Department of Mathematics

MTH 620. Analysis I
This course extends and enriches the ideas of elementary calculus by emphasizing the logical development of the subject. The definitions, theorems, and proofs of concepts from the real number system, limits and continuity, the differential calculus, the integral calculus, and selected topics from vector calculus and multivariable calculus are explored. This course combines the content of analysis with pedagogy appropriate to teach pre-algebra, algebra, pre-calculus and calculus to adolescents. 3 credits.

MTH 621. Analysis II
Series and sequences of functions; power series; uniform convergence and boundedness; partial differentiation; implicit function Theorems; Taylor's formula, numerical series and sequences. 3 credits.

MTH 622. Analysis III
Transformations and mappings; vector analysis; multiple integrals; line and surface in Theorem; exact differential forms. 3 credits.

MTH 650. Linear Algebra
Vector spaces; linear transformation; matrices, determinants, canonical forms; eigenvalues and eigenvectors; Hamilton-Cayley Theorem; linear functionals; bilinear forms; normed linear spaces. 3 credits.

MTH 651. Abstract Algebra
Study of structures of groups, rings, fields, polynomial forms and functions. Appropriate applications to content of high school algebra course. 3 credits.

MTH 701. Complex Function Theory
Complex numbers; point set topology; functions of a complex variable; integral Theorems; calculus of residues; infinite series and infinite products; conformal mapping; analytic continuation. 3 credits.

MTH 702. Number Theory
Analytical, algebraic and combinational methods in the additive and multiplicative theory of numbers; divisibility and factorization; Theorems of Fermat, Euler, and Wilson; primitive roots, quadratic reciprocity; sums of squares. 3 credits.

MTH 703. Topology
Topological spaces; continuous functions; induced topological structures; separation properties; connectedness; compactifications; metrizability; uniform spaces; fixed point theorems. 3 credits.

MTH 704. Discrete Mathematical Models
Combinations, logic set theory, Boolean algebra, relations and functions, graph theory, linear programming, and game theory. 3 credits.

MTH 705. Topics in Modern Geometry
An examination of modern and classical geometries especially the axiomatic development of Euclidean and hyperbolic geometry. The historical evolution of non-Euclidean geometries will be considered with an emphasis on the philosophical and pedagogical implications. This course combines the content of modern geometry with the pedagogy appropriate to teach geometrical concepts to adolescents. 3 credits.

MTH 707. Differential Equations
Fundamental existence theorems; exact equations; linear equations; series solutions of nonsingular and singular equations; systems of equations; Sturm-Liouville eigenvalue problems. 3 credits.

MTH 708. History of Mathematics
Development of mathematical concepts and methods from ancient times to the present including bases for number systems, arithmetic, geometries, algebra, trigonometry and calculus. This course offers to teachers of mathematics material that can enliven their pedagogy with the stories of the great discoveries and changes in mathematics and the people who made them. 3 credits.

MTH 709. Foundations of Mathematics
Symbolic logic; truth functions and quantifiers; axiomatization of first-order logic; deductive theories; mathematical induction; set operations; real and complex number systems. 3 credits.

MTH 710. Probability and Statistics
A course that explores discrete probability, probability distributions, data analysis, descriptive statistics, and both parametric and non-parametric statistical inference. This course combines the content of probability and statistics with the pedagogy appropriate to teaching these subjects to adolescents. 3 credits.

MTH 990. Special Topics

MTH 999. Independent Study
This course will provide an opportunity for the serious student to engage in directed research or analysis in a chosen area. The student must select an advisor from the department and submit, in writing, an outline of the proposed study prior to registration. An interim report will be followed by the submission of the final research project. Available only in the Fall or Spring semester. Admission only with the approval of the department chair. May be repeated once with the permission of the department chair. 3 credits.

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