Mathematics and Computer Science Major
Program Requirements
- Total Units Required: 51
- Grade Requirement: All required courses (both lower- and upper-level) must be taken for a letter grade and completed with a grade of C– or better.
This major, developed through a collaboration between the McKelvey School of Engineering and the College of Arts & Sciences, 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 3100 Technical Writing and 8 units of courses designated as NSM (Natural Sciences & Math) from Anthropology (ANTHRO), Biology and Biomedical Sciences (BIOL), Chemistry (CHEM), Earth, Environmental, and Planetary Sciences (EEPS), Physics (PHYSICS), or Environmental Studies (ENST).
Arts & Sciences students who declare this major must fulfill the distribution requirements and all other requirements for the Bachelor of Arts (BA) degree in addition to the specific requirements listed below.
Core Course Requirements*
| Code | Title | Units |
|---|---|---|
| CSE 1301 | Introduction to Computer Science | 3 |
| CSE 2400 | Logic and Discrete Mathematics ** | 3 |
| CSE 2407 | Data Structures and Algorithms | 3 |
| CSE 3407 | Analysis of Algorithms | 3 |
| MATH 1510 | Calculus I ** | 3 |
| MATH 1520 | Calculus II ** | 3 |
| MATH 2130 | Calculus III ** | 3 |
| MATH 3010 Foundations for Higher Mathematics ** or MATH 3015 Foundations for Higher Mathematics With Writing ** | 3 | |
| MATH 3300 | Matrix Algebra ** | 3 |
| SDS 3020 Elementary to Intermediate Statistics and Data Analysis or SDS 3030 Statistics for Data Science I or ESE 3260 Probability and Statistics for Engineering | 3 | |
| Total Units | 30 | |
- *
Each of these core courses must be passed with a C- or better.
- **
AP credit may be applied in place of MATH 1510 and/or MATH 1520. Students who complete the MATH 2801 Honors Mathematics I and MATH 2802 Honors Mathematics II sequence will be considered to have completed MATH 1510, MATH 1520, MATH 2130, and CSE 2400; these students are also recommended to bypass MATH 3010/MATH 3015 and MATH 3300, for which they may substitute any other upper-level Mathematics courses.
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 4000 or CSE 4001 Independent Study may be taken for a maximum of 3 units and must be approved by a CS+Math review committee.
- For each of the following pairs of electives, students may count one as an elective toward the major but not both:
- CSE 2107 Introduction to Data Science or BME 4400 Biomedical Data Science
- CSE 4107 Introduction to Machine Learning or ESE 4170 Introduction to Machine Learning and Pattern Classification
- CSE 4109 Introduction to AI for Health or CSE 5310 AI for Health
- MATH 4560 Topics in Financial Mathematics or ESE 4270 Financial Mathematics
List of Approved Electives
Computer Science & Engineering
| Code | Title | Units |
|---|---|---|
| CSE 2107 | Introduction to Data Science | 3 |
| CSE 3401 | Parallel and Sequential Algorithms | 3 |
| CSE 4061 | Text Mining | 3 |
| CSE 4101 | AI and Society | 3 |
| CSE 4102 | Introduction to Artificial Intelligence | 3 |
| CSE 4106 | Data Science for Complex Networks | 3 |
| CSE 4107 | Introduction to Machine Learning | 3 |
| CSE 4109 | Introduction to AI for Health | 3 |
| CSE 4207 | Cloud Computing with Big Data Applications | 3 |
| CSE 4402 | Introduction to Cryptography | 3 |
