The Master of Science Degree in Secondary Mathematics is designed to meet needs of the Secondary Teacher of Mathematics as both teacher and scholar. Each course has been structured to relate to a subject area central to the secondary school curriculum and, at the same time, present those subject areas at a mathematically advanced level.
Students in this program will have had the opportunity to build upon an undergraduate background in algebra, analysis, geometry and probability and/or statistics by electing further work in these areas. Additionally, students can pursue courses in applied mathematics, computational mathematics, or the history of mathematics to supplement their undergraduate training.
Students must have completed the basic undergraduate courses normally required for the baccalaureate in Mathematics. This should include single and multivariate calculus and at least one course in each of the following areas:
Algebra (modern algebra, linear algebra, etc.)
Analysis (advanced calculus, real variables, etc.)
Geometry (foundations of geometry, non-Euclidean geometry)
Probability and/or Statistics (calculus based)
The masters candidate must complete a total of 33 Credit Hours with the following requirements:
MATH 521: Foundations of the Calculus
MATH 532: Classical Algebra
MATH 533: Applied Linear Algebra
MATH 535: Transformational Geometry
MATH 536: Euclidean and non-Euclidean Geometry
MATH 537: Applied Combinatorics
MATH 560: Statistical Methods
MATH 570: History and Fundamental Concepts of Mathematics
MATH 575: Applied and Computational Mathematics
MATH 599: Directed Study
Our Masters Program is designed primarily for working teachers seeking permanent certification who are not on the Geneseo campus as full time students. Thus the mathematics department will offer one course each semester (including summers) according to the following schedule.
Math 521 - Foundations of the Calculus
This course is designed for teachers who desire to renew and to strengthen their knowledge of elementary calculus as well as for those who wish to probe the subject at greater depth. Beginning with familiar material, the course attempts to develop the intermediate supporting theory. Topics covered include: limit theory, differentiation, properties of continuous functions and the theory of Riemann integration. Prerequisites: A course in analysis. 3(3-0).
Math 532 - Classical Algebra
An introduction to number theory and higher algebra within an historical context. Topics include elementary number theory, theory of equations and an introduction to abstract algebra. Pre-requisite: A course in elementary linear algebra. 3(3-0).
Math 533 - Applied Matrix Techniques
Many models can be formulated as a system of linear equations. The main emphasis of this course is to investigate a number of models that can be solved using matrix techniques and linear algebra. Applications may include, but are not restricted to, Least Squares Fitting of Data, Markov Chains, and Population Growth Models. Prerequisite: A course in elementary linear algebra. 3(3-0).
Math 535 - Transformational Geometry
The concept of a geometric transformation is studied in conjunction with the basic structure of a group and properties of a space that remain invariant under specified transformations. Isometric and similarity transformations of the plane will be studied in depth in both a synthetic and analytic framework. As time permits, inversions, affine, projective and topological transformations will be investigated. Prerequisite: A course in geometry. 3(3-0).
Math 536 - Euclidean and non-Euclidean Geometry
This course presents the discovery of non-Euclidean geometry and the subsequent reformulation of the foundations of Euclidean geometry. Euclid's geometry, modern axiomatics, Hilbert's geometry and hyperbolic geometry are studied with a view of expanding the student's knowledge and perception of geometry, but also to gain an appreciation for Euclid's original work. Prerequisite: A course in geometry. 3(3-0)
Math 537 - Applied Combinatorics
This course will cover the fundamentals of combinatorics, beginning with elementary counting techniques (combinations and permutations) and including such topics as generating functions, Polya's enumeration formula and graph theory. There will be an emphasis on discrete modeling. Prerequisite: A course in either discrete mathematics or probability theory. 3(3-0).
Math 560 - Statistical Methods
This course will cover basic statistical methods including the chi-square test, regression and correlation, analysis of variance and experimental design, and non-parametric statistics. The emphasis is on the art of statistical thinking and data analysis based on real-world problems. The use of the computer and its peripheral devices as tools to understanding statistical concepts will be included in this course. Prerequisite: A course in probability and statistics. 3(3-0).
Math 570 - History and Fundamental Concepts of Mathematics
This course is a chronological development of the fundamental principles of modern mathematics. The underlying concepts that form a basis for the axiomatic development of geometry, algebra and analysis are discussed within the scope of the mathematics curriculum. Prerequisites: One course in each of the areas: algebra, analysis, geometry. 3(3-0).
Math 575 - Applied and Computational Mathematics
Problems arising in a variety of fields will be investigated from a mathematical modeling perspective. The basic mathematical concepts and techniques widely used in Applied Mathematics and Numerical Analysis will be studied in the context of the applications. Numerical methods, involving the use of calculators and/or computer technology, which aid in the investigation, will be introduced dependent on the specific application. Prerequisites: Calculus III and elementary linear algebra. 3(3-0).