifier courses can count toward the additional course requirements for Distinction.
Distinctions in Mathematics and Computer Science
Distinction
 For Distinction in Mathematics and Computer Science, a student must take an additional two electives for a total of 10 electives.
 The student's GPA in the 10 electives must be at least 3.7. If the student takes additional courses that satisfy these requirements, the courses with the lowest grades may be omitted when calculating the GPA for this purpose.
 The student must complete at least four courses from the list of approved courses, each with a grade of B or better. These courses can be in either department (i.e., Mathematics and Statistics or Computer Science & Engineering). The list of courses will be maintained by both departments. Current approved courses include the following:

Course List Code Title Units Math 4111 Introduction to Analysis 3 Math 4121 Introduction to Lebesgue Integration 3 Math 4171 Topology I 3 Math 4181 Topology II 3 Math 429 Linear Algebra 3 Math 4351 Number Theory and Cryptography 3 Math 439 Linear Statistical Models 3 Math 4392 Advanced Linear Statistical Models 3 Math 449 Numerical Applied Mathematics 3 Math 450 Topics in Applied Mathematics 3 Math 456 Topics in Financial Mathematics 3 Math 459 Bayesian Statistics 3 Math 461 Time Series Analysis 3 Math 470 Topics in Graph Theory 3 Math 475 Statistical Computation 3 Math 494 Mathematical Statistics 3 CSE 411A AI and Society 3 CSE 416A Analysis of Network Data 3 CSE 417T Introduction to Machine Learning 3 CSE 427S Cloud Computing with Big Data Applications 3 CSE 442T Introduction to Cryptography 3 CSE 447T Introduction to Formal Languages and Automata 3 CSE 468T Introduction to Quantum Computing 3 CSE 513T Theory of Artificial Intelligence and Machine Learning 3 CSE 514A Data Mining 3 CSE 515T Bayesian Methods in Machine Learning 3 CSE 516A MultiAgent Systems 3 CSE 517A Machine Learning 3 CSE 518A HumanintheLoop Computation 3 CSE 541T Advanced Algorithms 3 CSE 543T Algorithms for Nonlinear Optimization 3 CSE 544T Special Topics in Computer Science Theory 3 CSE 546T Computational Geometry 3 CSE 554A Geometric Computing for Biomedicine 3 CSE 581T Approximation Algorithms 3 CSE 587A Algorithms for Computational Biology 3  All of the above courses must be classroom courses (not independent study).

High Distinction
 Complete all requirements for Distinction.
 Complete an honors thesis in either department (Mathematics and Statistics or Computer Science & Engineering).
Highest Distinction
 Complete the requirements for High Distinction.
 Complete one of the two options described below:
 Qual Option: Complete two semesters of graduate course work and qualifier exams in the Department of Mathematics and Statistics as described above for Highest Distinction for mathematics and statistics majors.
 Course Option: Complete three additional electives for a total of 13 courses. As with Distinction, the student's GPA in the 13 electives must be at least 3.7, and additional courses beyond 13 can be disregarded when calculating the GPA. The 13 electives must include at least eight courses selected from the list under Distinction, with the student earning a grade of B+ or better in each course. At least two of these eight courses must be from each department (Mathematics and Statistics and Computer Science & Engineering).
Latin Honors
At the time of graduation, the Department of Mathematics and Statistics will recommend that a candidate receive Latin Honors (cum laude, magna cum laude, or summa cum laude) if that student has completed the department's requirements for High Distinction or Highest Distinction in Mathematics, including an Honors Thesis. The actual award of Latin Honors is managed by the College of Arts & Sciences.
The Honors Thesis
Arts & Sciences mathematics and statistics majors who want to be candidates for Latin Honors, High Distinction, or Highest Distinction must complete an honors thesis. Writing an honors thesis involves a considerable amount of independent work, reading, creating mathematics, writing a paper that meets acceptable professional standards, and making an oral presentation of the results.
Types of Projects
An honors thesis can take three forms:
 A thesis that presents significant work by the student on one or more nontrivial mathematics problems.
 A project in mathematical or applied statistics that involves an indepth analysis of a large data set. To do an honors thesis involving data analysis, it is usually necessary to have completed Math 3200, Math 493 and Math 494 by the end of the junior year and to have the ability to work with statistical software such as SAS, R, or Python.
