# Combinatorics and Optimization

This degree concentration differs from the BA in Mathematics without a concentration only in the Concentration Requirements.

## Bachelor of Arts - Mathematics; Combinatorics & Optimization Concentration

### College Humanities & Sciences

**Degree Specific Credits:** 67

**Required Cumulative GPA:** 2.0

### Catalog Year: 2018-2019

**Note:** The degree specific credits are much lower for double-majors and for students completing an additional minor (in another subject): 41 credits for students completing a second major, and 46 credits for students completing a minor.

## General Education Requirements

Information regarding these requirements can be found in the General Education Section of the catalog.

## Summary

Code | Title | Hours |
---|---|---|

Mathematics Core Courses | 23 | |

Upper-Division Mathematics Requirement | 23 | |

Upper-Division Elective Courses | ||

Upper-Division Elective Computer Labs | ||

Science Requirement | 18 | |

Advanced College Writing Requirement (usually fulfilled with a course that counts towards the Upper-Division Mathematics Requirement) | ||

Foreign Language/Computer Science Requirement | 3 | |

Requirements for the Combinatorics & Optimization Concentration (usually fulfilled with courses that count towards the Upper-Division Mathematics Requirement) | ||

Combinatorics & Optimization Concentration: Core Courses | ||

Combinatorics & Optimization Concentration: Elective Courses | ||

Total Hours | 67 |

### Mathematics Core Courses

**Rule:** Take all of the following courses.

Code | Title | Hours |
---|---|---|

M 171 | Calculus I | 4 |

or M 181 | Honors Calculus I | |

M 172 | Calculus II | 4 |

or M 182 | Honors Calculus II | |

M 210 | Introduction to Mathematical Software | 3 |

M 221 | Introduction to Linear Algebra | 4 |

M 273 | Multivariable Calculus | 4 |

M 300 | Undergraduate Mathematics Seminar | 1 |

M 307 | Introduction to Abstract Mathematics | 3 |

Total Hours | 23 |

Minimum Required Grade: C-

### Upper-Division Mathematics Requirement

**Rule:** Take 23 credits in this category.

**Note:**

- Students completing a minor (in another subject) need take only 20 credits.
- Students completing a second major need take only 18 credits.

Minimum Required Grade: C-

23 Total Credits Required

#### Upper-Division Elective Courses

**Note:**

- Students completing a minor (in another subject) or a second major need take only 6 courses (totaling 18 credits or more).
- Residency Requirement: At least 4 of the courses in this category must be taken at UM-Missoula (only 3 if M 307 is taken at UM-Missoula).
- Note that STAT 451 does not count toward this requirement.

Code | Title | Hours |
---|---|---|

Take 7 courses from the following list; at least 3 of them must be at the 400 level: | ||

Mathematics Technology for Teachers | ||

Ordinary Differential Equations and Systems | ||

Discrete Mathematics | ||

Number Theory | ||

Discrete Optimization | ||

Linear Optimization | ||

Advanced Calculus I | ||

Partial Differential Equations | ||

Deterministic Models | ||

History of Mathematics | ||

Abstract Algebra I | ||

Abstract Algebra II | ||

Euclidean and NonEuclidean Geometry | ||

Numerical Analysis | ||

Statistical, Dynamical, and Computational Modeling | ||

Data Science Analytics | ||

Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms | ||

Introduction to Complex Analysis | ||

Introduction to Real Analysis | ||

Graph Theory | ||

Introduction to Probability and Statistics | ||

Probability Theory | ||

Mathematical Statistics | ||

Statistical Methods II |

Minimum Required Grade: C-

#### Upper-Division Elective Computer Labs

**Rule:** Computer labs from the following list are optional; if taken (0-2 credits), they count toward the total number of credits required for the Upper-Division Mathematics Requirement.

Code | Title | Hours |
---|---|---|

M 317 | Ordinary Differential Equations Computer Lab | 1 |

M 363 | Linear Optimization Laboratory | 1 |

M 418 | Partial Differential Equations Computer Lab | 1 |

STAT 457 | Computer Data Analysis I | 1 |

STAT 458 | Computer Data Analysis II | 1 |

Minimum Required Grade: C-

### Science Requirement

**Rule:** Take 18 credits in at most 3 areas selected from astronomy (ASTR), biology (BIO*), chemistry (CHMY), computer science (CSCI, except CSCI TR*), economics (ECNS), forestry (FORS, WILD), geosciences (GEO), management information systems (BMIS), and physics (PHSX).

**Note:**

- Students completing a minor (in another subject) or a second major are exempt from this requirement.
- Transfer courses listed on the transcript as “CSCI TR*” may include course work in other areas such as Computer Applications (CAPP) and therefore do not count towards this requirement unless a student successfully petitions the Department of Mathematical Sciences.

Minimum Required Grade: C-

18 Total Credits Required

### Advanced College Writing Requirement

**Rule:** Take 1 of the following 2 courses, or any other approved Advanced College Writing course.

Code | Title | Hours |
---|---|---|

M 429 | History of Mathematics | 3 |

or M 499 | Senior Thesis | |

Total Hours | 3 |

Minimum Required Grade: C-

### GPA Requirement

**Note:**

- A cumulative GPA of 2.0 is required for all courses used to fulfill major requirements.
- In addition, a cumulative GPA of 2.0 is required for all mathematical sciences courses used to fulfill major requirements. (Mathematical sciences courses are those with a prefix of M or STAT.)

### Foreign Language/Computer Science Requirement

**Rule:** Either complete the General Education Requirement "Group III: Modern and Classical Language" (not the symbolic systems exception), or take one course from the following list.

**Note:** Students completing a second major are exempt from this requirement.

Code | Title | Hours |
---|---|---|

Select one of the following: | 3 | |

Intro to Programming | ||

Computation in the Sciences with Calculus | ||

Fund of Computer Science I | ||

Fund of Computer Science II | ||

Total Hours | 3 |

Minimum Required Grade: C-

### Requirements for the Combinatorics & Optimization Concentration

Minimum Required Grade: C-

12-13 Total Credits Required

#### Combinatorics & Optimization Option: Core Courses

**Rule:** Take all of the following courses.

Code | Title | Hours |
---|---|---|

M 361 | Discrete Optimization | 3 |

M 362 | Linear Optimization | 3 |

M 485 | Graph Theory | 3 |

Total Hours | 9 |

Minimum Required Grade: C-