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Master of Arts in Teaching - Secondary Education: Mathematics

M.A.T. Mathematics Courses

Mathematics Course Descriptions

MATH 5000 - History of Mathematics (3-0-3): This course is an exploration of the historical development of mathematics in various civilizations, ranging from Ancient Egypt through classical Greece, the Middle and Far East, and on to modern Europe. Topics may include the development of areas such as arithmetic, geometry (practical, deductive, and axiomatic), number theory, trigonometry, syncopated and symbolic algebra, probability and statistics, algebraic geometry, and calculus. Prerequisite(s): MATH 3005 or Permission of the instructor.

MATH 5010 - Modern Methods of Mathematics Instruction (3-0-3): This course will explore theory and pedagogy of mathematics instruction with a focus on teaching methods across a variety of topics. Appropriate integration of technology into mathematics teaching and learning will be emphasized. Pre-requisite: MATH 3005 or Admission to M.A.T. program.

MATH 5130 - Applied Algebra (3-0-3): This course is an investigation of how the theory of abstract algebra is applied to solve non-theoretical problems. Topics are selected from applications in exact computing, error correcting codes, block designs, crystallography, integer programming, cryptography and combinatorics. Students will work both individually and in groups on projects from the chosen topics. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5220 Applied Statistics (3-0-3): This course is an introduction to multiple regressions, analysis of variance, and other selected inference methods. Topics will be selected from chi-square tests, non-parametric statistical methods, analysis of variance using simple experimental designs, and multiple regression methods, including model building, model checking, and analysis of residuals. Throughout the course, real data and computer software will be utilized. Prerequisite(s): MATH 1231 or Permission of the instructor

MATH 5231 - Modern Geometry (3-0-3): This course is a study of Euclidean and non-Euclidean geometries. Topics will be explored through historical perspectives, formal geometric proofs, technology-based investigations, and modern applications. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5250 - Elementary Number Theory (3-0-3): This course is an introduction to the mathematical treatment of concepts related to the system of integers. Topics will include divisibility, factorization, prime numbers, congruencies, number theoretic functions, and Diophantine equations. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5261 - Introductory Probability (3-0-3): This is an introductory course in Mathematical Probability. It explores the topics of probability, random variables and their distributions, mathematical expectation, moment generating functions and sampling distributions. Prerequisite(s): MATH 2502 or Permission of the instructor

MATH 5255 - Factoring & Primality Testing (3-0-3): This course is a study of deterministic and probabilistic methods for factoring large integers and testing whether an integer is prime or composite. Topics to include Pollard's algorithms, Pseudoprime tests, the Rabin-Miller test, the Quadratic Sieve, Lucas Sequences, Pratt Certificates, and other methods according to time and student interest. Computer technology will be used heavily in this course. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5350 - Graph Theory (3-0-3): This course is a study of graph theory and graph theoretical problem solving techniques. Topics are selected from connectivity, Eulerian graphs, Hamiltonian graphs, algorithms, properties of trees, counting trees, planar graphs, Euler’s formula, graphs on other surfaces, dual graphs, infinite graphs, coloring vertices, Brook’s Theorem, coloring maps, coloring edges, chromatic polynomials, Eulerian digraphs and tournaments, Markov chains, Hall ‘marriage’ theorem, transversal theory, Application of Hall’s theorem, Menger’s theorem, and network flows. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5360 – Combinatorics (3-0-3): This course is a study of combinatorial problems and solving techniques. Topics are selected from counting principles, enumeration, generating functions, recurrence relations, Polya’s theory of counting, Ramsey Theory, extremal graph theory, probabilistic methods, and the Szemeredi Regularity Lemma. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5365 - Applied Combinatorics (3-0-3): This course is a study of some applications of combinatorics. Some of the topics that are explored in this course are: Pólya theory of counting, combinatorial design, coding theory, existence problems in graph theory, matching and covering, optimization problems for graphs and networks. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5520 - Introduction to Analysis (3-0-3): This course is a rigorous introduction to analysis functions on Euclidean space. Topics include limits, continuity, sequences, series, differentiation, integration, and sequences and series of functions. Prerequisite(s): MATH 2503 and MATH 3005 or permission of the instructor

MATH 5525 – Topology (3-0-3): This course is an introduction to topology via a variety of different techniques and applications involving point set, geometric, and algebraic topology. Topics include, but are not limited to: continuity, open and closed sets, compactness and connectedness, identification spaces, the fundamental group, triangulations, and surfaces. Further topics may include: simplicial homology, degree and Lefshetz number, knots, and covering spaces. Prerequisite(s): MATH 3005 or Permission of the instructor