 A substantial expository paper that follows independent study on an advanced topic under the guidance of a department faculty member. Such a report would involve the careful presentation of ideas and the synthesis of materials from several sources.
Process and Suggested Timeline
Junior Year, Spring Semester:
 Talk with a faculty advisor about possible projects.
 Complete the Honors Proposal Form and submit it to Blake Thornton.
Senior Year:
 By the end of January, provide the advisor with a draft abstract and outline of the paper.
 By the end of February, submit a rough draft, including an abstract, to the advisor.
 The student and the advisor should agree on a date that the writing will be complete and on a date and time for the oral presentation in midMarch (the deadline is March 31).
Departmental Prizes
Each year, the department considers graduating majors for three departmental prizes and also awards a prize to a junior. Recipients are recognized at an annual awards ceremony in April where graduating majors each receive a certificate and a set of honors cords to be worn as part of the academic dress at Commencement. Awards are noted on the student's permanent university record.
Ross Middlemiss Prize
The Ross Middlemiss Prize is awarded to a graduating math major with an outstanding record. The award was established by former Professor Ross Middlemiss, who taught at Washington University for 40 years. From 1936 through the 1960s, Middlemiss authored several books, including a widely popular calculus text that was used in courses offered by the School of Continuing & Professional Studies until the late 1970s.
Putnam Exam Prize
The Putnam Exam Prize is awarded to a graduating senior who has participated regularly in the Putnam Exam Competition and done exceptionally well throughout their time at Washington University.
Martin Silverstein Award
The Martin Silverstein Award was established in memory of Professor Martin Silverstein, who, until his death in 2004, was a pioneer in work at the interface of probability theory and harmonic analysis. Each year, the department considers students in any major track, but especially those with strengths in probability or statistics, for this award.
Brian Blank Award
The Brian Blank Award was established in memory of Professor Brian Blank, who passed away in 2018. Each year, the Department of Mathematics and Statistics selects distinguished junior(s) majoring in mathematics and statistics for this prize.
 Math 318 Introduction to Calculus of Several VariablesandMath 308 Mathematics for the Physical Sciencescannot both be used to fulfill major requirements.
 Courses transferred from other accredited colleges and universities can be counted, with the following caveats, if they receive department approval:
 Courses transferred from a twoyear college (e.g., a community college) cannot be used to satisfy upperlevel requirements.
 At least half of the upperlevel units required in a major must be earned at Washington University or in a Washington Universityapproved overseas study program.
 Courses from the School of Continuing & Professional Studies cannot be used to fulfill major requirements.
The Minor in Mathematics
Units required: 27
Required courses:
Code  Title  Units 

CSE 131  Introduction to Computer Science  3 
Math 131  Calculus I  3 
Math 132  Calculus II  3 
Math 233  Calculus III  3 
Math 309  Matrix Algebra  3 
or Math 429  Linear Algebra  
Math 310  Foundations for Higher Mathematics (or any 400level course with Math 310 or Math 310W as a prerequisite)  3 
or Math 310W  Foundations for Higher Mathematics with Writing  
Three additional upperlevel electives (any 300 or 400level course in the Department of Mathematics & Statistics)  9  
Total Units  27 
The Minor in Statistics
Units required: 27
Required courses:
Code  Title  Units 

CSE 131  Introduction to Computer Science  3 
Math 131  Calculus I  3 
Math 132  Calculus II  3 
Math 233  Calculus III  3 
Math 309  Matrix Algebra  3 
or Math 429  Linear Algebra  
Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
or Math 494  Mathematical Statistics  
Three upperlevel statistics electives chosen from the list below  9  
Total Units  27 
Statistics electives:
Code  Title  Units 

Math 3200  Elementary to Intermediate Statistics and Data Analysis  3 
Math 322  Biostatistics  3 
Math 420  Experimental Design  3 
Math 434  Survival Analysis  3 
Math 439  Linear Statistical Models  3 
Math 4392  Advanced Linear Statistical Models  3 
Math 459  Bayesian Statistics  3 
Math 460  Multivariate Statistical Analysis  3 
Math 461  Time Series Analysis  3 
Math 462  Mathematical Foundations of Big Data  3 
Math 475  Statistical Computation  3 
Math 493  Probability  3 
Math 494  Mathematical Statistics  3 
Math 495  Stochastic Processes  3 
Math 496  Topics in Statistics  3 
Additional Information
 All required courses (both lower and upperlevel courses) must be completed with a letter grade of C or better.
