Master of Arts in Mathematics

Transcription

1 Master of Arts in Mathematics Administrative Unit The program is administered by the Office of Graduate Studies and Research through the Faculty of Mathematics and Mathematics Education, Department of Mathematics and Computer Science, and the College of Arts and Sciences. Mission Statement The primary mission of the Master of Arts in Mathematics (MAM) degree is to prepare mathematics and mathematics education professions to enter the workforce and be highly productive in the fields of mathematics, mathematics education or other related fields requiring a high expertise in mathematics. Objectives MAM graduates are expected to: Develop a deep conceptual understanding of the CORE courses which include Principles of Algebra and Analysis. (Mathematics (M) and Mathematics Education (ME) tracks) Develop a deep conceptual understanding of both required and elective graduate level mathematics, mathematics education, education, and/or computer science courses which promote the ability to solve real-world modeling and computational problems. (M&ME) Opportunities to participate in research seminars and/or internships to promote research and collaboration with other professionals. (M&ME) Become proficient in the academic material to permit further study at the PhD level in mathematics, mathematics education and related areas. (M&ME) Develop the knowledge and skills to obtain employment in their area of mathematics, mathematics education or related fields. (M&ME) Develop an understanding of appropriate uses of technology and how technology can enhance mathematical research, learning and theory. (ME) Develop leadership skills and ability in the area of mathematics education. (ME) Admission Requirements General Students who wish to pursue the MAM degree program must meet the general UT Permian Basin graduate admissions requirements. Departmental The MAM degree has two emphasis tracks: Mathematics and Mathematics Education. In order to be deemed adequately prepared for the mathematics track, an undergraduate degree in mathematics is required. The mathematics education track highly recommends that a candidate possesses an undergraduate degree in mathematics but the candidate may still qualify if the candidate has at least 12 hours of appropriate upper level undergraduate mathematics credit. Candidates designated as not being adequately prepared may be admitted conditionally with an approved leveling plan documenting additional coursework required to enable the candidate to be adequately prepared to pursue the MAM degree. Students admitted conditionally must complete the assigned leveling requirements before officially being admitted to the MAM degree program. Degree Requirements Mathematics Track (Thesis Option) Free Electives 6 Thesis 6 142

2 Mathematics Track (Non-Thesis Option) Free Electives 12 Mathematics Education Track (Thesis Option) Free Electives 6 Thesis 6 Mathematics Education Track (non-thesis Option) Free Electives 12 Mathematics Track (Thesis Option) MATH 6399 Master s Thesis 6 Prefix and Number Prescribed Elective Courses SCH MATH 6333 Applied Probability 3 MATH 6361 Complex Variables 3 MATH 6365 Introduction to Topology 3 Mathematics Track (Non-Thesis Option) 143

3 Prefix and Number Prescribed Elective Courses SCH MATH 6333 Applied Probability 3 MATH 6361 Complex Variables 3 MATH 6365 Introduction to Topology 3 Mathematics Education Track (Thesis Option) MATH 6399 Master s Thesis 6 Prefix and Number Prescribed Elective Courses SCH MATH 6333 Applied Probability 3 MATH 6381 Curriculum Development and Assessment for 3 Secondary Teachers MATH 6382 Mentoring/Leadership for Secondary Teachers 3 MATH 6383 Integrating Technology for Secondary Teachers 3 Mathematics Education Track (Non-Thesis Option) Prefix and Number Prescribed Elective Courses SCH 144

4 MATH 6333 Applied Probability 3 MATH 6381 Curriculum Development and Assessment for 3 Secondary Teachers MATH 6382 Mentoring/Leadership for Secondary Teachers 3 MATH 6383 Integrating Technology for Secondary Teachers 3 Course Descriptions MATH 6300 History of Mathematics (3). A study of the personalities and motivations of historical mathematicians with an emphasis on many of the important results that lead to modern mathematics. Prerequisite: one year of college level mathematics MATH 6301 Statistics (3). Statistical concepts emphasizing simple and multiple regression, hypothesis testing and analysis of variance. Prerequisite: one year of college level mathematics MATH 6310 Algebraic Structures for Teachers (3). Requirement: Middle School Mathematics Teaching Certificate and/or consent of instructor. Course designed for middle school pre-service and in-service mathematics teachers to foster a deep conceptual understanding of the following topics: Adding Fractions, The Group of Integers, The Ring of Integers, The Rational Number Field, Equivalence of Fractions, Square Root of 2, Decimal Representation, Division Algorithm, Geometric Series, and The Least Upper Bound Principle. MATH 6311 Geometry for Teachers (3). Course designed for middle and high school pre-service and in-service mathematics teachers to foster a deeper conceptual understanding of Geometry. Course examines issues, trends, and research related to the teaching/learning of secondary geometry topics. Specific topics will vary, but could include: technology in the classroom, problem solving and the use of applications in teaching mathematics. (Prerequisite: Middle or High School Mathematics Teaching Certificate and/or consent of instructor. MATH 6312 Problem Solving for Secondary Teachers (3). Course designed for middle and high school pre-service and in-service mathematics teachers. The course examines research related to teaching/learning problem solving skills with a major emphasis on promoting active learning and critical thinking, (Prerequisite: Middle or High School Mathematics Teaching Certificate and/or consent of instructor.) MATH 6313 Concept of Size: Theory and Practice for Teachers (3). Requirement: Middle School Mathematics Teaching Certificate and/or consent of instructor. Course designed for middle school pre-service and in-service mathematics teachers to foster a deep conceptual understanding of the following topics: 0-Dimensional size, 1-Dimensional size, 2-Dimensional size, 3-Dimensional size, and 4- Dimensional MATH 6315 Principles of Algebra (3). Theory of rings, with an emphasis on commutative rings, integral domains, and principal ideal domains as generalizations of number systems. Topics include rings of polynomials, ideals, and quotient rings. Prerequisite: MATH MATH 6317 Advanced Linear Algebra (3). Vector spaces, linear transformations and matrix representations, canonical forms, eigenvalues, invariant subspaces, orthogonal and unitary transformations, and bilinear and quadratic forms. Prerequisite: MATH

