This course examines the structure and properties of mathematics while focusing on the development of mental mathematics strategies and problem solving skills. Topics include sets, functions, applications of rational numbers, integers, fractions, decimals, percentages, and number theory. Appropriate grade level techniques are utilized to investigate algorithms, probability and statistics, counting techniques, scientific notation, complex numbers, exponents, geometry, and measurement. Students will also investigate ratios, proportion, data analysis, patterns, and the connections to algebra and geometry topics in the context of the 5-12 grades mathematics curriculum.

This course is the first semester of a calculus sequence dealing with applications and modeling of the differential and integral calculus. The course focuses on functions and their graphs, limits, continuity, differentiation, integration, the derivative and its uses in optimization and mathematical modeling, as well as the Fundamental Theorem. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts.

This course examines concepts in algebra including: patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greater common divisor, inequalities, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, linear equations. The course develops the mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, systems of linear equations, and linear transformations. Students engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in secondary and middle school mathematics. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya's four steps for solving problems. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics chosen from the following areas: functions and relations, set theory, number theory, and logic, Euclidian and non-Euclidian geometry, algebra, mathematical reasoning, proof, and problem solving. Connections to middle and secondary school mathematics curriculum emphasized. Students enrolled in this course at the 700 level will meet additional academic requirements including an applied project. Pre-calculus required prior to taking this course.