 Math 318 Introduction to Calculus of Several Variables and Math 308 Mathematics for the Physical Sciences cannot both be used to fulfill minor requirements.
 Courses transferred from other accredited colleges and universities can be counted with department approval and with the following caveats:
 Courses transferred from a twoyear college (e.g., a community college) cannot be used to satisfy upperlevel requirements.
 At least 6 of the upperlevel units required in a minor must be earned at Washington University or in a Washington Universityapproved overseas study program.
 Courses from the School of Continuing & Professional Studies cannot be used to fulfill minor requirements.
 No upperlevel course used to satisfy a minor requirement can be counted toward the requirements of any other major or minor (i.e., no doublecounting of courses).
 At most, one approved upperlevel course from another department may be used for the upperlevel courses for the minor. Approved substitutions can be found on the Majors tab of this Bulletin page.
Visit online course listings to view semester offerings for L24 Math.
L24 Math 100 Foundations for Calculus
A limited enrollment class for students planning to take calculus but who need additional precalculus preparation. The course aims to build both the technical skills and the conceptual understanding needed to succeed in calculus. Course emphasizes links between the graphical, numeric and algebraic viewpoints. A variety of approaches are used to present the material. Prerequisites: two years of high school algebra and a course in geometry (or the equivalent).
Credit 3 units. A&S IQ: NSM
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L24 Math 1011 Introduction to Statistics
Basic concepts of statistics. Data collection (sampling, designing experiments), data organization (tables, graphs, frequency distributions, numerical summarization of data), statistical inference (elementary probability and hypothesis testing). Prerequisite: two years of high school algebra.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 109 Mathematics and Music
An elementary introduction to the connections between mathematics and musical sound. Review of integers, ratios, prime numbers, functions, rationality, exponents, logarithms, trigonometry. Review of scales, clefs, key signatures, intervals, time signatures. Frequency and pitch. The connection between intervals and logarithms. Tuning and temperament, just intonation. Scales and modular arithmetic. The mathematics of harmony; the sound of the low prime numbers and their roles in harmony. Harmonics, partials and overtones. Numerical integration and basic Fourier analysis. The nature of complex tones. Analysis of instrument sounds. Human vowels and formants. Prerequisites: two years of high school algebra, and trigonometry.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 131 Calculus I
Derivatives of algebraic, trigonometric and transcendental functions, techniques of differentiation, Mean Value Theorem, applications of the derivative. The definite integral and Fundamental Theorem of Calculus. Areas. Simpler integration techniques. Prerequisites: highschool algebra and precalculus, including trigonometry.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 131E Calculus I Extended
Math 131E covers the same content as Math 131 but includes the additional review of precalculus concepts integrated throughout the semester. It is aimed at students whose precalculus skills are not yet fully developed. By the end of this course, students should be ready to enroll in Math 132.
Credit 4 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 132 Calculus II
Continuation of Math 131. A brief review of the definite integral and Fundamental Theorem of Calculus. Techniques of integration, applications of the integral, sequences and series, Taylor polynomials and series, and some material on differential equations. Prerequisite: Math 131 or a B or better in a oneyear high school calculus course, or permission of the department.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 139A Real Mathematical Applications: Solving Problems with Calculus I
The purpose of this course is to show how mathematics can solve realworld problems and how calculus dramatically expands the range of problems that can be tackled. Each class will be devoted to the analysis of some problems, which may include dimensional analysis, the mathematics of convoys, Fibonacci numbers, fractals, linear regression, Euclid's algorithm, Stein's algorithm, network capacities, Braess's paradox, Galton's approach to surnames, how genes spread through populations, and the SIR model of infectious diseases. The first few classes will not use differentiation. Course enrollment preference is given to firstyear students. Corequisite: Math 131.
