# MST Course Descriptions

Required Courses

MATH 900: Bridges From Classroom to Mathematics (1 credit)    ONLINE
An introduction to the goals of the MST program.  Students will have the opportunity to explore mathematical problems; to complete activities that make connections between several areas of mathematics, including the mathematical content in the MST degree program and the secondary school mathematics classroom; and to participate in readings/on-line discussions on the nature of mathematics.

MATH 905: Euclidean and Non-Euclidean Geometries from a Synthetic Perspective
An axiomatic development of geometry, beginning with finite geometries; emphasis is given to the fundamental concepts of Euclidean and non-Euclidean geometries from a synthetic perspective.

MATH 906: Analytic and Transformational Geometry
Fundamental concepts of transformational, projective geometry, and inversive geometry, including the properties of conics and quadratic surfaces.

MATH 909: Probability and Statistics for Teachers
An introduction to the fundamental concepts of probability, including combinatorics and probability distributions; statistical applications, including sampling, statistical inference and significance tests; linear regression; and the Central Limit Theorem.

MATH 913:  Graph Theory and Discrete Mathematics
Key theoretical, and computational aspects of graph theory and related areas of discrete mathematics. Applications of graph theory as well as current “open” problems will be explored.

MATH 915:  Algebraic Structures
An exploration of the structural similarities between and among seemingly disparate number systems, beginning with counting numbers, and progressing to the integers, the rational numbers, the real numbers, and the complex numbers; and leading to a discussion of polynomials as an integer analogue and to fields as polynomial “quotients” through the basic concepts of splitting fields and Galois Theory.

MATH 918:  Analysis – Real Numbers and Real Functions
An introduction to the fundamental concepts in real analysis that provide the mathematical foundation for calculus.  Content focuses on properties of sequences and series; properties of functions, including continuity, the derivative and the Riemann integral.

MATH 925:  Problem Solving Seminar (Pass/Fail)
A study of a variety of problem solving strategies and techniques used in the context of solving mathematical problems.  Problems will emphasize the connections between the core areas of Algebra, Geometry, and Analysis.  Other mathematical topics may also be included.  Typically, taken in conjunction with Concluding Experience Problem Set.

Elective Courses

MATH 902: Classroom Practicum (1 credit)    ONLINE
A follow-up course to the six core mathematics content courses of the MST degree program. During the course, students will choose a mathematical topic and/or set of concepts learned in one of the core MST courses and develop and teach a unit based on these concepts at the middle school or secondary school level.

MATH 910:  Topics in Mathematics Education (1 credit)    ONLINE
Special topics in Mathematics Education that are not included in the regularly offered courses. Possible topics include: development of mathematical reasoning across the grades, action research in mathematics classrooms, algebraic thinking across the grades, formal and informal assessment strategies, cooperative learning strategies, and mathematical software in secondary teaching.

MATH 914:  Topology for Teachers
An introduction to the foundational notions of general topology, including neighborhood, open set, closed set, limit point and closure; and to the topological properties of separation, connectedness and compactness.  Emphasis is given to the usual topology for the real line.

MATH 916:  Number Theory    ONLINE
An introduction to number theory, including divisibility theory, congruences, perfect and amicable numbers, Fermat’s Little Theorem, Euler’s phi-function and other number-theoretic functions, Diophantine equations, and cryptography.

MATH 917:  Proof and Problem Solving
Introduction to abstract mathematics with an emphasis on problem solving and proof structure, methods, and techniques. Content includes logic, set theory, and basic number theory.

MATH 919:  The Real Number System
A postulational approach to fundamental aspects of algebraic structure; limits, sequences, and continuity.

MATH 920:  History of Mathematics    ONLINE
An examination of the historical development of number theory, geometry, probability, algebra, and analysis that notes the significant mathematical contributions to these topics by prominent mathematicians.

MATH 928:  Topics in Mathematics (1 credit)
Special topics in Mathematics that are not included in the regularly offered courses. Possible topics include: knot theory, and spherical geometry.

MATH 929: Directed Reading (variable credit)
A directed reading project on a selected topic in mathematics or mathematics education, planned in collaboration with a faculty member.