# 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*

Code | Title | Units |
---|---|---|

CSE 131 | Introduction to Computer Science | 3 |

CSE 240 | Logic and Discrete Mathematics | 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 | |

Math 309 | Matrix Algebra | 3 |

SDS 3200 | Elementary to Intermediate Statistics and Data Analysis | 3 |

or ESE 326 | Probability and Statistics for Engineering | |

or SDS 3211 | Statistics for Data Science I | |

CSE 347 | Analysis of Algorithms | 3 |

Total Units | 30 |

- *
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 III. These 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

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 | Data Science for Complex Networks | 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 457A | Introduction to Visualization | 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 | Multi-Agent Systems | 3 |

CSE 517A | Machine Learning | 3 |

CSE 518A | Human-in-the-Loop Computation | 3 |

CSE 533T | Coding and Information Theory for Data Science | 3 |

CSE 534A | Large-Scale 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

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 410 | Introduction to Fourier Series and Integrals | 3 |

Math 4111 | Introduction to Analysis | 3 |

Math 4121 | Introduction to Lebesgue Integration | 3 |

Math 4171 | Topology I | 3 |

Math 429 | Linear Algebra | 3 |

Math 430 | Modern Algebra | 3 |

Math 4351 | Number Theory and Cryptography | 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 470 | Topics in Graph Theory | 3 |

Math 493C/SDS 493 | Probability | 3 |

Math 495C/SDS 495 | Stochastic Processes | 3 |

##### Statistics and Data Science

Code | Title | Units |
---|---|---|

SDS 420 | Experimental Design | 3 |

SDS 434 | Survival Analysis | 3 |

SDS 439 | Linear Statistical Models | 3 |

SDS 459 | Bayesian Statistics | 3 |

SDS 460 | Multivariate Statistical Analysis | 3 |

SDS 4601 | Statistical Learning | 3 |

SDS 461 | Time Series Analysis | 3 |

SDS 462 | Mathematical Foundations of Big Data | 3 |

SDS 475 | Statistical Computation | 3 |

SDS 493/Math 493C | Probability | 3 |

SDS 494 | Mathematical Statistics | 3 |

SDS 495/Math 495C | 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 |

## 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 at least one of the following conditions holds:
- 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).
- 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.*

- 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.
- 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 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:

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 430 | Modern Algebra | 3 |

Math 4351 | Number Theory and Cryptography | 3 |

Math 449 | Numerical Applied Mathematics | 3 |

Math 450 | Topics in Applied Mathematics | 3 |

Math 456 | Topics in Financial Mathematics | 3 |

Math 470 | Topics in Graph Theory | 3 |

CSE 411A | AI and Society | 3 |

CSE 416A | Data Science for Complex Networks | 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 | Multi-Agent Systems | 3 |

CSE 517A | Machine Learning | 3 |

CSE 518A | Human-in-the-Loop 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 |

#### 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 |