Credit 1 unit. A&S: FYO Arch: NSM Art: NSM
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L24 Math 203 Honors Mathematics I
This is the first half of a oneyear calculus sequence for first year students with a strong interest in mathematics with an emphasis on rigor and proofs. The course begins at the beginning but assumes the students have already studied the material from a more "mechanical" view. Students who complete both semesters will have completed the material Calc III and other topics that may let them move through the upperlevel math curriculum more quickly. Sets, functions, real numbers, and methods of proof. The RiemannDarboux integral, limits and continuity, differentiation, and the fundamental theorems of calculus. Sequences and series of real numbers and of functions. Vector spaces and linear maps. Prerequisite: Score of 5 on the AP Calculus Exam, BC version, or the equivalent.
Credit 4 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 204 Honors Mathematics II
Matrices, linear systems, and determinants. Eigenvalues and eigenvectors, diagonalization, and the spectral theorem. Scalar and vector fields, differential and integral calculus of several variables, and the fundamental theorems of Green, Gauss, and Stokes. Restricted to first year students who have completed Math 203 in the fall semester. Math 204 can replace Math 233 in major/minor requirements.
Credit 4 units. A&S IQ: NSM, AN Art: NSM
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L24 Math 217 Differential Equations
Introduction to ordinary differential equations: firstorder equations, linear equations, systems of equations, series solutions, Laplace transform methods, numerical solutions. Prerequisite: Math 233 (or Math 233 concurrently).
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 220 Finite Mathematics
Topics from discrete mathematics will be explored with an emphasis on problemsolving and methods of proofs. Modules on counting; combinatorial tools; binomial coefficients and Pascal's triangle; Fibonacci numbers; combinatorial probability; integers, divisors and primes; and graphs will be covered as well as additional topics as time permits. Addressed mainly to college freshmen and sophomores; it would also be suitable to advanced high school students with an interest in mathematics. Prerequisites: A good understanding of high school mathematics.
Credit 3 units. A&S IQ: NSM, AN Art: NSM
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L24 Math 2200 Elementary Probability and Statistics
An elementary introduction to statistical concepts, reasoning and data analysis. Topics include statistical summaries and graphical presentations of data, discrete and continuous random variables, the logic of statistical inference, design of research studies, point and interval estimation, hypothesis testing, and linear regression. Students will learn a critical approach to reading statistical analyses reported in the media, and how to correctly interpret the outputs of common statistical routines for fitting models to data and testing hypotheses. A major objective of the course is to gain familiarity with basic R commands to implement common data analysis procedures. Students intending to pursue a major or minor in mathematics or wishing to take 400level or above statistics courses should instead take Math 3200. Prerequisite: Math 131.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 233 Calculus III
Multivariable calculus. Topics include differential and integral calculus of functions of two or three variables: vectors and curves in space, partial derivatives, multiple integrals, line integrals, vector calculus at least through Green's Theorem. Prerequisite: Math 132 or a score of 45 on the Advanced Placement Calculus Exam (BC version).
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 2331 Calculus III Enhanced
An enriched treatment of the topics of Math 233, designed for students with a strong background in differential and integral calculus and serious interest in mathematics. Not offered concurrently with Math 201. Students with credit for 2331 cannot also receive credit for 233 or 201. Prerequisite: score of 5 on Advanced Placement calculus BC, or permission of instructor.
Credit 4 units. A&S IQ: NSM Art: NSM
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L24 Math 302 Elementary Geometry from an Advanced Point of View
A rigorous modern treatment of Euclidean geometry and an introduction to nonEuclidean geometry. Prerequisite: Math 310 or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 308 Mathematics for the Physical Sciences
Continuation of Math 233 emphasizing topics of interest in the physical sciences. Topics in multivariable and vector calculus (div, grad, curl); line, surface integrals and connections to electromagnetism; Fourier series and integrals; boundary value problems (diffusion and wave equations); additional topics if time permits. Students may not receive credit toward a math major or minor for both Math 308 and Math 318. Prerequisite: Math 233 and 217, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM BU: SCI
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L24 Math 309 Matrix Algebra
An introductory course in linear algebra that focuses on Euclidean nspace, matrices and related computations. Topics include: systems of linear equations, row reduction, matrix operations, determinants, linear independence, dimension, rank, change of basis, diagonalization, eigenvalues, eigenvectors, orthogonality, symmetric matrices, least square approximation, quadratic forms. Introduction to abstract vector spaces. Prerequisite: Math 132.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 310 Foundations for Higher Mathematics
Introduction to the rigorous techniques used in more advanced mathematics. Topics include postpositional logic, use of quantifiers, set theory, methods of proof and disproof (counterexamples), foundations of mathematics. Use of these tools in the construction of number systems and in other areas such as elementary number theory, combinatorial arguments and elementary proofs in analysis. Prerequisite: Math 233.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 310W Foundations for Higher Mathematics with Writing
This course introduces the rigorous techniques used in more advanced mathematics. Topics include basic logic, set theory, methods of proof and counterexamples, foundations of mathematics, construction of number systems, counting methods, combinatorial arguments and elementary analysis. At least three papers will be required, with at least one revision. Prerequisite: Math 233.
