Mathematics (MTH)                  Course Schedules

MTH 520 Optimization Theory 3(3-0) D
The theory of and computer methods in classical and modern optimization, using linear programming. Prerequisites: Knowledge of FORTRAN, MTH 223 or 137, 233 or consent of instructor.

MTH 521 Theory of Numbers 3(3-0) D
Properties of integers, congruencies, quadratic residues, elementary Diophantine problems. Prerequisite: MTH 332.

MTH 523 Modern Algebra I 3(3-0) F, Sp
The nature of proof. Equivalence relations, congruence, and residue classes, groups, rings, integral domains, and fields. Prerequisite: MTH 332 or graduate status.

MTH 525 Modern Algebra II 3(3-0) D
Vector spaces, matrices, and linear transformations. Prerequisite: MTH 523.

MTH 532 Advanced Calculus I 3(3-0) F
Rigorous development of calculus for functions of one variable. Sequences, limits, continuity, differentiation, integration, exponential and logarithmic functions, arc length, series. Prerequisites: MTH 233 and 332, or graduate status.

MTH 533 Advanced Calculus II 3(3-0) Sp
A continuation of 532. Functions of several variables. Prerequisite: MTH 532.

MTH 539 Mathematical Foundation of Actuarial Science 3(3-0) Sp
Develop a knowledge of fundamental mathematical tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. Does not count toward graduate degree. CR/NC only. Prerequisites: FIN 257 and STA 584.

MTH 545 Introduction to Point-Set Topology 3(3-0) D
Development of elementary point-set topology. Sets, functions, metric spaces, topological spaces, separation axioms, compactness, and connectedness. Prerequisite: MTH 332 or graduate status.

MTH 551 Number Systems for Elementary Teachers 3(3-0) D
Continuation of 151 and 152. Integers, real numbers, mathematical sentences, number theory, mathematical systems. Admission limited to students pursuing a B.S. in Ed., Elementary Emphasis. Credit will not apply toward master’s degree in mathematics. Prerequisites: MTH 107, 152.

MTH 554 Probability and Statistics for Elementary and Middle School Teachers 3(3-0) D
Examines experimental probability and statistics suitable for elementary and middle school. Data gathering, organizing and presenting. Credit will not apply toward Master’s degree in mathematics. Prerequisites: MTH 107, 551.

MTH 556 Microcomputers for Elementary Mathematics Teachers 3(3-0)
Develops the use of microcomputers in elementary education with particular emphasis on mathematical applications. Computer literacy and BASIC Programming are included. Open only to those students pursing a B S. in Education, Elementary Emphasis. Prerequisite: MTH 107 and 251 or equivalent.

MTH 565 Using Graphics Calculators in Mathematics Education 1(1-0)
Course is designed for secondary mathematics education majors and minors. Emphasis will be on the classroom use of graphics calculators to teach mathematics. Prerequisites: MTH 132 with MTH 223 as a corequisite.

MTH 566 Microcomputers for Secondary Mathematics Teachers 3(3-0)
Examines microcomputer use in secondary education with particular emphasis on mathematical applications. Open only to those students pursuing a B.S. in Ed., Secondary Emphasis. Prerequisite: MTH 223 or equivalent.

MTH 570 Mathematical Logic 3(3-0) D
Logical connectives, truth tables, quantifiers, models, logical truth. Incompleteness and undecidability of elementary number theory. Prerequisite: MTH 332.

MTH 573 History of Mathematics 3(3-0) F, Sp
History of arithmetic, algebra, geometry, calculus. Prerequisites: MTH 332 or 341 or graduate status.

MTH 578 Combinatorics I 3(3-0) D
Construction of mathematical models, combinatorics and graph theory. Prerequisite: MTH 523.

MTH 586 Operations Research I 3(3-0) D
Mathematical theory and applications of mathematical programming. Linear programming duality, integer programming, mixed integer programming, and dynamic programming. Prerequisites: MTH 233, knowledge of FORTRAN.

MTH 587 Operations Research II 3(3-0) D
Continuation of 586. Theory and application of stochastic models in operations research. Inventory models, queuing theory, Markov chains, stochastic programming. Prerequisites: STA 382, MTH 586, or equivalent.

MTH 591 Seminar in the Solution of Putnam Problems 1-3(Spec) D
Problem-solving techniques demonstrated through solutions of the Putnam Examination problems. Designed particularly for those students interested in participating in the Putnam Examination. Prerequisite: MTH 233 and consent of instructor.

MTH 594 Seminar in Higher Mathematics 3(3-0) D
Class presentation of results of independent study, and final comprehensive written report in an approved subject. Prerequisite: One year of calculus and consent of instructor.

MTH 595 Special Topics in Mathematics Education 1-6(Spec) D
Subject matter not included in regular mathematics education course. May be taken for credit more than once, total credit not to exceed six hours. Does not count as one of two 400- or 500-level courses required on mathematics major. May not be counted toward a major or minor in mathematics except for students pursuing a B.S. in Ed. degree. Prerequisite: Consent of instructor.