MATH 5800 - Special Topics (3-0-3): This course is a directed study in areas of special interest not covered in listed courses. This course may be repeated if topics vary. Prerequisite(s): Permission of the instructor

MATH 6530 - Real Analysis (3-0-3): This is a rigorous introduction to measure and integration theory. Topics include sequences and series of functions, the Riemann Integral, the Riemann-Stieltjes Integral, Lebesgue Measure, and Lebesgue Integral. Prerequisite(s): MATH 3520 or MATH 5520 or Permission of the instructor

Education Course Descriptions

EDUC 5100 - Social and Cultural Awareness in American Education (3-0-3): An examination of multicultural and social concerns that influence the teaching and learning process. Study current issues and trends impacting American public schools as related to preparing pre-service teachers to teach diverse learners in a cross-cultural society. Technology will be used to perform word processing, Internet research, software reviews and electronic portfolio assignments. Pre-requisite: Admission to M.A.T. program

EDUC 5101 - Exceptionalities and Cognitive Development of Learners (3-0-3): A survey of basic characteristics and educational needs of learners with physical, emotional, intellectual disabilities. Additional study will concentrate on the cognitive and learning developmental aspects of teaching adolescents and young adults with a variety of abilities and disabilities. Course will focus on learning theories and models used in education. Technology will be used to conduct word processing, Internet research, software reviews and electronic portfolio assignments. Pre-requisite: Admission to M.A.T. program

EDUC 5102 - Practicum I (0-3-1): This course will be the Summer Semester portion of the field experiences for this program. It is designed for candidates to observe and participate in experiential learning in public school classrooms, before or after school programs, youth centers, or similar situations where diverse groups of adolescents are engaged in the teaching and learning process. The practicum experiences will allow candidates to observe, reflect and/or work with learners based on topics presented in EDUC 5100-5101. Candidates will be required to spend approximately ten hours per week in the field and must have proof of liability insurance to participate in the course. Co-requisite: EDUC 5100 and EDUC 5101

EDUC 5200 - Curriculum and Instruction for Teaching Secondary School Learners (3-0-3): This course is designed to teach candidates the theory and best practices for developing and delivering instruction in high school settings. Focus will be on instructional strategies, motivational and classroom management techniques, pedagogical knowledge, skills and dispositions for effective teaching and learning, and the construction and administration of learning assessment instruments. Technology will be used to perform word processing, Internet research, software reviews and electronic portfolio assignments. Pre-requisite: Admission to M.A.T. program

EDUC 5201 - Practicum II (0-3-1): This course is the Fall Semester portion of the field experiences for the program. It is designed for candidates to observe and participate in experiential learning in public school classrooms, before- or after-school programs, youth centers, or similar situations where diverse groups of adolescents are engaged in the teaching and learning process. The practicum experiences will allow candidates to observe, reflect and/or work with learners based on topics presented in EDUC 5200 and in content courses. Candidates will be required to spend approximately ten hours per week in the field and must have proof of liability insurance to participate in the course. Pre-requisite: EDUC 5102; Co-requisite: EDUC 5200

EDUC 5300 - Internship Seminar (1-0-1): This seminar is designed to discuss common issues, concerns and successes that candidates are having as teaching interns. Some topics will include developing curriculum and instruction for diverse and special needs learners, designing and implementing thematic units using Georgia Performance Standards (GPS), using classroom management techniques, developing and using data from student assessments, interpreting standardized testing data, using instructional technology to facilitate student learning, and recognizing legal, ethical, and professional responsibilities. Technology will be used to perform word processing, Internet research, software review, and electronic portfolio assignments. Co-requisite: EDUC 5301

EDUC 5301 - Secondary School Internship (0-12-4): This course is a clinical experience in high school settings for teaching the major concentration during the Spring semester. Candidates will be responsible for two weeks of observations and reflections before eight weeks of taking full-time responsibility for classroom instruction, and end with two final weeks of observations and reflections. School-based mentor teachers will work with interns in meeting program outcomes through teaching assignments. University field supervisors will observe and assess performance. Candidates must have proof of liability insurance to participate in course. Co-requisite: EDUC 5300

EDUC 5400 - Action Research Project (2-1-2): This course provides candidates with an opportunity to develop an action research project based on coursework, practicums, and clinical experiences. Candidates will demonstrate an understanding of the theory behind action research in teacher education and will utilize qualitative and/or quantitative research methods. They will design and implement an action research project, independently or in small groups, with the goals of publication, staff development, school policy change, or curriculum restructuring, in mind. All projects must be approved by the instructor and follow IRB specifications. Participants will define questions, determine research methods, and gather and assess data. This directed research project is a capstone experience in the M.A.T. degree program. Pre-requisites: EDUC 5300 & 5301.