Credit 3 units. A&S IQ: NSM, WI Art: NSM
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L24 Math 312 Differential Equations and Dynamical Systems
Qualitative theory of ordinary differential equations. Picard's existence and uniqueness theorem, the phase plane, PoincareBendixon theory, stationary points, attractors and repellors, graphical methods. Physical applications, including chaos, are indicated. Prerequisite: Math 217.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 318 Introduction to Calculus of Several Variables
Selected topics for functions of several variables involving some matrix algebra and presented at a level of rigor intermediate between that of Calculus III and higherlevel analysis courses. Students may not receive credit toward a mathematics major or minor for both Math 308 and 318. Prerequisites: Math 233 and Math 309.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 3200 Elementary to Intermediate Statistics and Data Analysis
An introduction to probability and statistics. Major topics include elementary probability, special distributions, experimental design, exploratory data analysis, estimation of mean and proportion, hypothesis testing and confidence, regression, and analysis of variance. Emphasis is placed on development of statistical reasoning, basic analytic skills, and critical thinking in empirical research studies. The use of the statistical software R is integrated into lectures and weekly assignments. Required for students pursuing a major or minor in mathematics or wishing to take 400level or above statistics courses. Prerequisite: Math 132. Though Math 233 is not essential, it is recommended.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 322 Biostatistics
A second course in elementary statistics with applications to life sciences and medicine. Review of basic statistics using biological and medical examples. New topics include incidence and prevalence, medical diagnosis, sensitivity and specificity, Bayes' rule, decision making, maximum likelihood, logistic regression, ROC curves and survival analysis. Prerequisites: Math 3200, or a strong performance in Math 2200 and permission of the instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 331 Algebraic Systems
Polynomials, binomial expansions, factoring, rings (integers and polynomials), unique factorization, and other topics relevant to the high school curriculum. Designed for future secondary school teachers and other students looking for a course in algebra at a less abstract level than Math 430. Prerequisite: Math 310 or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 350 Topics in Applied Mathematics
Topics change with each offering of the course. Past topics have included "Mathematics and Multimedia," "The Mathematics and Chemistry of ReactionDiffusion Systems", "Mathematical Biology," and "Simulation Analysis of Random Processes" and "Intrrduction to Monte Carlo Methods." Prerequisites will vary, but always include at least Math 233, Math 309 and basic programming skills in some language.
Credit 3 units. A&S IQ: NSM Art: NSM
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L24 Math 370 Introduction to Combinatorics
Basics of enumeration (combinations, permutations and enumeration of functions between finite sets), generating functions; the inclusionexclusion principle, partition theory and introductory graph theory. As time permits, additional topics may include Ramsey's Theorem, probabilistic methods in combinatorics and algebraic methods in combinatorics. Prerequisites: Math 132, 309 and 310, or permission of the instructor.
Credit 3 units. A&S IQ: NSM, AN Arch: NSM Art: NSM
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L24 Math 371 Graph Theory
Introduction to graph theory including the basic definitions and theorems and some more advanced topics that drive much current research in graph theory: Ramsey's Theorem, random graph theory and, if time permits, Szemeredi's regularity lemma. Graphs are studied as abstract objects; however, graph theory is also of interest to applied mathematicians because graphs are natural models for networks (social, electric). Prerequisite: Math 310 or a roughly equivalent course, or permission of instructor. Students should know what a proof is and how to produce one. Some informal understanding of probability is helpful, but students need not have taken a probability course.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 407 An Introduction to Differential Geometry
A study of properties of curves and surfaces in 3dimensional Euclidean space. The course is essentially a modern recounting of a seminal paper of Gauss. Prerequisites: Math 233, Math 309, Math 310.
