| Master of Science in Adolescent (Secondary) Mathematics 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. ADMISSION REQUIREMENTS 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) DEGREE REQUIREMENTS
The masters candidate must complete: A.Twelve semester hours of graduate study
in mathematics selected under advisement from six basic sub-areas of mathematics
(algebra, analysis, applied and computational mathematics, history of mathematics,
geometry and statistics). B. Twelve
semester hours in the Education Core: C.
One semester hour in the
Interdepartmental Seminar: D. A
minimum of nine semester hours of elective courses selected under Mathematics
Courses for the Masters Degree
MATH 421 Foundations
of the Calculus
MATH 432 Classical
Algebra
MATH 433 Applied
Linear Algebra
MATH 435 Transformational
Geometry
MATH 436 Euclidean
and non-Euclidean Geometry
MATH 437 Applied
Combinatorics
MATH 460 Statistical
Methods
MATH 470 History
and Fundamental Concepts of Mathematics
MATH 475 Applied
and Computational Mathematics
MATH 499 Directed
Study ROTATION SCHEDULE 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.
COURSE DESCRIPTIONS Math 421
- 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
432 - 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
433 - 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
435 - 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
436 - 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
437 - 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
460 - 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
470 - 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
475 - 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). |