**New Requirements! **Effective Fall 2016 the Mathematics Major has been revised. This website details the new requirements. Currently declared majors may switch to these new requirements by emailing their academic advisor or one of our Mathematics Undergraduate Advisors, or they may stick with the major requirements in place at the time of their major declaration. To review the major requirements from recent years, see the Fact Sheet for Mathematics Major Pre-Fall 2016.

The Department of Mathematical Sciences offers both the Bachelor of Science and the Bachelor of Arts degree in Mathematics. In addition to the requirements for the major, students must also satisfy all of the university general education requirements and the College of Letters & Science breadth and other degree requirements. Degree requirements will vary depending on when you took your first college class, and upon whether you are pursuing the BA or the BS. You are strongly advised to consult your advisor *every semester* to ensure you stay on track towards a degree. Read more about College of Letters and Science Degree Requirements.

To clarify any requirements, contact one of our Mathematics Undergraduate Advisors.

### Recommendations

The mathematics major has been designed to be flexible so that students could complete their major requirements via courses that match their interests and goals. Many students should find it relatively easy to complete double majors in mathematics and another subject. Most mathematics courses belong in one of the following four groups: applied mathematics, computational mathematics, pure mathematics, and statistics.

A major in mathematical sciences allows students to design, in conjunction with an advisor, a personalized program to fit individual interests and talents.

## Mathematics **Major Requirements**

**Preparatory Curriculum**

Students in all majors in the Department of Mathematical Sciences must complete MATH 231 (or MATH 213), MATH 232, and MATH 233 (or equivalent). MATH 221 and MATH 222 are equivalent to MATH 231, MATH 232, and MATH 233. Students majoring in mathematics must have an average GPA of at least 2.500 in these courses. All majors must take either MATH 234 or MATH 240, as well as a course in computer programming in a modern, high-level language (e.g., COMPSCI 151, COMPSCI 202, COMPSCI 240, COMPSCI 250, or COMPSCI 251). The department also recommends strongly one year of calculus-based physics.

#### Capstone Experience

Students in all majors and major options in the Department of Mathematical Sciences must complete a "Capstone Experience." The aim of the department's capstone experience is to encourage independent learning. Students complete a research paper in the context of this course, which satisfies the L&S research requirement. Mathematics majors may choose either MATH 599 or MATH 575. Students must obtain consent of a professor to enroll in MATH 599.

#### Requirements

The following courses are required for the Mathematics major:

Code | Title | Credits |
---|---|---|

MATH 341 | Seminar: Introduction to the Language and Practice of Mathematics | 3 |

Select 24 credits in upper-division math courses (those numbered 300 and above, and in curricular areas MATH, MTHSTAT, or ACTSCI). Required among these 24 upper-division math credits are at least six credits in math courses numbered 500 and above, excluding MATH 591, MATH 599, MATH 699, ACTSCI 490, or ACTSCI 599. | 24 | |

Total Credits | 27 |

### Additional Requirements

- Note that MATH 381 and MTHSTAT 465 and MTHSTAT 467 are not open for credit in the Mathematics major.
- Actuarial Science majors wishing to complete Math as a second major must take 9 cr of upper div Math/MthStat courses beyond the major requirements of Actuarial Science.
- Students completing an AMCS degree who wish to add Mathematics as a second major must take 9 cr of additional upper division Math/MthStat/ActSci courses beyond those used to fulifill the AMCS degree Math/MthStat/ActSci requirements.
- Students must complete at least 15 upper-division (numbered 300 and above) credits in the major in residence at UWM.
- The College requires that students attain at least a 2.0 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.0 GPA on all major credits attempted, including transfer work.

### Recommendations

Mathematics courses fall naturally into the following groups (see below for individual courses):

- Applied Mathematics
- Computational Mathematics
- Probability and Statistics
- Pure Mathematics

*For students planning to pursue graduate* studies in mathematics, we recommend students take at least 36 cr upper division mathematics courses, with as many courses as possible from Pure Mathematics, Group 1. Many PhD programs require reading knowledge of French, German, or Russian.