Credit 3 units. A&S IQ: NSM
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L24 Math 410 Introduction to Fourier Series and Integrals
The basic theory of Fourier series and Fourier integrals including different types of convergence are introduced, along with their applications to certain differential equations. Prerequisites: Math 233, Math 309, and Math 310.
Credit 3 units. A&S IQ: NSM
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L24 Math 4111 Introduction to Analysis
The real number system and the least upperbound property; metric spaces (completeness, compactness and connectedness); continuous functions (in R^n; on compact spaces; on connected spaces); C(X) (pointwise and uniform convergence; Weierstrass approximation theorem); differentiation (mean value theorem; Taylor's theorem); the contraction mapping theorem; the inverse and implicit function theorems. Prerequisite: Math 310 or permission or instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 4121 Introduction to Lebesgue Integration
Riemann integration; measurable functions; measures; Lebesgue measure; the Lebesgue integral; integrable functions; L^p spaces; modes of convergence; decomposition of measures; product measures. Prerequisite: Math 4111 or permission of the instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 415 Partial Differential Equations
This course presents an introduction to the theory of PDEs, with applications to selected classical problems in physics and engineering. Other topics include linear and quasilinear firstorder equations, the derivation of some of the classical PDEs of physics, and standard solution techniques for boundary and initial value problems. Preliminary topics such as orthogonal functions, Fourier series, and variational methods are introduced as needed. Prerequisites: Math 217, Math 309, and Math 310, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 416 Complex Variables
Topics include analytic functions, elementary functions and their properties, line integrals, the Cauchy integral formula, power series, residues, poles, and conformal mapping and applications. Prerequisites: Math 310 plus Math 318 or Math 4111, or permission of instructor.
Credit 3 units. A&S IQ: NSM Art: NSM
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L24 Math 4171 Topology I
An introduction to the most important ideas of topology. Course includes necessary ideas from set theory, topological spaces, subspaces, products and quotients, compactness and connectedness. Some time is also devoted to the particular case of metric spaces (including topics such as separability, completeness, completions, the Baire Caregory Theorem, and equivalents of compactness in metric spaces). Prerequisite: Math 310 or permission of instructor.
Credit 3 units. A&S IQ: NSM Art: NSM
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L24 Math 4181 Topology II
A continuation of Math 4171 featuring more advanced topics in topology. The content may vary with each offering. Prerequisite: Math 4171, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 420 Experimental Design
A first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, splitplot, Latin square, and similar design. Prerequisite: CSE 131 or 200, Math 3200, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 4211 Statistics for Data Science II
This builds on the foundation from the first course (SDS I) and further develops the theory of statistical hypotheses testing. It also covers advanced computer intensive statistical methods, such as the Bootstrap, that will make extensive use of R. The emphasis of the course is to expose students to modern statistical modeling tools beyond linear models that allow for flexible and tractable interaction among response variables and covariates/feature sets. Statistical modeling and analysis of real datasets is a key component of the course. Prerequisites: Math 3211 ad Math 439 (Math 439 can be taken concurrently).
Credit 3 units. A&S IQ: NSM, AN
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L24 Math 429 Linear Algebra
This course is an introduction to the linear algebra of finitedimensional vector spaces. It includes systems of equations, matrices, determinants, inner product spaces, and spectral theory. Prerequisite: Math 310 or permission of instructor. Math 309 is not an explicit prerequisite, but students should already be familiar with such basic topics from matrix theory as matrix operations, linear systems, row reduction, and Gaussian elimination. (Material on these topics in early chapters of the text will be covered very quickly.)
Credit 3 units. A&S IQ: NSM Art: NSM
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L24 Math 430 Modern Algebra
This course introduces groups, rings, and fields as well as permutation groups, group and ring homomorphisms, field extensions, and connections with linear algebra. Prerequisites: Math 310 and Math 429, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 434 Survival Analysis
Life table analysis and testing, mortality and failure rates, KaplanMeier or productlimit estimators, hypothesis testing and estimation in the presence of random arrivals and departures, and the Cox proportional hazards model. Techniques of survival analysis are used in medical research, industrial planning and the insurance industry. Prerequisites: CSE 131 or 200, Math 309 and 3200, or permission of the instructor.
