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.

MA 501 Mathematical Representation, Reasoning and Patterns 3 cr.
  • Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
Historical and philosophical foundations of mathematics and their relationships to problem solving and applications; proof, logic and mathematical reasoning; algebraic structures and functions; and mathematical representations and coding.
MA 502 Spatial Visualization, Shape and Measurement 3 cr.
  • Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
Historical and philosophical foundations of mathematics and their relationships to measurement, Euclidean and non-Euclidean geometries, analytical geometry, trigonometry, transformations, shape and dimension, and applications.
MA 503 Mathematical Modeling, Number and Data 3 cr.
  • Prerequisites: Mathematics education major or elementary education major with a concentration in mathematics
Historical and philosophical foundations of mathematics and their relationships to numerical algorithms, approximation, error analysis, data representation, distributions, counting techniques, mathematical modeling and prediction.
MA 511 Advanced Linear Algebra 4 cr.  (4-0-0)
  • 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.

MA 513 Analysis: Real and Complex 4 cr.  (4-0-0)
  • 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:​ ​L​p​ spaces, analytic continuation, the Mellin transform, or the Laplace transform.

MA 516 Topology 4 cr.  (4-0-0)
  • 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.

MA 521 Topics in Algebra 4 cr.  (4-0-0)
  • 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​.

MA 541 ​Topics in Geometry​ 4 cr.  (4-0-0)
  • 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.

MA 550 Number Systems and Number Theory 3 cr.  (3-0-0)
  • 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.

MA 552 Problem Solving Strategies 3 cr.  (3-0-0)
  • 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.

MA 563 Topics in Analysis 4 cr.  (4-0-0)
  • 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​.

MA 565 Topics in Foundations 4 cr.  (4-0-0)
  • 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​. 

MA 570 Mathematical Finance 4 cr.  (4-0-0)
  • 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).

MA 571 Probability 4 cr.  (4-0-0)
  • 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).

MA 580 Study in Actuarial Mathematics 1-4 cr.  (Arr.-0-0)
  • 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.

MA 589 Research in Mathematics 1-4 cr.  (Arr.-0-0)
  • 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.

MA 594 Project in Mathematics 1-4 cr.  (Arr.-0-0)
  • 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.

MA 599 Thesis in Mathematics 1-4 cr.  (Arr.-0-0)
  • 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.