Courses - NMU Bulletin

MA 354 Topics in Teaching Middle School Mathematics 3 cr.

• Offered: Winter
• Prerequisites: Admission to the methods phase of teacher education, junior standing, and a "C" or better in MA 331.

The study of content and current methods in teaching middle school mathematics.

Notes: May not be applied toward a non-teaching major or minor in mathematics. Cross-listed with ED 354 Topics in Teaching Middle School Mathematics.

MA 361 Differential Equations 3 cr.

• Offered: Winter
• Prerequisites: MA 265 or instructor permission.

First-order equations, theory of second-order linear equations, higher-order linear equations and systems, series solutions, Laplace transform and applications, and stability.

MA 363 Analysis I 3 cr.

• Offered: On demand
• Prerequisites: MA 211 and MA 265.

Sets and functions, topological ideas, and sequences. Continuity and uniform continuity. Properties of continuous functions and mean value theorems. Integration theory in one and two variables. Evaluation of double and improper integrals.

MA 366 General Topology 3 cr.

• Offered: On demand
• Prerequisites: MA 211 and MA 265.

Introduction to concepts such as topological space, connectedness, compactness and homeomorphism.

MA 370 Interest Theory 3 cr.

• Offered: Contact department
• Prerequisites: MA 161.

The goal of the course is to provide an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The student will also be given an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics.

MA 370 covers all topics on the current SOA Exam FM / CAS Exam 2 syllabus. 

MA 371 Probability 3 cr.  (3-0-0)

• Offered: Fall Winter
• Prerequisites: MA 163 or instructor permission.

A general introduction to the mathematics underlying statistics, including the standard discrete and continuous parametric distributions, moment generating functions, and multivariable distributions.

Notes: Formerly Applied Probability and Statistics

MA 380 Linear Programming 3 cr.

• Offered: Winter semester of odd-numbered years
• Prerequisites: MA 211.

Introduction to the fundamental principles and techniques of linear programming with strong emphasis on mathematical modeling, analysis and application to non-trivial problems arising in various areas of the physical, social and decision sciences.

MA 412 Abstract Algebra II 3 cr.

• Offered: On demand
• Prerequisites: MA 312, junior standing or instructor's permission.

Topics selected from the following: groups, subgroups, homomorphisms, the isomorphism theorems, sylow theorems, rings, ideals, quotient rings, Euclidean rings, integral domains, factorization of ring elements, extension fields, splitting fields and Galois theory.

MA 430 Introduction to Optimization 3 cr.

• Offered: Contact Department
• Prerequisites: MA 265 and MA 380.

The course focuses on the fundamental theory of nonlinear optimization. The topics covered in this course include elements of convex analysis, theorems of the alternative, optimality criteria, and duality theory in nonlinear programming.

MA 461 Mathematics Seminar 3 cr.  (3-0-0)

• Offered: Fall
• Prerequisites: MA 265 and MA 211, or instructor permission.

A course examining the mathematical foundations of fundamental concepts of arithmetic, algebra, geometry, number theory, and other topics from across the mathematics curriculum and the connections that unify those concepts. Emphasis is on thinking deeply about fundamental concepts while further developing students' mathematical reasoning, representation, and problem-solving abilities.

MA 463 Real Analysis 3 cr.

• Offered: Contact Department
• Prerequisites: MA 363 or instructor permission.

This course will provide a general introduction to the fundamental features of real numbers, real-valued functions, Lebesgue measure, Lebesgue integral, differentiation, and general concepts of metric and normed spaces.

MA 464 Analysis II 3 cr.

• Offered: On demand
• Prerequisites: MA 363, junior standing or instructor’s permission.

Covers selected topics from real analysis and / or complex analysis.  This course serves as a second course in analysis.

Notes: Formerly Advanced Calculus II

MA 465 Complex Variables 3 cr.

• Offered: On demand
• Prerequisites: MA 211, MA 265, junior standing or instructor’s permission.

Complex numbers, analytic functions, conformal mapping, residues and poles, analytic continuation and Riemann surfaces.

