University of Montana Catalog 2023-2024

Mathematics B.A. - 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

General Education Requirements

Summary

Mathematics Core Courses23
Mathematics Electives23
Science Requirement18
Language/Computer Science Requirement3
Requirements for the Combinatorics & Optimization Concentration (usually fulfilled with courses that count towards the Upper-Division Mathematics Requirement)
Total Hours67

Degree Specific Credits: 67

Required Cumulative GPA: 2.0

Note on degree specific credits: 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.

Notes on the GPA requirement:

  1. A cumulative GPA of 2.0 is required for all courses used to fulfill major requirements.
  2. 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.)

Mathematics Core Courses

Complete all of the following courses:
M 171Calculus I4
or M 181 Honors Calculus I
M 172Calculus II4
or M 182 Honors Calculus II
M 210Introduction to Mathematical Software3
M 221Introduction to Linear Algebra4
M 273Multivariable Calculus4
M 300Undergraduate Mathematics Seminar1
M 307Introduction to Abstract Mathematics3
Total Hours23

Minimum Required Grade: C-

Mathematics Electives

Rule: Complete 23 credits in this category.

Notes:

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

Elective Courses

Notes:

  1. Students completing a minor in another subject or a second major need take only 6 courses.
  2. 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).
  3. Note that STAT 451 does not count toward this requirement.
  4. In addition to counting towards this requirement, M 429 (History of Mathematics) is also an advanced college writing course. Most Mathematics majors use M 429 to meet the advanced college writing general education requirement.
Complete 7 courses from the following list; at least 3 of them must be at the 400 level
M 274
Introduction to Differential Equations
M 301
Teaching Mathematics with Technology
M 325
Discrete Mathematics
M 326
Number Theory
M 361
Discrete Optimization
M 362
Linear Optimization
M 381
Advanced Calculus I
M 412
Partial Differential Equations
M 414
Deterministic Models
M 429
History of Mathematics
M 431
Abstract Algebra I
M 432
Abstract Algebra II
M 439
Euclidean and NonEuclidean Geometry
M 440
Numerical Analysis
M 445
Statistical, Dynamical, and Computational Modeling
M 461
Data Science Analytics
M 462
Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms
M 472
Introduction to Complex Analysis
M 473
Introduction to Real Analysis
M 485
Graph Theory
STAT 341
Introduction to Probability and Statistics
or STAT 342
 Probability and Simulation
STAT 421
Probability Theory
STAT 422
Mathematical Statistics
STAT 452
Statistical Methods II

Minimum Required Grade: C-

Elective Computer Labs and Independent Study Courses

Rule: Computer labs and independent study courses from the following list are optional; if taken (0-2 credits), they count toward the total number of credits required for the Mathematics Elective requirement.

M 275Differential Equations Computer Lab1
M 363Linear Optimization Laboratory1
M 392Independent Study1-9
M 418Partial Differential Equations Computer Lab1
M 492Independent Study1-9
STAT 457Computer Data Analysis I1
STAT 458Computer Data Analysis II1

Minimum Required Grade: C-

Science Requirement

Notes:

  1. Students completing a minor (in another subject) or a second major are exempt from this requirement.
  2. 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.
Complete 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).18
Total Hours18

Minimum Required Grade: C-

Language/Computer Science Requirement

Rule: Either complete the General Education Requirement Group III: Modern and Classical Language or take one course from the following list.

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

Complete one of the following courses:3
CSCI 126
Computation in the Sciences with Calculus
CSCI 150
Introduction to Computer Science
CSCI 151
Interdisciplinary Computer Science I
CSCI 152
Interdisciplinary Computer Science II
Total Hours3

Minimum Required Grade: C-

Requirements for the Combinatorics & Optimization Concentration

Rule: Complete the following subcategories.12-13 total credits required. 

Combinatorics & Optimization Concentration: Core Courses

Complete all of the following courses:
M 361Discrete Optimization3
M 362Linear Optimization3
M 485Graph Theory3
Total Hours9

Minimum Required Grade: C-

Combinatorics & Optimization Concentration: Elective Courses

Complete one of the following courses:3-4
CSCI 332
Advanced Data Structures and Algorithms
M 414
Deterministic Models
M 440
Numerical Analysis
STAT 341
Introduction to Probability and Statistics
STAT 342
Probability and Simulation
Total Hours3-4

Minimum Required Grade: C-