Credit 3 units. A&S IQ: NSM Art: NSM
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L24 Math 4351 Number Theory and Cryptography
The course covers many of the basics of elementary number theory, providing a base from which to approach modern algebra, algebraic number theory and analytic number theory. It also introduces one of the most important realworld applications of mathematics, namely the use of number theory and algebraic geometry in public key cryptography. Topics from number theory involve divisibility (Euclidean algorithm, primes, Fundamental Theorem of Arithmetic), congruences (modular arithmetic, Chinese Remainder Theorem, primality testing and factorization). Topics from cryptography include RSA encryption, DiffieHellman key exchange and elliptic curve cryptography. Topics about algebraic numbers may be include if time permits. Prerequisites: Math 233, 309 and 310 (or permission of instructor).
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 436 Algebraic Geometry
This course provides an introduction to affine and projective algebraic varieties, the Zariski topology, regular and rational mappings, simple and singular points, divisors and differential forms, genus, and the RiemannRoch theorem. Prerequisites: Math 310, Math 429, and Math 430, or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 439 Linear Statistical Models
Theory and practice of linear regression, analysis of variance (ANOVA) and their extensions, including testing, estimation, confidence interval procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares, etc. The theory will be approached mainly from the frequentist perspective, and use of the computer (mostly R) to analyze data will be emphasized. Prerequisite: CSE 131 or 200, Math 3200 and a course in linear algebra (such as Math 309 or 429), or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 4392 Advanced Linear Statistical Models
Review of basic linear models relevant for the course; generalized linear models including logistic and Poisson regression (heterogeneous variance structure, quasilikelihood); linear mixedeffects models (estimation of variance components, maximum likelihood estimation, restricted maximum likelihood, generalized estimating equations), generalized linear mixedeffects models for discrete data, models for longitudinal data, optional multivariate models as time permits. The computer software R will be used for examples and homework problems. Implementation in SAS will be mentioned for several specialized models. Prerequisites: Math 439 and a course in linear algebra (such as Math 309 or 429), or consent of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 444 The Mathematics of Quantum Theory
An introduction to the mathematical foundations of quantum theory aimed at advanced undergraduate/beginning graduate students in Mathematics and Engineering, although students from other disciplines are equally welcome to attend. Topics include: the mathematical postulates of quantum theory and simple physical systems, spectral theory of selfadjoint operators, rudiments of Lie groups, Lie algebras and unitary group representations, elements of quantum probability and quantum information theory. Prerequisites: Linear algebra at the level of Math 429 or equivalent, multivariate calculus at the level of Math 318, and basic probability theory at the undergraduate level such as Math 493 or instructor's permission.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 449 Numerical Applied Mathematics
Computer arithmetic, error propagation, condition number and stability; mathematical modeling, approximation and convergence; roots of functions; calculus of finite differences; implicit and explicit methods for initial value and boundary value problems; numerical integration; numerical solution of linear systems, matrix equations and eigensystems; Fourier transforms; optimization. Various software packages may be introduced and used. Prerequisites: CSE 200 or CSE 131 (or other computer background with permission of the instructor); Math 217 and Math 309.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 450 Topics in Applied Mathematics
Topic may vary with each offering of the course. Prerequisites: CSE 131 (or 200) and Math 449, or permission of the instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 456 Topics in Financial Mathematics
An introduction to the principles and methods of financial mathematics, with a focus on discretetime stochastic models. Topics include noarbitrage pricing of financial derivatives, riskneutral probability measures, the CoxRossRubenstein and BlackScholesMerton options pricing models, and implied volatility. Prerequisites: Math 233, Math 3200, Math 310 or permission of instructor.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 459 Bayesian Statistics
Introduces the Bayesian approach to statistical inference for data analysis in a variety of applications. Topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, choice of priors, computational methods such as rejection sampling, and stochastic simulation (Markov chain Monte Carlo), empirical Bayes method, handson Bayesian data analysis using appropriate software. Prerequisites: CSE 131; Math 309; Math 493 or Math 3211; and Math 3200, Math 494, or Math 4211.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 460 Multivariate Statistical Analysis
