# 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 total of 33 Credit Hours with the following requirements:

**Core Area of Study (12 Credit Hours)**- EDUC 501 - Nature of Learning: Philosophical and Psychological Foundations of Education
- EDUC 503 - The School and Society
- EDUC 504 - Educational Research Methodology
- INTD 510 - Seminar on Secondary School Mathematics and Pedagogy

**Departmental Area of Study (12 Credit Hours)**

Select four courses from the graduate Mathematics courses listed below.**Electives under advisement selected from any graduate course offering (3-6 Credit Hours)**

These elective hours may be selected from mathematics, mathematics education, or other academic areas that complements the students program.**Culminating Experience (3-6 Credit Hours)**

Research project conducted under the supervision of a faculty member from the Department of Mathematics and/or the School of Education. Theses format must conform to that prescribed by the*MLA Style Manual and Guide to Scholarly Publishing*.

### Mathematics Courses for the Masters Degree

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

### 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.

Spring 2012Summer 2012Fall 2012Spring 2013Summer 2013Fall 2013 | 533 570 535 521 575 532 | Spring 2014Summer 2014 Fall 2014 Spring 2015 Summer 2015 Fall 2015 | 560 536 521 537 533 570 | Spring 2016Summer 2016 Fall 2016 | 535 521 575 |

Spring 2006Summer 2006Fall 2006Spring 2007Summer 2007Fall 2007 | 535 521 575 532 560 536 | Spring 2008Summer 2008 Fall 2008 Spring 2009 Summer 2009 Fall 2009 | 521 537 533 570 535 521 | Spring 2010Summer 2010 Fall 2010 Spring 2011 Summer 2011 Fall 2011 | 575 532 560 536 521 537 |

### COURSE DESCRIPTIONS

**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).