The Master of Science in Mathematics with an emphasis in mathematics education program provides mathematics teachers with advanced study in mathematics and mathematics education. The program offers teachers additional experience in higher-level mathematics to enhance their teaching with additional depth and breadth of content. At the same time, it strengthens their background in school mathematics curriculum, instructional practices, assessment and technology and research in mathematics education.
Admission Requirements
The general admission requirements are found in the section “Graduate Admission Requirements.” In addition to the requirements listed, students must hold a bachelor’s degree in mathematics or a bachelor’s degree in some other field with extensive coursework in mathematics.
Residency Requirements
A minimum of 30 semester hours of graduate credit must be earned at Aurora University in order to receive this degree. A maximum of six semester hours of graduate credit may be transferred from a regionally accredited college or university and applied to the requirements of this degree. Any coursework submitted for transfer must be approved by the mathematics program faculty and the chair of the division.
All graduate transfer credit from other institutions must be submitted at the time of acceptance into the program. Once the applicant has been accepted for enrollment in the program, it is expected that he/she will complete all coursework for the degree at Aurora University. No coursework may be transferred to Aurora University after enrollment. See the section “Transfer of Credit” for other conditions governing the transfer of credit.
Academic Standards and Evaluation
At the graduate level, a “C” grade indicates less than complete mastery of the content of a course. Only two grades of “C” are accepted at the graduate level in this program and they must be balanced by two grades of “A.” See the section “Academic Standards” for other conditions governing academic standards and the graduate grading system.
Degree Requirements
Twenty-four (24) semester hours in mathematics plus 12 semester hours in professional education.
Section A: Required courses in mathematics (24 semester hours)
- MTH5100 Foundations of Higher Mathematics (3)
- MTH5200 Modern Geometries (3)
- MTH5300 Number Theory (3)
- MTH5400 Probability and Statistics (3)
- MTH6100 Abstract Algebra I (3)
- MTH6200 Abstract Algebra II (3)
- MTH6300 Advanced Calculus I (3)
- MTH6400 Advanced Calculus II (3)
Section B: Required courses in education (12 semester hours)
- MTH5500 Technology in the Mathematics Classroom (3)
- MTH5600 Assessment and Curriculum Development in Mathematics (3)
- MTH5700 Mathematics Education Research I (3)
- MTH6700 Mathematics Education Research II (3)
Course Descriptions
MTH5100 Foundations of Higher Mathematics 3 semester hours
The fundamentals of advanced mathematics and an introduction to mathematical proofs. Topics include logic, quantifier notation, set operations, functions, relations, the integers, and study of rational, real, and complex numbers as fields. Various types of proof techniques will be studied and applied to problems from number theory, geometry, analytic geometry, discrete mathematics, logic, and calculus.
Prerequisite: Open to graduate students only.
MTH5200 Modern Geometries 3 semester hours
A study of absolute, finite, and non-Euclidean geometries from an axiomatic viewpoint.
Prerequisite: Open to graduate students only.
MTH5300 Number Theory 3 semester hours
Topics include the theory of mathematical induction, divisibility theory in the integers, prime numbers and their distribution, the theory of congruences and modular arithmetic, Fermat’s theorem, quadratic reciprocity, Diophantine equations, and number theoretic functions and their applications.
Prerequisite: Open to graduate students only.
MTH5400 Probability and Statistics 3 semester hours
This course includes probability for discrete sample spaces, probability distributions, Chebyshev’s theorem, moment generating functions, continuous random variables, sampling distributions, point and interval estimation, theory of hypothesis testing, regression and correlation, and introductory analysis of variance.
Prerequisite: Open to graduate students only.
MTH5500 Technology in the Mathematics Classroom 3 semester hours
Hands-on experiences working with current technology (scientific calculators, graphic calculators, computers, and computer software) for elementary, middle school, and secondary school mathematics. Presentation and evaluation of methods and strategies for employing technology as a regular part of instruction and assessment, including discussion of educational foundations.
Prerequisite: Open to graduate students only.
MTH5600 Assessment and Curriculum Development in Mathematics 3 semester hours
A balanced study of theoretical research-based foundations and classroom-reform-based perspectives on assessment and evaluation in school mathematics. Consideration of alternate forms of assessment and evaluation of mathematics teaching and of students’ mathematical learning. Topics include assessment standards, scoring rubrics, performance assessment, and portfolios. Curriculum goals and issues are also addressed; recent developments in curriculum; learning research; alternate modes of presentation.
Prerequisite: Open to graduate students only.
MTH5700 Mathematics Education Research I 3 semester hours
Investigates recent developments and relevant research in mathematics education. An introduction to methods of critical reading of research reports and to the structure and scope of mathematics education research. Reading and evaluation of original research; issues of validity and reliability in research; assembling components for the writing of research.
Prerequisite: Open to graduate students only.
MTH6100 Abstract Algebra I 3 semester hours
Introduction to group theory. Topics include equivalence relations, groups, subgroups, cyclic groups, permutation groups, isomorphisms, cossets, external direct products, normal subgroups, factor groups, group homeomorphisms, rings, and integral domains.
Prerequisite: Open to graduate students in mathematics only.
MTH6200 Abstract Algebra II 3 semester hours
Continuation of MTH6100. Introduction to commutative rings, with emphasis on polynomial rings; fields vector spaces, and algebraic extensions.
Prerequisite: MTH6100.
MTH6300 Advanced Calculus I 3 semester hours
Reexamination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral.
Prerequisite: Open to graduate students in mathematics only.
MTH6400 Advanced Calculus II 3 semester hours
Further study of sequences and series of functions, functions of several variables, and an introduction to complex analysis.
Prerequisite: MTH6300.
MTH6700 Mathematics Education Research II 3 semester hours
Students will determine a problem and investigate the problem as a research project. The project must deal with a problem in mathematics education and may be local or national in scope.
Prerequisite: MTH5700.
Please Note: The information listed on this page is current according to the 2007-2009 Graduate Catalog, unless otherwise noted.