*For students planning to pursue graduate studies in statistics or economics*, we recommend MATH 523, MATH 524, and as many as possible of MTHSTAT 361, MTHSTAT 362, and MTHSTAT 562-MTHSTAT 568.

*For students seeking employment in statistics after the bachelor's degree,* we recommend MTHSTAT 361, MTHSTAT 362, and as many as possible of MTHSTAT 562-MTHSTAT 568, as well as courses in computer programming (COMPSCI 250, COMPSCI 251, etc.).

*For students seeking general non-academic employment after the bachelor’s* degree, we recommend courses from the Probability and Statistics group (including MTHSTAT 362), the Applied Mathematics group (including both modeling and differential equations), the Computational Mathematics group, Linear Algebra (MATH 535), and courses in computer programming (COMPSCI 240, COMPSCI 250, COMPSCI 251, etc.).

*For students intending to become high school mathematics teachers*, we recommend courses in algebra (MATH 431, MATH 531), geometry (MATH 451, MATH 453), linear algebra (MATH 535), numerical methods (MATH 413), advanced calculus (MATH 523, MATH 524), the math education capstone (MATH 575), and probability and statistics (MTHSTAT 361 & MTHSTAT 362).

*For students pursuing a major in mathematics as a liberal art,* for general logical and critical thinking skills, we recommend the Pure Mathematics courses.

### Mathematics Groups

#### Applied Mathematics

Code | Title | Credits |
---|---|---|

MATH 305 | Introduction to Mathematical and Computational Modeling | 3 |

MATH 320 | Introduction to Differential Equations | 3 |

MATH 322 | Introduction to Partial Differential Equations | 3 |

MATH 325 | Vector Analysis | 3 |

MATH 405 | Mathematical Models and Applications | 3 |

MATH 431 | Modern Algebra with Applications | 3 |

MATH 581 | Introduction to the Theory of Chaotic Dynamical Systems | 3 |

MATH 603 | Advanced Engineering Mathematics I | 3 |

MATH 604 | Advanced Engineering Mathematics II | 3 |

#### Computational Mathematics

Code | Title | Credits |
---|---|---|

MATH 313 | Linear Programming and Optimization | 3 |

MATH 315 | Mathematical Programming and Optimization | 3 |

MATH 413 | Introduction to Numerical Analysis | 3 |

MATH 415 | Introduction to Scientific Computing | 3 |

MATH 417 | Computational Linear Algebra | 3 |

MATH 610 | Numerical Solution of Partial Differential Equations | 3 |

MATH 617 | Optimization | 3 |

#### Probability and Statistics

Code | Title | Credits |
---|---|---|

MATH 583 | Introduction to Probability Models | 3 |

MTHSTAT 361 | Introduction to Mathematical Statistics I | 3 |

MTHSTAT 362 | Introduction to Mathematical Statistics II | 3 |

MTHSTAT 562 | Design of Experiments | 3 |

MTHSTAT 563 | Regression Analysis | 3 |

MTHSTAT 564 | Time Series Analysis | 3 |

MTHSTAT 565 | Nonparametric Statistics | 3 |

MTHSTAT 566 | Computational Statistics | 3 |

MTHSTAT 568 | Multivariate Statistical Analysis | 3 |

#### Pure Mathematics

Code | Title | Credits |
---|---|---|

MATH 523 | Advanced Calculus I | 3 |

MATH 524 | Advanced Calculus II | 3 |

MATH 531 | Modern Algebra | 3 |

MATH 535 | Linear Algebra | 3 |

MATH 551 | Elementary Topology | 3 |

MATH 623 | Introduction to Analysis I | 3 |

MATH 624 | Introduction to Analysis II | 3 |

MATH 635 | Modern Algebra I | 3 |

MATH 636 | Modern Algebra II | 3 |

MATH 427 | Complex Analysis | 3 |

MATH 451 | Axiomatic Geometry | 3 |

MATH 453 | Transformations in Geometry | 3 |

MATH 511 | Symbolic Logic | 3 |

MATH 537 | Number Theory | 3 |

MATH 553 | Differential Geometry | 3 |