MAD 513 Topics in Secondary School Mathematics Education 3 SH

This course provides an in-depth study of a single topic or collection of related topics of current interest in secondary school mathematics education. Topics will vary depending on developments in mathematics education and student or program needs. Topics might include curriculum developments, applications, research on teaching, technology, current research on mathematics education or similar topics. The course may be repeated for credit with different topics. Prerequisite: must hold a valid teaching certificate or be admitted to the Master of Arts in Teaching program in mathematics.

MAD 549 Teaching Mathematics in Secondary Schools: Content and Pedagogy 3 SH

This course provides secondary teacher candidates with the content and pedagogy necessary to develop an understanding of the methods and materials needed to become effective teachers of mathematics. Candidates are introduced to assessment methods and learn to integrate current instructional technologies into their teaching. Emphasis is placed on strategies for differentiating instruction. Candidates develop lesson plans and units of instruction, practice delivering instruction, and observe secondary teachers of mathematics in the field. In addition, students examine current curricular-reform movements and consider their impact on mathematics education in the secondary school. The implications of state, national, and international testing movements, state standards/frameworks, the National Council of Teachers of Mathematics (NCTM) standards, as well as the NCATE standards, are considered. This course will be taught by a member of the Mathematics Department.  Prerequisite: admission to the Professional Secondary Education Teacher Preparation program and registration in secondary education professional semester courses or admission to the Master of Arts in Teaching program or permission of both the chair of the Education and Educational Psychology Department and the chair of the Mathematics Department.

MAT 505 Logic 3 SH

An introduction to formal mathematical logic, including sentential (propositional) logic and first-order (predicate) logic. Logical consequence and formal deducibility. Soundness, completeness, and compactness of sentential logic and first-order logic. Examples of a variety of first-order mathematical structures. Applications of the compactness of first-order logic, including the existence of arbitrarily large infinite structures, nonstandard models of arithmetic, and hyperreal numbers. Prerequisite: MAT 375 or equivalent.

MAT 507 – 508 Applied Statistics I, II 3 SH each

Topics will be taken from both descriptive and inferential statistics. These include estimation, hypothesis testing, simple- and multiple-regression analysis, analysis of variance, and one or more multivariate techniques such as factor, cluster, discriminant, or principal components analysis. Applications from a range of subject areas from the behavioral to the physical sciences will be given. Computer statistical packages will be used throughout both semesters. Prerequisite: MAT 120 or equivalent.

MAT 512 – 513 Modern Algebra I, II
3 SH each

This is a review of the concepts of groups, rings, fields, and vector spaces. Discussion of quotient groups and rings, extension fields, linear transformations, and canonical forms. Prerequisites: Introduction to Abstract Algebra and Introduction to Linear Algebra.

MAT 514 – 515 Real Analysis I, II 3 SH each

Construction of real numbers by Delekind cuts, continuity, functions of several variables, Heine-Borel and Bolzano-Weierstrass theorems. Series, Riemann-Stieltjes integrals and Lebesque integration and measure. Prerequisite: Calculus III or equivalent.

MAT 518 Complex Analysis I 3 SH

Complex number systems and properties of such, continuity, differentiability, analyticity, line integration, and power series. Residues and poles, conformal mapping, analytic continuation and the well-known classical theorems associated with the theory of complex analysis.

MAT 522 Topics in Advanced Geometry 3 SH

This course offers a synthetic and analytic approach to Euclidean, non-Euclidean, affine and projective geometry. The construction of geometry systems from sets of axioms will be emphasized. Prerequisite: one year of calculus.

MAT 526 – 527 Numerical Analysis I, II 3 SH each

This course provides the student with a wide range of numerical methods and strategies to deepen his/her insight. The main emphasis will be on numerical treatment of eigenvalue problems and of partial differential equations. More recent applications in linear programming, analysis of network flows ,and Monte-Carlo methods are included. Prerequisite: MAT 431-432 or equivalent.

MAT 528 Number Theory 3 SH

This course covers fundamental theorems and divisibility, prime numbers and congruence of numbers, as well as theorems of Fermat, Euler, and Wilson, Euclid’s algorithm, and Diophantine equations. Prerequisite: one year of calculus.

MAT 529 Historical Development of Mathematics 3 SH

This course offers a study of mathematical concepts from arithmetic to calculus in their historical perspective. Attention will also be given to contributions of great mathematicians and various cultures and to the relation of mathematics to other sciences. Designed for students with an undergraduate mathematics major or equivalent.

MAT 540 Topics in Mathematics 3 SH

This course offers an opportunity for students to pursue in greater depth topics introduced in other courses or topics not included in other courses. The topic varies from year to year and from student to student. Typical subjects might include mathematical models, combinatorics, field theory, algebraic topology, decision theory, and harmonic analysis or applications.

MAT 590 Mathematics and Computer Science Department Seminar 3 SH

This seminar course is for students fulfilling the non-thesis requirements for the M.S. in Education with an Option in Mathematics. The seminar will consist of independent research into a topic which has interfaces with several branches of mathematics; and oral presentation of the topic for the seminar. Prerequisite: ED 501, permission of the department graduate committee and the Dean of Arts and Sciences. The topic must be approved by the adviser and the department graduate committee during the semester immediately prior to registering for the seminar.

MAT 591 Independent Thesis Research in Mathematics/Mathematics Education 0-6 SH

This course is designed for students fulfilling the thesis requirements for the M.A. in Mathematics degree. The submitted topic and outline for the thesis must be approved by the adviser, the department graduate committee, and the Dean of Arts and Sciences prior to registration for the course. The student will be required to work independently on the thesis research and writing. Credit for the thesis will be awarded upon the submission of one copy of the approved final draft of the thesis and thesis abstract. Prerequisite:s ED 501 and permission of the department and the Dean of Arts and Sciences.

MAT 592 Independent Thesis Research in Mathematics 0-6 SH

This course is designed for the student fulfilling the requirements for the Master of Arts in Mathematics. The student must submit an acceptable thesis topic and outline in mathematics, and the student will be required to work independently on the thesis research and writing in consultation with the thesis advisor. Credit for the thesis will be awarded upon the submission of one copy of the approved thesis and abstract. Prerequisite: permission of the thesis adviser and the Dean of Arts and Sciences.

MAT 598 Faculty-Developed Course

This experimental course is offered by the Mathematics Department as a means of determining its value to the total department program or in response to a particular request from a group of students.

MAT 599 Student-Developed Study

This vehicle is designed to provide the student with an opportunity to develop his/her own learning experience. A student will design a project and secure a faculty sponsor. The vehicle may be utilized more than once. Prerequisite: written permission of faculty sponsor and department. Registration through the Division of Graduate Studies Office is required.

MAT 704 Matrix Theory and Methods 3 SH

This course is concerned with properties and applications of matrices and finite dimensional vector spaces. Prerequisite: MAT 272 or equivalent.

MAT 708 Applied Mathematics 3 SH

This course offers a mathematical analysis and linear algebra applied to problems from engineering and science. The design and validation of models will be examined. Prerequisite: MAT 272, MAT 281, or equivalent.

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