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Courses in Mathematics

MTH 101: Topics in Mathematics (G)

Topics selected from various areas of mathematics such as discrete mathematics, logic, number systems, geometry, probability, and graph theory. The course is designed to give the student an appreciation of mathematics as an integral part of our culture as well as applications to various other disciplines.

MTH 104: Statistical Methods (G)

An introduction to statistical methods, including descriptive statistics, sampling, estimation, hypothesis testing, correlation and regression, and the chi-square distribution. Three meetings and a computer lab per week. Students may not receive credit for both MTH 104 and MTH 144.

MTH 114: Fundamentals of Mathematics (G)

A study of fundamental mathematical principles underlying the concepts of number and shape. Topic include number systems, number theory, measurements systems, geometry, and functions with emphasis on applications and problem solving. Four meetings per week. Prerequisite: admission to elementary teacher certification program. Meets general academic requirement G.

MTH 121: Calculus I (G)

Differentiation of algebraic and trigonometric functions, application of the derivative to related rates, max-min problems, and graphing. Introduction to integration, the Fundamental Theorem of Calculus. Four meetings per week. Prerequisite: 3-1/2 years of high school mathematics and placement by exam.

MTH 122: Calculus II (G)

A continuation of MTH 121. Studies in differentiation and integration of transcendental functions, integration techniques, applications of the integral, infinite sequences and series, L'Hopital's Rule, improper integrals. Four meetings per week. Prerequisite: MTH 121 or permission of department.

MTH 144: Statistical Analysis

Fundamental problems and principles of probability, discrete and continuous distributions and random variables, sampling distributions, parameter estimation and confidence intervals, hypothesis testing, regression analysis, analysis of variance, and non-parametric statistics. Students may not receive credit for both MTH 104 and MTH 144. Three meetings and one laboratory per week. Prerequisite: MTH 121 or equivalent, or permission of the instructor.

MTH 210: Transition to Abstract Mathematics

An introduction to abstract mathematical thought, with emphasis on understanding and applying definitions, writing arguments to prove valid statements, and providing counterexamples to disprove invalid ones. Topics may include logic, introductory set theory, and elementary number theory, but the focus is on the process of reasoning rather than any particular subject or subdiscipline. It is strongly recommended that mathematics majors complete this course by the end of the sophomore year. Prerequisite: MTH 122 (Calculus II).

MTH 215: Discrete Structures

Topics from logic, combinatorics, recursion, relations, trees and graphs, and finite state automata, computability and algorithm design.

MTH 223: Calculus III

Geometry of the plane and space including vectors and surfaces. Multivariable calculus including partial derivatives, Taylor's Theorem in two variables, line and surface integrals, and Green's Theorem. Prerequisite: MTH 122.

MTH 226: Linear Algebra

Matrices and systems of linear equations, determinants, real vector spaces and inner product spaces, linear transformations, eigenvalue problems, applications. Four meetings per week. Prerequisite: MTH 122.

MTH 227: Differential Equations

A study of the theory, methods of solution, and applications of differential equations and systems of differential equations. Topics will include the Laplace transformation, some numerical methods, and applications from the physical sciences and geometry. Prerequisite: MTH 122.

MTH 251: Landmarks of Greek Mathematics (0.5 course unit)

This half-credit course examines selected masterpieces of classical mathematics, including Euclid's Elements, Archimedes' determination of the surface area of a sphere, Heron's formula for triangular area, and Ptolemy's table of chords. Emphasis will be placed on the brilliance of the mathematics and the reverberations of these ideas down to the present age. Prerequisite: one course in calculus. Offered in alternate years. Does not satisfy a major/minor requirement.

MTH 252: Landmarks of Modern Mathematics (0.5 course unit)

This half-credit course examines selected mathematical masterpieces from the Renaissance to the dawn of the twentieth century. Theorems to be considered include those of Cardano, Newton, the Bernoullis, Euler, Gauss, and Cantor. Besides the mathematics, the course focuses on the context in which the theorems were discovered and the lives of the discoverers. Prerequisite: one course in calculus. Offered in alternate years. Does not satisfy a major/minor requirement.

MTH 314: Applied Mathematics and Modeling

Models describing physical and economic conditions will be constructed, analyzed, and tested. The computer will be used in model verification. Prerequisite: MTH 227. Offered in alternate years.

MTH 318: Operations Research

Linear programming, the transportation model, dynamic programming, decision analysis, game theory, and inventory and queuing models. Prerequisite: MTH 121 or permission of instructor. Offered in alternate years.

MTH 326: Abstract Algebra

A study of the algebraic structures of groups, rings, fields, and integral domains. Prerequisites: MTH 210 and MTH 226. Offered in alternate years.

MTH 331: Mathematical Statistics I

Probability, discrete and continuous random variables, the binomial, normal, Poisson, chi-square, t, and F distribution. Prerequisite: MTH 223. Offered in alternate years.

MTH 332: Mathematical Statistics II

A continuation of MTH 331. Topics will include estimation, hypothesis testing, regression, correlation, and analysis of variance. Prerequisite: MTH 331. Offered in alternate years.

MTH 334: Numerical Analysis

The numerical solutions of equations, numerical integration and differentiation, systems of equations, curve fitting, numerical solutions of ordinary and partial differential equations. Prerequisite: MTH 226 and programming experience. Offered in alternate years.

MTH 337: Mathematical Analysis

Rigorous treatment of the real number system and functions of one variable, the Riemann integral, and the role of uniform convergence in sequences and series of functions. Prerequisites: MTH 210 and MTH 223. Offered in alternate years.

MTH 342: Advanced Geometry

An examination of the axioms and theorems of at least one type of non-Euclidean geometry, a synthetic approach to plane projective geometry, an analytic approach to plane projective geometry with specialization leading to plane Euclidean geometry. Prerequisite: MTH 226. Offered in alternate years.

MTH 345: Combinatorics and Graph Theory

This advanced course in discrete mathematics emphasizes counting and finite structures. The material is taken from three broad areas of combinatorics: counting theory, graph theory and design theory. Topics include fundamental laws of counting, generating functions, recursion, partitions, existence and optimization problems, graphs and digraphs, networks, the relationships between graphical invariants, lattices, simple game theory, Latin squares, design and coding theory, and Ramsey Theory. Prerequisite: MTH 210.

MTH 550: Special Topics

Topics chosen from: Topology, Complex Variables, Methods of Mathematical Physics, Number Theory, Differential Equations II, History of Mathematics, Problem Solving, etc. Offered on demand.