Courses
Search for courses listed in this bulletin. To find a semester course schedule (including instructors, meeting times and locations), go to mynmu.nmu.edu.
- Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
- Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
- Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in linear algebra. The instructor will cover the following topics: vector spaces and subspaces over an arbitrary field, linear transformations, similar matrices, the rank-nullity theorem, change of coordinates, linear operators, matrix conjugacy, rational and Jordan canonical form. Additionally, the instructor may focus on topics such as: rational canonical form, dual vector spaces, quotient vector spaces, inner products, bilinear forms, tensors, orthogonal and unitary operators, or the spectral theorem.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course covering a selection of topics from real analysis and complex analysis. The instructor will cover the following topics from real analysis: measurable sets and functions, the Lebesgue Integral, Fourier series, Hilbert spaces, and the Fourier transform. Then the instructor will cover the following topics from complex analysis: holomorphic functions, the Cauchy-Riemann equations, the Cauchy-Goursat theorem,Taylor and Laurent series, and the residue theorem. Additionally, the instructor may focus on topics from real and complex analysis such as: Lp spaces, analytic continuation, the Mellin transform, or the Laplace transform.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in topology. The instructor will cover the following topics: topological spaces, continuous functions, compactness, connectedness, the fundamental group, and homology. Additionally, the instructor may focus on topics such as: the classification of surfaces, cohomology, the Lefschetz fixed-point theorem, the Borsuk-Ulam theorem, or topics from knot theory.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in modern algebra. Depending on the instructor’s interest and expertise, this course will focus on one or more of the following topics central to advanced algebra: group theory, Galois theory, or representation theory.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in modern geometry. The instructor will cover the following topics: metrics (Euclidean and hyperbolic), isometries, geodesics, and curvature. Depending on the instructor’s interest and expertise, additional topics may include: manifolds, vector fields, tensors, vector bundles, and connections.
- Graded: A/F
- Prerequisites: Graduate standing
Examination of the structure and properties of sets of numbers; development of models for each of the operations and their algorithms; proportional reasoning. Intended audience K-8 teachers.
- Graded: A/F
- Prerequisites: Graduate standing
Development of mathematical approaches to solving problems using a wide range of problem solving strategies, including guess and check, consider a simpler problem, case analysis, use algebra, and others. Intended audience K-8 teachers.
- Graded: A/F
- Prerequisites: Graduate standing
Exploration of a variety of geometric concepts, including trigonometry and conic sections. Intended audience K-12 teachers.
- Graded: A/F
- Prerequisites: Graduate standing
The history and development of mathematics, and the newest technological innovations. Intended audience K-12 teachers.
- Graded: A/F
- Prerequisites: Graduate standing
Investigations of problems in various branches of mathematics, such as logic, probability, graph theory, number theory, algebra, and geometry. Intended audience K–12 teachers.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in analysis. Depending on the instructor’s interest and expertise, this course will focus on one of three topics central to advanced analysis: functional analysis, numerical analysis, or nonsmooth analysis.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is an advanced course in the foundations of mathematics. Depending on the instructor’s interest and expertise, this course will focus on one of three topics central to the foundations of mathematics: formal logic, type theory, or category theory.
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is a graduate level course in mathematical finance. The instructor will cover the following topics: forwards, swaps and options, replication, risk-neutrality, Martingales, options and derivatives pricing, continuous-time stochastic processes, Brownian motion. This course contributes to a student’s readiness for professional actuarial exams such as CAS I/SOA P (Casualty Actuarial Science Examination #1/Society of Actuaries Probability Exam) and CAS II/SOA FM (Casualty Actuarial Science Examination #2/Society of Actuaries Financial Mathematics Exam).
- Graded: A/F
- Prerequisites: Graduate student in mathematics or instructor permission.
This is a graduate level course in probability. The instructor will cover the following topics: probability spaces, probability distributions, stochastic independence, limiting operations, strong limit theorems for independent random variables, the Central Limit Theorem, martingales, continuous-time stochastic processes, Brownian motion, Bayesian methods. This course contributes to a student’s readiness for professional actuarial exams such as CAS I/SOA P (Casualty Actuarial Science Examination #1/Society of Actuaries Probability Exam) and CAS II/SOA FM (Casualty Actuarial Science Examination #2/Society of Actuaries Financial Mathematics Exam).
- Graded: S/U
- Prerequisites: Graduate student in mathematics or instructor permission.
Independent study and preparation for examinations equivalent to professional actuarial society examinations will be pursued by qualified students under the supervision of a faculty member of the Mathematics and Computer Science department. Supervisor must be selected prior to enrollment in this course.
- Graded: S/U
- Prerequisites: Graduate student in mathematics or instructor permission.
Independent research or study in mathematics is pursued by qualified students under the supervision of a faculty member of the Mathematics and Computer Science department. Supervisor and research problem must be selected prior to enrollment in this course.
This course will be used to meet the specific needs of teachers in Upper Peninsula school systems.
- Graded: S/U
- Prerequisites: MA 580 or MA 589 or instructor permission
For capstone option 2 - Project: A continuation of MA 589. At the conclusion of the course, a written project must be submitted; subject to the approval of the student’s graduate committee.
For capstone option 3 - Actuarial Project: A continuation of MA 580. At the conclusion of the course, the verified passing of two internal or external professional actuarial exams not already passed; subject to the approval of the student’s graduate committee.
The student should consult the Mathematics and Computer Science department and the College of Graduate Studies and Research for specific requirements.
- Graded: S/U
- Graded: S/U
- Prerequisites: MA 589 or instructor permission
A continuation of MA 589. At the conclusion of the course, a written thesis acceptable to the student’s graduate committee and to the College of Graduate Studies and Research must be submitted. Additionally, the student must complete an acceptable oral defense of their thesis. The student should consult the Mathematics and Computer Science department and the College of Graduate Studies and Research for specific requirements.