Mathematics and Computer Science Major

Program Requirements

  • Total units required: 51

The McKelvey School of Engineering and the College of Arts & Sciences developed a 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*

CSE 131Introduction to Computer Science3
CSE 240Logic and Discrete Mathematics3
CSE 247Data Structures and Algorithms3
Math 131Calculus I (AP credit may satisfy this requirement) **3
Math 132Calculus II (AP credit may satisfy this requirement) **3
Math 233Calculus III **3
Math 310Foundations for Higher Mathematics3
or Math 310W Foundations For Higher Mathematics With Writing
Math 309Matrix Algebra3
SDS 3200Elementary to Intermediate Statistics and Data Analysis3
or ESE 326 Probability and Statistics for Engineering
or SDS 3211 Statistics for Data Science I
CSE 347Analysis of Algorithms3
Total Units30
*

Each of these core courses must be passed with a C- or better.

**

Students who complete the Math 203 Honors Mathematics I and Math 204 Honors Mathematics II sequence will be considered to have completed Math 131 Calculus I, Math 132 Calculus II, and Math 233 Calculus IIIThese students can also choose to take additional electives in place of Math 309 Matrix Algebra and Math 310 Foundations for Higher Mathematics.

Electives

Seven upper-level 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 courses must be taken from Math.
  • At most one preapproved course 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.
  • Students may count either Math 456 or ESE 427 as an elective toward the major, but not both. Likewise, students may count either CSE 417T or ESE 417 as an elective toward the major, but not both.

List of Approved Electives

Computer Science & Engineering
CSE 217AIntroduction to Data Science3
CSE 341TParallel and Sequential Algorithms3
CSE 411AAI and Society3
CSE 412AIntroduction to Artificial Intelligence3
CSE 416AData Science for Complex Networks3
CSE 417TIntroduction to Machine Learning3
CSE 427SCloud Computing with Big Data Applications3
CSE 442TIntroduction to Cryptography3
CSE 447TIntroduction to Formal Languages and Automata3
CSE 457AIntroduction to Visualization3
CSE 468TIntroduction to Quantum Computing3
CSE 513TTheory of Artificial Intelligence and Machine Learning3
CSE 514AData Mining3
CSE 515TBayesian Methods in Machine Learning3
CSE 516AMulti-Agent Systems3
CSE 517AMachine Learning3
CSE 518AHuman-in-the-Loop Computation3
CSE 533TCoding and Information Theory for Data Science3
CSE 534ALarge-Scale Optimization for Data Science3
CSE 541TAdvanced Algorithms3
CSE 543TAlgorithms for Nonlinear Optimization3
CSE 544TSpecial Topics in Computer Science Theory3
CSE 546TComputational Geometry3
CSE 554AGeometric Computing for Biomedicine3
CSE 555TAdversarial AI3
CSE 559AComputer Vision3
CSE 581TApproximation Algorithms3
CSE 584AAlgorithms for Biosequence Comparison3
CSE 587AAlgorithms for Computational Biology3
Mathematics
Math 350Topics in Applied Mathematics3
Math 370Introduction to Combinatorics3
Math 371Graph Theory3
Math 407An Introduction to Differential Geometry3
Math 410Introduction to Fourier Series and Integrals3
Math 4111Introduction to Analysis3
Math 4121Introduction to Lebesgue Integration3
Math 4171Topology I3
Math 429Linear Algebra3
Math 430Modern Algebra3
Math 4351Number Theory and Cryptography3
Math 444The Mathematics of Quantum Theory3
Math 449Numerical Applied Mathematics3
Math 450Topics in Applied Mathematics3
Math 456Topics in Financial Mathematics3
Math 470Topics in Graph Theory3
Math 493C/SDS 493Probability3
Math 495C/SDS 495Stochastic Processes3
Statistics and Data Science
SDS 420Experimental Design3
SDS 434Survival Analysis3
SDS 439Linear Statistical Models3
SDS 459Bayesian Statistics3
SDS 460Multivariate Statistical Analysis3
SDS 4601 Statistical Learning3
SDS 461Time Series Analysis3
SDS 462Mathematical Foundations of Big Data3
SDS 475Statistical Computation3
SDS 493/Math 493CProbability3
SDS 494Mathematical Statistics3
SDS 495/Math 495CStochastic Processes3
Electrical & Systems Engineering
ESE 4031Optimization for Engineered Planning, Decisions and Operations3
ESE 415Optimization3
ESE 417Introduction to Machine Learning and Pattern Classification3
ESE 427Financial Mathematics3
ESE 429Basic Principles of Quantum Optics and Quantum Information3
ESE 520Probability and Stochastic Processes3
Economics
Econ 4151Applied Econometrics3
Econ 467Game Theory3
Linguistics
Ling 317Introduction to Computational Linguistics3
Ling 427Computation and Learnability in Linguistic Theory3
Biology and Biomedical Sciences
Biol 5657Biological Neural Computation3
Biomedical Engineering
BME 470Mathematics of Imaging Science3