5 MATH 6325 Number Theory (3). A study of congruences, Euclidean algorithms, properties of prime numbers, primality testing, factorization algorithms, theory of quadratic residues, rational integers, Diophantine equations, linear congruences, and Euler- Fermat theorems. Prerequisite: MATH MATH 6328 Discrete Models (3). Applications of discrete mathematics, including linear programming, game theory, Markov chains, and graph theory. Prerequisite: MATH 3315 MATH 6329 Continuous Models (3). Applications of continuous mathematics, including both deterministic and stochastic models for population growth and competition, epidemiology, and queuing. Prerequisite: MATH 3360 MATH 6332 Combinatorics (3). Topics from enumerative (e.g. basic enumeration, bijections, inclusion-exclusion, recurrence relations, partitions, Polya theory) and nonenumerative (e.g. graph theory, connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, Latin squares) combinatorics. Prerequisite: MATH MATH 6333 Applied Probability (3). Populations, permutations, combinations, random variables, distribution and density functions, conditional probability and expectation; binomial, poisson, and normal distributions; laws of large numbers, central limit theorem. Prerequisite: MATH 3360 MATH 6350 Topics in Geometry (3). Advanced two-dimensional Euclidean geometry, including theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Non-Euclidean (e.g. hyperbolic and finite) geometries in comparison to Euclidean geometry. Integrated use of dynamic geometry software tools. Prerequisite: MATH 3360 MATH 6360 Principles of Analysis (3). Investigation of convergence, continuity, differentiability, compactness and connectedness, the Riemann-Stieljes integral, and sequences of functions. Prerequisite: MATH MATH 6361 Complex Variables (3). Complex integration and the calculus of residues. Analytical continuation and expansions of the analytic function. Entire, meromorphic, and periodic functions. Prerequisite: Math 6360 MATH 6381 Curriculum Development and Assessment for Secondary Teachers (3). Requirement: Middle or High School Mathematics Teaching Certificate and/or consent of instructor. The course is designed to prepare teachers to 1) develop curriculum that results in a deep conceptual understanding in mathematics, and 2) research and develop both formal and informal assessment skills. MATH 6382 Mentoring/Leadership for Secondary Teachers (3). Requirement: Middle or High School Mathematics Teaching Certificate and/or consent of instructor. The course explores the mentor teacher s role in guiding a pre-service or in-service teacher in pedagogical issues related to designing lessons that are rich in problem solving, critical thinking, and inquiry based. MATH 6383 Integrating Technology for Secondary Teachers (3). Requirement: Middle or High School Mathematics Teaching Certificate and/or consent of instructor. The course is designed to provide experiences for teachers to research, explore and develop a broad knowledge base and level of technological skill associated with new and innovative instructional technology tools. 146

6 MATH 6389 Special Topics in Mathematics (3). Graduate mathematics courses which will be offered only once, will be offered infrequently, or are being developed before a regular listing in the catalog. MATH 6391 Contract Study in Mathematics (1-3). For students who are pursuing independent study or research (as described in the contract study format). MATH 6398 Masters Project (3). Meets the research requirements for the non-thesis option in master s degree program. MATH 6399 Masters Thesis (3 or 6). Meets the research requirements for the thesis option in the masters degree program. EDUC 6335 Innovations in Teaching Science and Mathematics (3) Examination and critical evaluation of innovative curricula and programs in light of current literature and research in the teaching and learning of science and mathematics. Emphasis on translating theory into practice in the classroom. EDUC 6336 Current Issues in Teaching Science and Mathematics (3) Current issues and trends in teaching science and mathematics will be identified and explored. Emphasis on the interface of theory and practice. EDUC 6305 Research Design in Education and the Social Sciences (3) This course is designed to acquaint students with how research is conducted in the fields of education and the social sciences. Students will select and evaluate research findings within their fields and learn how to design their own research studies. COSC 6390 Theory of Computation (3) The goal of the course is to discover what is (and is not) computable. Mathematical models of computation, including regular expressions, grammars, recursive functions, and the automata that model them including Turing machines. The course culminates with a discussion of Church s thesis, Gödel numbering, and the Halting Problem. Prerequisite: COSC 3312 or equivalent or permission of instructor COSC 6385 Analysis of Algorithms (3) A study of efficient algorithms for a variety of problems, with mathematical proof of correctness and analysis of space and time complexities. Topics include upper bound, lower bound, and average case analysis for sorting, amortized analysis of data structures, tree and graph algorithms, parallel algorithms, and NP-completeness. Prerequisite: COSC 3312 or equivalent or permission of instructor 147