An in-depth, college-level study of the foundational structure underlying the major mathematical concepts taught in the middle grades. Content strands include number and operations, patterns and algebra, geometry and measurement and data analysis and probability. Includes emphasis on key transitions in mathematical thinking and connection of middle-level concepts to college math course content.

A study of foundational secondary level mathematics concepts from an advanced, college-level perspective. Content strands include number system structures, functions and equations, integers and polynomials, congruence and symmetry, area and volume, trigonometry, data analysis and probability and discrete math topics. Includes emphasis on extensions and generalizations, applications, problem solving and connection of secondary level concepts to college math course content.

The study of Euclidean and non-Euclidean geometry from axiomatic, synthetic, analytic and transformational approaches with emphases on modeling, inductive and deductive reasoning and proof techniques.

Fundamental concepts from linear algebra, including: systems of linear equations, the algebra of matrices, linear transformations, eigenvalues and determinants. Fundamental concepts from abstract algebra, including: group theory, ring theory, field theory, equivalence relations, isomorphisms and homomorphisms. Fundamental structures such as congruences, number systems, polynomials, permutations and symmetry groups.

Descriptive and inferential statistics include methods for describing data, binomial and normal probability distributions, tests of hypotheses, simple linear regression, analysis of variance, nonparametric techniques, two-sample testing and contingency tables.