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.

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.

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.

A continuation of Math 611. Techniques of symbolic and numerical integration with geometric applications. Sequences, series, power series, and Taylor series. Offered every Spring.

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.

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.

Topics include the development of calculus, probability theory, number theory, non-Euclidean geometry, and set theory. Offered every Winter. MAT 650 is a corequisite.

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.

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.

Central limit theorem, point and interval estimation of parameters, hypothesis testing, least squares and regression. Offered every Spring.

Logic and proof, number theory, sequences and mathematical induction, sets and functions, cardinality recursion, and introduction to combinatorics.

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.

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.