MA 467 Convex Analysis 3 cr.

• Offered: Contact Department
• Prerequisites: MA 211 and MA 265.

This is an introduction course for convex sets and functions. The main emphasis will be on the theory of subdifferential calculus and the applications to convex programming problems and duality theory in convex and nonconvex optimization. 

MA 470 Financial Economics 3 cr.

• Offered: On demand
• Prerequisites: MA 370, MA 371, and a passing score on SOA Exam FM / CAS Exam 2 or instructor permission.

MA 470 covers selected topics on the current SOA Exam MFE / CAS Exam 3F syllabus. The purpose of the course is to develop the student’s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks.

MA 471 Life Contingencies 3 cr.

• Offered: On demand
• Prerequisites: MA 370, MA 371, and a passing score on SOA Exam P / CAS Exam 1 or instructor permission.

The purpose of the course is to develop the student’s knowledge of the theoretical basis of life contingent actuarial models and the application of those models to insurance and other financial risks.

Covers selected topics on the current SOA Exam MLS / CAS Exam 3L syllabus. 

MA 473 Numerical Analysis 4 cr.

• Offered: Every other fall
• Prerequisites: MA 211 and either MA 265 or MA 361, junior standing or instructor’s permission.

Notions and definitions of numerical analysis and study of numerical methods applied to systems of linear algebraic equations, non-linear equations, polynomial equations, integration, ordinary and partial differential equations and integral equations.

MA 481 Mathematical Logic 3 cr.

• Offered: Winter 2007; every third winter thereafter
• Prerequisites: Junior standing and instructor's permission.

The propositional and predicate calculi, syntax and semantics, consistency and completeness and undecidability. Included are Goedel’s theorems, recursive function theory, model theory and applications.

MA 482 Foundations of Mathematics 3 cr.

• Offered: On demand
• Prerequisites: Junior standing and instructor’s permission.

Informal axiomatic set theory, cardinal and ordinal arithmetic, transfinite induction and issues in the philosophy of mathematics.

MA 483 Introduction to Number Theory 3 cr.  (3-0-0)

• Offered: On demand
• Prerequisites: MA 163 and MA 211 or instructor permission.

Peano’s axioms, Euclidean algorithm, congruence, quadratic reciprocity law, Gaussian integers, continued fractions, Diophantine equations and theory of equations.

MA 484 History of Mathematical Thought 3 cr.

• Offered: Winter
• Prerequisites: MA 312 or MA 331, junior standing or instructor’s permission.

A historical view of mathematics. Studies in discovery, rigorization and generalization through abstraction.

MA 485 Stochastic Models in Operations Research 3 cr.

• Offered: On demand
• Prerequisites: MA 371, MA 381, junior standing or instructor’s permission.

Survey of stochastic models in operations research with emphasis on dynamic programming, Markovian decision processes, queuing, inventory control, production planning and simulation models.

MA 490 Senior Seminar 3 cr.

• Offered: On demand
• Prerequisites: MA 312 and senior standing or instructor permission.

In this capstone course, a wide a variety of mathematical concepts and applications are studied and connections between them are explored. Students choose a senior project which explores relationships; either between different areas of mathematics or between an area of mathematics and an interesting external application. Students work closely with a faculty member on the senior project, which includes an oral presentation and a formal written submission. Senior standing or permission from the instructor is required, and this course is required for the major.

MA 491 Internship in Applied Mathematics 3-6 cr.

• Offered: On demand
• Graded: S/U
• Prerequisites: Junior status in good standing with an overall grade point average of 2.75, a GPA in the major of 3.00 and departmental approval.

Supervised practical experience in some area of applied mathematics in an industrial, business or governmental setting. Students are required to document their work experience and write a report which will be evaluated by their faculty supervisor in consultation with the employer.

MA 495 Special Topics in Mathematics 1-4 cr.

• Offered: On demand
• Prerequisites: For upper division students and majors and minors or instructor’s permission.

Topics of special interest to students and staff. Notes: May be repeated, with instructor’s permission, if topic differs.