MTH 105 - Mathematics and Deductive Reasoning
3 Credit(s)
This course is designed to explore the nature of mathematics and give the student an introduction to logic and mathematical reasoning as a means for that investigation. The content may include Aristotelian logic and deductive reasoning, mathematical arguments and proof, and the study of axiomatic systems such as Euclidean geometry. Fall and Spring, every year.

MTH 112 - Integrated Calculus I-A
3 Credit(s)
The first of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the concepts of functions, limits, continuity and differentiation, exploring them in the context of algebraic functions. Prerequisites: none. Fall, every year.

MTH 113 - Integrated Calculus I-B
3 Credit(s)
The second of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the Differential Calculus of transcendental functions, including exponential, logarithmic and trigonometric functions. The course will introduce integration including the Fundamental Theorem of Calculus. The successful completion of MTH 113 is equivalent to successful completion of Calculus I. Prerequisites: MTH 112 with a grade of C- or better. Spring, every year.

MTH 120 - Calculus I
4 Credit(s)
A comprehensive study of limits, continuity and differentiation of functions of one real variable and their applications. Introduction to integrals. Credit will not be granted for both MTH 113 and MTH 120. Prerequisites: College precalculus credit or, for students in their first two years of college, an ACT mathematics score of 27 or higher. Fall and Spring, every year.

MTH 220 - Integral Calculus
4 Credit(s)
A continuation of MTH 120. Techniques and applications of integration. Infinite sequences and series. Prerequisite: MTH 113 or 120 with a grade of C- or better. Fall and Spring, every year.

MTH 303 - Symbolic Logic
3 Credit(s)
A thorough treatment of the techniques of formal reasoning. Topics include truth-functional logic, quantification logic and construction of correct deductions. Prerequisite: MTH 105 or higher mathematics course. Spring, even-numbered years.

MTH 310 - Linear Algebra
3 Credit(s)
The theory and applications of vector spaces, matrix algebra, linear transformations and eigenvalues. Prerequisite: MTH 220. Fall and spring, every year.

MTH 320 - Multivariable Calculus
4 Credit(s)
A third-semester calculus course. Topics will include vectors and three-dimensional coordinate systems, partial differentiation and multiple integrals, vector calculus and Green's Theorem. Prerequisite: MTH 220. Fall and spring, every year.

MTH 330 - Theory of Numbers
3 Credit(s)
Properties of the integers, the Euclidean Algorithm, divisibility, diophantine equations, prime numbers, congruences and residues. Prerequisite: MTH 220. Spring, odd-numbered years.

MTH 340 - Differential Equations
3 Credit(s)
A study of the techniques and theory of solving ordinary differential equations. Topics may include series solutions, numerical methods, Fourier and Laplace transforms, linearization, stability theory, periodic orbits, and bifurcations and chaos. Prerequisite: MTH 310 or PHY 304. Fall, every year.

MTH 360 - Non-Euclidean Geometry
3 Credit(s)
A college-level approach to Euclidean and non-Euclidean geometries. The course will pursue an in-depth investigation into the following topics: Hilbert’s postulates for Euclidean geometry, the parallel postulates, neutral geometry and non-Euclidean geometry. Prerequisite: MTH 220. Fall, every year.

MTH 370 - Theory of Probability
3 Credit(s)
Introduction to the mathematical theory of probability. Discrete probability spaces, conditional probability, discrete and continuous random variables, expectations and distributions. Prerequisite: MTH 320. Spring, every year.

MTH 380 - Mathematical Modeling
3 Credit(s)
This course serves as an introduction to the formulation, analysis and interpretation of mathematical models in the study of problems in the natural, management and social sciences. Topics will include optimization, dimensional analysis, Markov chains and autonomous systems. The course will require the use of the Eaton Corporation Computer Laboratory and the software packages Minitab, Mathematica, and Matlab. Prerequisite: MTH 310. Fall, even-numbered years.

MTH 390 - History of Mathematics
3 Credit(s)
A study of the historical development of various branches of mathematics from antiquity through the end of the nineteenth century. Topics include mathematics prior to classical antiquity, mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of the calculus, and the nineteenth century evolution of algebra, geometry, and analysis. The course will emphasize primary source materials. Prerequisites: MTH 310 and 320. Spring, odd-numbered years.

MTH 391 - Sophomore Seminar
1 Credit(s)
An introduction to proof writing, oral presentations, literature research, and computer software applied to mathematics. Prerequisite: MTH 220. Spring, every year.

MTH 403 - Real Analysis
3 Credit(s)
A rigorous treatment of the calculus of one variable, including limits, continuity, sequences, differentiation and Riemann integrals. This course should be taken in the junior or senior year. Prerequisite: MTH 320, and senior standing or permission of the instructor. Spring, every year.

MTH 405 - Complex Analysis
3 Credit(s)
The theory of functions of a single complex variable. Complex numbers, elementary complex functions, differentiation and integration of complex functions, complex series and residue theory. Prerequisite: MTH 320. Fall, odd-numbered years.

MTH 406 - Numerical Analysis
3 Credit(s)
Numerical methods for approximation of roots, systems of linear equations, interpolation and curve fitting, numerical integration and differentiation and differential equations. Problems are generally approached through structured algorithms. Prerequisites: MTH 310 and 320 and CMP 101. Spring, even-numbered years.

MTH 410 - Abstract Algebra
3 Credit(s)
An introduction to the theory of algebraic structures, including the elementary properties of groups, rings and fields. This course should be taken in the junior or senior year. Prerequisite: MTH 400, and senior standing or permission of the instructor. Fall, every year.

MTH 415 - Topics in Mathematics
3 Credit(s)
Further study of upper-level mathematics in areas including algebra, analysis, geometry, and dynamical systems. Please consult the Mathematics Department for course descriptions. Prerequisite: Consult instructor. Offered as needed.

MTH 430 - Topology
3 Credit(s)
An introductory course in the fundamental concepts of general topology, including metric spaces, topological spaces, connectedness and compactness. Prerequisite: MTH 403. Fall, even-numbered years.

MTH 458 - The Teaching of Elementary Mathematics
1 Credit(s)
This course includes an introduction to and the use of K-12 Michigan Curriculum framework in mathematics and an introduction to and the use of NCTM standards in mathematics. Also included will be the study of the principles and methods involved in classroom instruction of mathematics at the elementary level including current pedagogical techniques, assessment/evaluation methods, and the use of technology and resources in the mathematics classroom. Prerequisite: admission to Teacher Education. Spring, every year.

MTH 459 - The Teaching of Secondary Mathematics
1 Credit(s)
This course includes an introduction to and the use of K-12 Michigan Curriculum framework in mathematics and an introduction to and the use of NCTM Standards in mathematics. Also included will be the study of the principles and methods involved in classroom instruction of mathematics at the secondary level including current pedagogical techniques, assessment/evaluation methods, and the use of technology and resources in the mathematics classroom. Prerequisite: admission to Teacher Education. Spring, every year.

MTH 575 - Honors Thesis
1-2 Credit(s)
Investigation of a mathematical topic, under faculty supervision, leading to the honors thesis option in mathematics or computational mathematics. Prerequisite: permission of the instructor. Offered as needed.

MTH 597 - Special Problems
1-2 Credit(s)
Investigation of special problems under faculty supervision. Prerequisite: permission of the instructor. Offered as needed.