A modern course in multivariate statistics. Elements of classical multivariate analysis as needed, including multivariate normal and Wishart distributions. Clustering; principal component analysis. Model selection and evaluation; prediction error; variable selection; stepwise regression; regularized regression. Crossvalidation. Classification; linear discriminant analysis. Treebased methods. Time permitting, optional topics may include nonparametric density estimation, multivariate regression, support vector machines, and random forests. Prerequisites: CSE 131; Math 233; Math 309 or Math 429; Math 493 or Math 3211; Math 494 or Math 4211; and Math 439. Prior knowledge of R at the level introduced in Math 439 is assumed.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 461 Time Series Analysis
Time series data types; autocorrelation; stationarity and nonstationarity; autoregressive moving average models; model selection methods; bootstrap condence intervals; trend and seasonality; forecasting; nonlinear time series; filtering and smoothing; autoregressive conditional heteroscedasticity models; multivariate time series; vector autoregression; frequency domain; spectral density; statespace models; Kalman filter. Emphasis on realworld applications and data analysis using statistical software. Prerequisites: Math 493 or Math 3211; Math 3200, Math 494, or Math 4211.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 462 Mathematical Foundations of Big Data
Mathematical foundations of data science. Core topics include: probability in high dimensions; curses and blessings of dimensionality; concentration of measure; matrix concentration inequalities. Essentials of random matrix theory. Randomized numerical linear algebra. Data clustering. Depending on time and interests, additional topics will be chosen from: compressive sensing; efficient acquisition of data; sparsity; lowrank matrix recovery. Divide, conquer and combine methods. Elements of topological data analysis; point cloud; Cech complex; persistent homology. Selected aspects of highdimensional computational geometry and dimension reduction; embeddings; JohnsonLindenstrauss; sketching; random projections. Diffusion maps; manifold learning; intrinsic geometry of massive data sets. Optimization and stochastic gradient descent. Random graphs and complex networks. Combinatorial group testing. Prerequisite: multivariable calculus (Math 233), linear or matrix algebra (Math 429 or 309), and multivariablecalculusbased probability and mathematical statistics (Math 493494). Prior familiarity with analysis, topology, and geometry is strongly recommended. A willingness to learn new mathematics as needed is essential.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 475 Statistical Computation
Introduction to modern computational statistics. Pseudorandom number generators; inverse transform and rejection sampling. Monte Carlo approximation. Nonparametric bootstrap procedures for bias and variance estimation; bootstrap confidence intervals. Markov chain Monte Carlo methods; Gibbs and MetropolisHastings sampling; tuning and convergence diagnostics. Crossvalidation. Time permitting, optional topics include numerical analysis in R, density estimation, permutation tests, subsampling, and graphical models. Prior knowledge of R at the level used in Math 494 is required. Prerequisite: Math 233, 309, 493, 494 (not concurrently); acquaintance with fundamentals of programming in R.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 493 Probability
This course involves mathematical theory and the application of probability at the advanced undergraduate level; it is a calculusbased introduction to probability theory. Topics include the computational basics of probability theory, combinatorial methods, conditional probability including Bayes' theorem, random variables and distributions, expectations and moments, the classical distributions, and the central limit theorem. Prerequisite: Math 233 or permission of instructor. Math 310 is recommended but not required.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 494 Mathematical Statistics
This course introduces the theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student's tdistribution and Fdistribution from a more advanced viewpoint, hypothesis testing, the NeymannPearson Lemma (about best possible tests), linear models, and other topics as time permits. Prerequisites: CSE 131 or CSE 200, Math 3200 and Math 493, or permission of instructor. Math 310 is recommended but not required.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 495 Stochastic Processes
The content of this course varies with each offering of the course. Past offerings have included such topics as random walks, Markov chains, Gaussian processes, empirical processes, Markov jump processes, and a short introduction to martingales, Brownian motion, and stochastic integrals. Prerequisites: Math 233 and Math 493, or permission of instructor. Math 310 is recommended but not required.
Credit 3 units. A&S IQ: NSM Arch: NSM Art: NSM
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L24 Math 496 Topics in Statistics
Topic varies with each offering.
Credit 3 units. A&S IQ: NSM Art: NSM
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