Additional Information

  1. A student cannot declare more than one major or minor in the Department of Mathematics. This restriction includes dual majors, such as Mathematics and Economics and Mathematics and Computer Science. These majors are considered "in the department" even if they are declared in another department.
  2. No upper-level course used to satisfy a major requirement can be counted toward the requirements of any other major or minor (i.e., no double-counting of courses).
  3. At most 3 units of independent study or research work can count toward the major requirements.
  4. Students may count courses from the Department of Statistics and Data Science (SDS) as Mathematics courses if at least one of the following conditions holds:
    1. The course is cross-listed in the Department of Mathematics (e.g., Math 493C and Math 495C are cross-listed versions of SDS 493 and SDS 495).
    2. The student matriculated in 2023-2024 or earlier, and the course was previously offered by the Department of Mathematics and Statistics, as reflected by the student’s matriculation-year Bulletin.
  5. At most one of the following courses can be used to fulfill major requirements: Math 308 Mathematics for the Physical Sciences or Math 318 Introduction to Calculus of Several Variables.
  6. Courses transferred from other accredited colleges and universities can be counted, with the following caveats, if they receive department approval:
    1. Courses transferred from a two-year college (e.g., a community college) cannot be used to satisfy upper-level requirements.
    2. At least half of the upper-level units required in a major must be earned at Washington University or in a Washington University-approved overseas study program.
    3. Courses from the School of Continuing & Professional Studies cannot be used to fulfill major requirements.

Latin Honors

At the time of graduation, the Department of Mathematics 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 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 two forms: 

  1. A thesis that presents significant work by the student on one or more nontrivial mathematics problems.
  2. 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:

  1. Talk with a faculty advisor about possible projects.
  2. Complete the Honors Proposal Form and submit it to Blake Thornton.

Senior Year: 

  1. By the end of January, provide the advisor with a draft abstract and outline of the paper.
  2. By the end of February, submit a rough draft, including an abstract, to the advisor.
  3. 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 mid-March (the deadline is March 31).

Departmental Prizes

Each year, the department considers graduating majors for three departmental prizes and also awards a prize to juniors. 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. 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. Graduating students completing any major we offer will be considered for this award, but preference is given to those who have done excellent work in applied mathematics or analysis.

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 selects distinguished juniors majoring in mathematics for this prize.

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 nine electives.
  • The student's GPA in the nine 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 or Computer Science & Engineering) and must be classroom courses, not independent study. The list of courses will be maintained by both departments. Current approved courses include the following:
Math 4111Introduction to Analysis3
Math 4121Introduction to Lebesgue Integration3
Math 4171Topology I3
Math 4181Topology II3
Math 429Linear Algebra3
Math 430Modern Algebra3
Math 4351Number Theory and Cryptography3
Math 449Numerical Applied Mathematics3
Math 450Topics in Applied Mathematics3
Math 456Topics in Financial Mathematics3
Math 470Topics in Graph Theory3
CSE 411AAI and Society3
CSE 416AData Science for Complex Networks3
CSE 417TIntroduction to Machine Learning3
CSE 427SCloud Computing with Big Data Applications3
CSE 442TIntroduction to Cryptography3
CSE 447TIntroduction to Formal Languages and Automata3
CSE 468TIntroduction to Quantum Computing3
CSE 513TTheory of Artificial Intelligence and Machine Learning3
CSE 514AData Mining3
CSE 515TBayesian Methods in Machine Learning3
CSE 516AMulti-Agent Systems3
CSE 517AMachine Learning3
CSE 518AHuman-in-the-Loop Computation3
CSE 541TAdvanced Algorithms3
CSE 543TAlgorithms for Nonlinear Optimization3
CSE 544TSpecial Topics in Computer Science Theory3
CSE 546TComputational Geometry3
CSE 554AGeometric Computing for Biomedicine3
CSE 581TApproximation Algorithms3
CSE 587AAlgorithms for Computational Biology3

High Distinction

  • Complete all requirements for Distinction.
  • Complete an honors thesis in either department (Mathematics or Computer Science & Engineering).

Highest Distinction

  • Complete the requirements for High Distinction.
  • Complete one of the two options described below: 
    • Qualifier Option: Complete two semesters of graduate course work and qualifier exams in the Department of Mathematics as described above for Highest Distinction for mathematics majors.
    • Course Option: Complete three additional electives for a total of 12 courses. As with Distinction, the student's GPA in the 12 electives must be at least 3.7, and additional courses beyond 12 can be disregarded when calculating the GPA. The 12 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 Computer Science & Engineering).

Contact Info

Phone:314-935-6301
Email:mathadvising@wustl.edu
Website:http://math.wustl.edu