MTH 596 Special Topics in Mathematics 1-6(Spec) D
Subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed six hours. Prerequisite: Consent of instructor.

MTH 597 Independent Study 1-6(Spec) F, Sp
Open to students with permission of instructor. May be taken for credit more than once, total credit not to exceed six hours.

MTH 619 Continuing Registration for Final Research Project 1(1-0)

MTH 623 The Theory of Groups 3(3-0) D
Introductory topics from classical theory of groups including mappings on groups, structure theorems for groups. Prerequisite: MTH 523 or consent of instructor.

MTH 625 Theory of Associative Rings 3(3-0) D
Theory of rings and ideals, including isomorphism theorems, unique factorization domains, and fields. Prerequisites: Any two of MTH 523, 525, and 623, or consent of instructor.

MTH 632 Introduction to Real Analysis and Its Applications 3(3-0) D
Development of integration theory with introduction to Lebesgue measure and integral on the real line. Elementary theory of normed spaces, bounded linear operators and linear functionals with applications. Prerequisite: MTH 532 or consent of instructor.

MTH 633 Real Variables 3(3-0) D
A study of functional analysis. Consideration of Banach spaces, metric spaces, and compact spaces. General measure and integration theory. Prerequisite: MTH 632 or consent of instructor.

MTH 634 Fourier Analysis 3(3-0)
Study of Fourier Series, convergence, summability, Fourier Transforms, distributions. Applications of fast Fourier Transform to Heat and Wave Equation. Signal Processing, Fourier Optics. Prerequisites: MTH 532.

MTH 636 Introduction to Complex Variables 3(3-0) D
Complex numbers, analytic functions, elementary functions, Cauchy's theorem, Integral formula, Taylor and Laurent series, residue theorem and its applications, Rouche's theorem. Prerequisite: MTH 532.

MTH 637 Complex Variable Theory 3(3-0) D
Conformal mapping, Mobius transformations, harmonic functions, Dirichlet problem, entire and meromorphic functions, analytic continuation, Reimann surfaces, applications of complex analysis. Prerequisite: MTH 636.

MTH 638 Theoretical Numerical Analysis 3(3-0) D
Numerical linear algebra with applications in linear and nonlinear systems. Interpolation and approximation and their applications to numerical differentiation, numerical integration, and differential equations. Prerequisite: MTH 532, corequisite 533.

MTH 641 Topics in Geometry 3(3-0) D
Advanced topics in geometry, foundations, non-Euclidean geometry. Prerequisite: MTH 341.

MTH 645 Point-Set Topology 3(3-0) D
A continuation of 545. Topics include convergence, axioms of countability and product spaces. Prerequisite: MTH 545.

MTH 651 Basic Ideas and Procedures in Elementary School Arithmetic 3(3-0) D
Mathematical concepts, fundamental processes, and mensuration formulas. Prerequisite: Successful completion of the Elementary Teachers Proficiency Tests.

MTH 652 The Teaching of Measurement 3(3-0) D
The history, concepts, and learning of measurement systems. The metric system and laboratory activities are emphasized. Prerequisite: Teaching experience or permission of instructor.

MTH 656 Teaching & Learning Mathematics with Technology 3(3-0)
Use of instructional technology for teaching and learning mathematics and an introduction to related research literature in mathematics and mathematics education. Prerequisites: MTH 566; or permission of instructor.

MTH 658 Workshop in Teaching Mathematics 1-6(Spec) D
Preparing materials and investigating methods for teaching mathematics in grades K-12. May be repeated, total credit not to exceed six hours. Prerequisite: Consent of the instructor.

MTH 660 Laboratory: Construction and Use of Teaching Aids in Mathematics 2(1-2) D
Multisensory aids produced and demonstrated. Devices and models constructed.

MTH 661 The Teaching of Middle School Mathematics 3(3-0) D
Objectives of mathematics instruction in the middle school. Prerequisite: minor in mathematics or teaching experience in middle or senior high school mathematics.

MTH 666 Seminar: Problems in the Teaching and Supervision of Secondary Mathematics 3(3-0) D
Current practices and significant research in secondary school mathematics.

MTH 671 Introduction to the Axiomatic Method 3(3-0) D
Study of the foundations of mathematics. Axiomatic set theory, ordinal and cardinal arithmetic. The axiom of choice and continuum hypothesis. Prerequisites: 521, 523, or 532, or consent of instructor.

MTH 673 History of Advanced Mathematics 3(3-0)
History of the development of modern mathematics from 1700 into the 20th century. Prerequisites: MTH 525 and 532.

MTH 678 Combinatorics II 3(3-0)
Finite geometries, combinatorial designs, strongly regular graphs, and error correcting codes. Prerequisites: MTH 578 and corequisite MTH 525.

MTH 692 Graduate Seminar in Mathematics Education 1-4(Spec)
Seminars will focus on current issues in mathematics education. May be taken for credit more than once, total credit not to exceed four hours. Three credits needed before it counts as elective on any graduate degree in mathematics. Prerequisites: Admission to graduate program in mathematics, or permission of instructor.