| CSE 4470 | Introduction to Formal Languages and Automata | 3 |
| CSE 4507 | Introduction to Visualization | 3 |
| CSE 4608 | Introduction to Quantum Computing | 3 |
| CSE 5100 | Deep Reinforcement Learning | 3 |
| CSE 5103 | Theory of Artificial Intelligence and Machine Learning | 3 |
| CSE 5104 | Data Mining | 3 |
| CSE 5105 | Bayesian Methods in Machine Learning | 3 |
| CSE 5106 | Multi-Agent Systems | 3 |
| CSE 5107 | Machine Learning | 3 |
| CSE 5108 | Human-in-the-Loop Computation | 3 |
| CSE 5270 | Natural Language Processing | 3 |
| CSE 5313 | Coding and Information Theory for Data Science | 3 |
| CSE 5310 | AI for Health | 3 |
| CSE 5401 | Advanced Algorithms | 3 |
| CSE 5403 | Algorithms for Nonlinear Optimization | 3 |
| CSE 5404 | Special Topics in Computer Science Theory | 3 |
| CSE 5406 | Computational Geometry | 3 |
| CSE 5504 | Geometric Computing for Biomedicine | 3 |
| CSE 5505 | Adversarial AI | 3 |
| CSE 5509 | Computer Vision | 3 |
| CSE 5519 | Advances in Computer Vision | 3 |
| CSE 5610 | Large Language Models | 3 |
| CSE 5801 | Approximation Algorithms | 3 |
| CSE 5804 | Algorithms for Biosequence Comparison | 3 |
| CSE 5807 | Algorithms for Computational Biology | 3 |
| ESE 5130 | Large-Scale Optimization for Data Science | 3 |
Mathematics
| Code | Title | Units |
|---|---|---|
| MATH 3410 | Introduction to Combinatorics | 3 |
| MATH 3420 | Graph Theory | 3 |
| MATH 3590 | Topics in Applied Mathematics | 3 |
| MATH 4101 | Introduction to Analysis | 3 |
| MATH 4102 | Introduction to Lebesgue Integration | 3 |
| MATH 4150 | Introduction to Fourier Series and Integrals | 3 |
| MATH 4201 | Topology I | 3 |
| MATH 4220 | An Introduction to Differential Geometry | 3 |
| MATH 4301 | Linear Algebra | 3 |
| MATH 4302 | Modern Algebra | 3 |
| MATH 4350 | Number Theory and Cryptography | 3 |
| MATH 4493 | Topics in Graph Theory | 3 |
| MATH 4501 | Numerical Applied Mathematics | 3 |
| MATH 4502 | Topics in Applied Mathematics | 3 |
| MATH 4560 | Topics in Financial Mathematics | 3 |
| MATH 4570 | The Mathematics of Quantum Theory | 3 |
| SDS 4010 | Probability | 3 |
| SDS 4720 | Stochastic Processes | 3 |
Statistics and Data Science
| Code | Title | Units |
|---|---|---|
| SDS 4010 | Probability * | 3 |
| SDS 4020 | Mathematical Statistics | 3 |
| SDS 4110 | Experimental Design | 3 |
| SDS 4120 | Survival Analysis | 3 |
| SDS 4130 | Linear Statistical Models | 3 |
| SDS 4140 | Advanced Linear Statistical Models | 3 |
| SDS 4155 | Time Series Analysis | 3 |
| SDS 4210 | Statistical Computation | 3 |
| SDS 4310 | Bayesian Statistics | 3 |
| SDS 4430 | Statistical Learning | 3 |
| SDS 4440 | Mathematical Foundations of Data Science | 3 |
| SDS 4720 | Stochastic Processes * | 3 |
- *
This course may be counted as a Mathematics elective.
Electrical & Systems Engineering
| Code | Title | Units |
|---|---|---|
| ESE 4031 | Optimization for Engineered Planning, Decisions and Operations | 3 |
| ESE 4150 | Optimization | 3 |
| ESE 4170 | Introduction to Machine Learning and Pattern Classification | 3 |
| ESE 4270 | Financial Mathematics | 3 |
| ESE 4290 | Basic Principles of Quantum Optics and Quantum Information | 3 |
| ESE 5130 | Large-Scale Optimization for Data Science * | 3 |
| ESE 5200 | Probability and Stochastic Processes | 3 |
- *
This course may be counted as a Computer Science & Engineering elective.
