Choose twelve courses from the following list:
Certain modifications may be made in consultation with and subject to the approval of the Program Director.
TEACHING AND LEARNING SECONDARY SCHOOL MATHEMATICS
Theories, methods, materials and techniques for teaching and learning mathematics in secondary and upper elementary schools. This course is required for students seeking secondary math certification.
CALCULUS FOR MATHEMATICS TEACHERS I
A review of topics from precalculus using algebraic, numerical, and graphical perspectives including linear functions, exponential functions, logarithms, polynomials, and trigonometric functions. An introduction to limits, continuity, the derivative, and basic properties of real numbers. Introduction to graphing calculators and free graphing software with applications to classroom teaching.
CALCULUS FOR MATHEMATICS TEACHERS II
A continuation of Math 610. The derivative and its applications, including optimization and related rates. Introduction to integration and numerical algorithms using graphing calculators. Offered every Winter.
MAT 610 is a prerequisite for this class.
CALCULUS FOR MATHEMATICS TEACHERS III
A continuation of Math 611. Techniques of symbolic and numerical integration with geometric applications. Sequences, series, power series, and Taylor series. Offered every Spring.
MAT 611 is a prerequisite for this class.
TOPICS IN CALCULUS AND DIFFERENTIAL EQUATIONS
Taylor's theorem, parametric equations, slope fields, Euler's method. The second half of the course will look at the history of calculus and the development of ideas such as limits, least upper bounds, convergence of series, countability, and cardinality.
MAT 612 is a prerequisite for this class.
GEOMETRY FOR MATHEMATICS TEACHERS
Axiom systems, types of reasoning used in proofs, Euclidean geometry results with concentration on triangles and circles, introduction to non-Euclidean geometry, and introduction to geometry classroom software. Offered every Spring.
HISTORY OF MATHEMATICS THROUGH PROBLEM SOLVING FOR MATHEMATICS TEACHERS
Topics include the development of calculus, probability theory, number theory, non-Euclidean geometry, and set theory. Offered every Winter. MAT 650 is a corequisite.
MULTIVARIABLE CALCULUS FOR MATHEMATICS TEACHERS
Functions of several variables, vectors, dot products and cross products, partial differentiation, directional derivatives, optimization, Lagrange multipliers, polar and spherical coordinates. Use of software packages to illustrate three dimensional objects.
MAT 612 is a prerequisite for this class.
PROBABILITY & STATISTICS FOR MATHEMATICS TEACHERS I
Combinatorics, sets, probability, random variables, distribution and density functions, multiple integration, standard probability laws, jointly distributed random variables. Use of graphing calculators, applets, and software packages to illustrate concepts. Offered every Winter.
PROBABILITY & STATISTICS FOR MATHEMATICS TEACHERS II
Central limit theorem, point and interval estimation of parameters, hypothesis testing, least squares and regression. Offered every Spring.
MAT 650 is a prerequisite for this class.
DISCRETE STRUCTURES FOR MATHEMATICS TEACHERS
Logic and proof, number theory, sequences and mathematical induction, sets and functions, cardinality recursion, and introduction to combinatorics.
ABSTRACT ALGEBRA FOR MATHEMATICS TEACHERS
Examines the integers, prime numbers, the Euclidean algorithm, the uniqueness of prime factorization, equivalence relations, rational numbers, real numbers, and complex numbers. Provides examples of groups, rings, and fields and also covers the Fundamental Theorem of Algebra, modular arithmetic, and roots of olynomials of small degree. Offered every Summer.
MAT 612 and MAT 660 are a prerequisite for this class.
ABSTRACT AND LINEAR ALGEBRA FOR MATHEMATICS TEACHERS
A continuation of Math 670. Examines the irreducibility of polynomials, criteria for solvability by radicals, rational values of trigonometric functions, difference functions, partial fraction decomposition, and geometric constructions with ruler and compass. Also examines linear independence, spanning sets, and the basis of a vector space. Along with Math 670, it provides the theoretical foundation for many topics covered in high school mathematics courses. Offered every Fall.
MAT 670 is a prerequisite for this class.