MTH 693 Graduate Seminar in Mathematics and Its Applications 1-4(Spec)
One hour seminars in subfields of mathematics and its applications; three credits needed before it counts as elective on graduate degrees in mathematics. Prerequisites: Graduate standing in mathematics and permission of instructor.

MTH 694 Practicum in Mathematics 3(3-0) D
To be taken during the last semester in the M.A. program. Experience in mathematics applications is gained by engaging in supervised consulting work in industry whenever possible. Prerequisites: MTH 623 and consent of instructor.

MTH 695 Special Topics in Mathematics Education 1-6(Spec) D
Consideration of subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed six hours. Prerequisite: Consent of instructor.

MTH 696 Special Topics in Mathematics 1-6(Spec) D
Consideration of subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed six hours. Prerequisite: Consent of instructor.

MTH 697 Independent Study 1-9(Spec) F, Sp
Open to graduate students in mathematics with permission of instructor. May be taken for credit more than once, total credit not to exceed nine hours.

MTH 698 Plan B Project 1-2(Spec)
Plan B paper is normally an expository paper or research project on an area or problem related to but in addition to material covered in a course, written under the direction of graduate faculty. Each Plan B project is one credit hour. May be taken for credit more than once. Total credit not to exceed two hours. CR/NC only. Prerequisites: Permission of advisor.

MTH 725 Topics in Algebra 3(3-0)
Advanced topics in abstract algebra. Designed to add breadth to the student's abstract algebra background and to open possible research areas. Prerequisites: MTH 625.

MTH 732 Functional Analysis 3(3-0)
Fundamentals of topological vector spaces, normed spaces, Banach and Hilbert spaces, functional on such spaces, operators on Banach and Hilbert spaces, spectral theorems, Banach algebras. Prerequisites: MTH 632 and 636.

MTH 734 Partial Differential Equations and Applications 3(3-0)
Solutions of partial differential equations by analytic and numerical techniques using standard methods, including Fourier series and Laplace transforms, perturbation, finite elements and finite differences. Prerequisites: MTH 334 and 636.

MTH 761 Methods for Teaching College Mathematics 3(3-0)
Methods in teaching undergraduate mathematics education including use of technology, cooperative learning, inquiry, and guided discovery. Students will create activities and debate issues surrounding undergraduate instruction. Prerequisites: Completion of 30 hours of coursework required for the Doctoral program and at least one semester of teaching experience at the post secondary level (this may include a teaching assistantship).

MTH 762 Research in Collegiate Mathematics Education 3(3-0)
Introduction to the research literature in collegiate mathematics education including learning theories for mathematics, literature search strategies, issues in mathematics education, and writing about and debating such issues. Prerequisites: Completion of 30 hours of coursework required for the Doctoral program and at least one semester of teaching experience at the post secondary level (this may include a teaching assistantship); MTH 761.

MTH 764 Qualitative Research Methods in Mathematics Education 3(3-0) D
Introduction to the qualitative research in mathematics education including research design, development of protocols, fieldwork, collecting and analyzing data and techniques for interviewing. Prerequisites: MTH 762; or permission of instructor.

MTH 766 Internship: College Teaching 3-6(Spec)
Teaching of undergraduate mathematics or statistics courses 200 level or above. Students will conduct their teaching internship under the supervision of a graduate faculty member. CR/NC only. Prerequisites: MTH 761; successful completion of all qualifying examinations.

MTH 767 Seminar in Collegiate Mathematics Education I 3(3-0) D
Use of a review of literature to focus research questions and to develop a research proposal. Each student develops a proposal for his/her dissertation research. This course requires a concurrent enrollment in MTH 692. Prerequisites: MTH 764; EDU 660

MTH 768 Seminar in Collegiate Mathematics Education II 3(3-0) D
Design and execution of a pilot study of student’s proposed dissertation research. This course requires a concurrent enrollment in MTH 692. Prerequisites: MTH 767

MTH 778 Topics in Combinatorics 3(3-0)
Advanced topics in combinatorics. Designed to add breadth to the student's combinatorial background and to open possible research areas. Prerequisites: MTH 678
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MTH 796 Special Topics in Mathematics 1-6(Spec) D
Consideration of subject matter not included in regular courses. May be taken for credit more than once; total credit not to exceed six hours. Prerequisites: Completion of 30 hours of coursework required for the Doctoral program.

MTH 797 Independent Study 1-9(Spec) F, Sp
Open to doctoral students in mathematics who have completed 30 hours of coursework required toward the Doctoral program, with permission of the instructor. May be taken for credit more than once; total credit not to exceed nine hours.

MTH 798 Thesis 1-6(Spec) D
CR/NC only.

MTH 898 Dissertation 1-30(Spec)
Doctoral Dissertation Research. CR/NC only.  Prerequisites: Permission of Department.
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