Economics
| Code | Title | Units |
|---|---|---|
| ECON 4151 | Applied Econometrics | 3 |
| ECON 4710 | Game Theory | 3 |
Linguistics
| Code | Title | Units |
|---|---|---|
| LING 3250 | Introduction to Computational Linguistics | 3 |
| LING 4250 | Computation and Learnability in Linguistic Theory | 3 |
Biomedical Engineering
| Code | Title | Units |
|---|---|---|
| BME 4400 | Biomedical Data Science | 3 |
| BME 4700 | Mathematics of Imaging Science | 3 |
| BME 5720 | Biological Neural Computation | 3 |
Physics
| Code | Title | Units |
|---|---|---|
| PHYSICS 4027 | Introduction to Computational Physics | 3 |
Additional Information
- 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.
- 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).
- At most 3 units of independent study or research work can count toward the major requirements.
- Students may count courses from the Department of Statistics and Data Science (SDS) as Mathematics courses if the student matriculated in 2023-24 or earlier and if the course was previously offered by the Department of Mathematics and Statistics, as reflected by the student’s matriculation-year Bulletin.
- At most one of the following courses can be used to fulfill major requirements: MATH 3180 Introduction to Calculus of Several Variables or MATH 3550 Mathematics for the Physical Sciences.
- Courses transferred from other accredited colleges and universities can be counted, with the following caveats, if they receive department approval:
- Courses transferred from a two-year college (e.g., a community college) cannot be used to satisfy upper-level requirements.
- 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.
- 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:
- A thesis that presents significant work by the student on one or more nontrivial mathematics problems.
- 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 mid-March (the deadline is March 31).
Departmental Prizes
Each year, the department considers graduating majors for two 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 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.
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 who have declared a major in the department to receive this award.
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:
| Code | Title | Units |
|---|---|---|
| MATH 4101 | Introduction to Analysis | 3 |
| MATH 4102 | Introduction to Lebesgue Integration | 3 |
| MATH 4201 | Topology I | 3 |
| MATH 4202 | Topology II | 3 |
| MATH 4301 | Linear Algebra | 3 |
| MATH 4302 | Modern Algebra | 3 |
| MATH 4350 | Number Theory and Cryptography | 3 |
| MATH 4493 | Topics in Graph Theory | 3 |
| MATH 4501 | Numerical Applied Mathematics | 3 |
| MATH 4502 | Topics in Applied Mathematics | 3 |
| MATH 4560 | Topics in Financial Mathematics | 3 |
| CSE 4101 | AI and Society | 3 |
| CSE 4106 | Data Science for Complex Networks | 3 |
| CSE 4107 | Introduction to Machine Learning | 3 |
| CSE 4207 | Cloud Computing with Big Data Applications | 3 |
| CSE 4402 | Introduction to Cryptography | 3 |
| CSE 4470 | Introduction to Formal Languages and Automata | 3 |
| CSE 4608 | Introduction to Quantum Computing | 3 |
| CSE 5103 | Theory of Artificial Intelligence and Machine Learning | 3 |
| CSE 5104 | Data Mining | 3 |
| CSE 5105 | Bayesian Methods in Machine Learning | 3 |
| CSE 5106 | Multi-Agent Systems | 3 |
| CSE 5107 | Machine Learning | 3 |
| CSE 5108 | Human-in-the-Loop Computation | 3 |
| CSE 5401 | Advanced Algorithms | 3 |
| CSE 5403 | Algorithms for Nonlinear Optimization | 3 |
| CSE 5404 | Special Topics in Computer Science Theory | 3 |
| CSE 5406 | Computational Geometry | 3 |
| CSE 5504 | Geometric Computing for Biomedicine | 3 |
| CSE 5801 | Approximation Algorithms | 3 |
| CSE 5807 | Algorithms for Computational Biology | 3 |
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 paths described below:
- Graduate Qualifier Path: Graduate qualifying courses* in Mathematics are two- or three-semester sequences that start in the fall, with a qualifying exam held at the end of each semester. Students must complete and pass two qualifying courses* and their corresponding qualifying exams. (These can be consecutive courses in the same sequence, or they can be courses from two different sequences.)
- Coursework Path: 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).
- *
These qualifying courses can count toward the additional course requirements for Distinction.
Contact Info
| Phone: | 314-935-6301 |
| Email: | mathadvising@wustl.edu |
| Website: | http://math.wustl.edu |