MATHEMATICS HONORS (MAT) MAT 1120. Calculus With Analytic Geometry II, Honors/(4).F. An honors section of MAT 1120. Enrollment by invitation of the departmental honors committee. A study of the logarithmic and exponential functions, circular functions and their inverses, techniques of integration, improper integrals, infinite series, Taylor polynomial and power series. Prerequisite: MAT 1110 (with a grade of C- or higher). (NUMERICAL DATA) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 2510. Sophomore Honors Seminar/(3).S. Proof techniques and their application to selected mathematical topics. Enrollment by invitation of the departmental honors committee. (Students may not receive credit for both MAT 2510 and MAT 2110.) Prerequisite: the calculus sequence. (WRITING; NUMERICAL DATA) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 3510. Junior Honors Seminar/(3).F;S. Development of selected concepts related to modern algebra, analysis, differential equations, and/or probability/statistics not generally found in the traditional curriculum. Enrollment by invitation of departmental honors committee. Prerequisite: calculus sequence, modern algebra, linear algebra. May be repeated for credit when content is not duplicated. (WRITING; NUMERICAL DATA) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 4510. Senior Honors Thesis/(3).F;S. Independent study and research. Thesis directed by a member of the Department of Mathematical Sciences. Prerequisite: completion of MAT 3510 and a 3.45 GPA in mathematics. Enrollment by invitation of the departmental honors committee. (WRITING) MATHEMATICS (MAT) MAT 0010. Developmental Mathematics/(3).F;S. This course is intended for those persons who have had previous exposure to Algebra but who still have deficiencies and are not prepared for MAT 1010 or MAT 1020. It is mandatory for students whose scores on the mathematics placement test indicate a deficiency. The course content is elementary algebra. Self-development and study skills are emphasized. The course meets five days per week, and counts as three hours credit toward course load and full-time student eligibility, but does not count toward hours required for graduation (see "Institutional Credit"). MAT 1010. Introduction to Mathematics/(4).F;S. This course is an introduction to mathematical problem solving for the non-technical liberal arts student. Emphasis is on the development of conceptual understanding rather than on computational drill. Using appropriate computational tools including computers is fundamental to the course. Problems are chosen from management sciences, statistics, and geometric and numerical patterns. Lecture three hours, laboratory two hours. Not open to students with credit for MAT 1020, 1025, 1030 or 1110. Prerequisite: must pass the placement test or MAT 0010. (Must also pass the English Placement Test or ENG 0900). (WRITING; NUMERICAL DATA; COMPUTER) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 1020. College Algebra with Applications/(4).F;S. A study of the algebraic concepts and their applications. Topics include algebraic relations and functions, equations, exponents and logarithms, inequalities, linear programming, and elementary probability. Problem solving will be emphasized throughout. Not open to students who have credit for MAT 1025, 1030 or 1110. Not appropriate preparation for MAT 1110. Prerequisite: must pass placement test or MAT 0010. (NUMERICAL DATA) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 1025. Algebra and Elementary Functions/(4).F;S. An overview of algebraic concepts and a thorough treatment of functions such as rational, logarithmic, exponential, and trigonometric. Included will be a rigorous treatment of analytic geometry. Recommended for students with less than four units of high school mathematics who plan to take MAT 1110. Students may not receive credit for MAT 1020 after receiving credit for MAT 1025. Not open to students who have credit for MAT 1110. Prerequisite: must pass placement test or MAT 0010. (NUMERICAL DATA) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 1030. Calculus With Business Applications/(4).F;S. An introduction to the concepts of differentiation and integration with particular emphasis upon their applications to solving problems that arise in business and economics. This course is designed primarily for business and economics majors and is not open to mathematics majors or students with credit for MAT 1110. Prerequisite: MAT 1020 or MAT 1025 or equivalent. (NUMERICAL DATA; COMPUTER) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 1110. Calculus With Analytic Geometry I/(4).F;S. A study of limits, continuity, differentiation, applications of the derivative, the differential, the definite integral, the fundamental theorem, and applications of the definite integral. Prerequisite: MAT 1025 (with a grade of C- or higher) or equivalent. (NUMERICAL DATA) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 1120. Calculus With Analytic Geometry II/(4).F;S. A study of the logarithmic and exponential functions, circular functions and their inverses, techniques of integration, improper integrals, infinite series, Taylor polynomial and power series. Prerequisite: MAT 1110 (with a grade of C- or higher). (NUMERICAL DATA) (CORE: MATHEMATICS) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 2030. Mathematics for the Elementary School Teacher/(3).F;S. This course is an introduction to mathematical concepts, processes, and reasoning for the prospective elementary school teacher. Topics include patterns, relationships, functions, data, probability, and statistics. Not open to mathematics majors or minors. Prerequisite: MAT 1010 or permission of instructor. (NUMERICAL DATA) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 2110. Techniques of Proof/(3).F. A study of methods of proof used in mathematics. Topics include propositional calculus, predicate calculus, and several first order theories. Prerequisite: MAT 1110 or permission of instructor. (WRITING) MAT 2130. Calculus With Analytic Geometry III/(4).F;S. A study of parametric equations, vectors, vector-valued functions, function of several variables, double and triple integrals, and vector analysis. Prerequisite: MAT 1120 (with a grade of C- or higher). (NUMERICAL DATA) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 2240. Introduction to Linear Algebra/(3).F;S. A study of vectors, matrices and linear transformations, principally in two and three dimensions, including treatments of systems of linear equations, determinants, and eigenvalues. Prerequisite: MAT 1120 or permission of instructor. (COMPUTER) MAT 2500. Independent Study/(1-3).F;S. MAT 3010. History of Mathematics/(2).On Demand. A study of the development of mathematical thought, mathematics and culture, and the persons who have made significant contributions to these. MAT 3030. Investigating Mathematics and Learning/(2).F;S. A study of mathematics and learning related to K-6 students and prospective teachers. Topics include assessment, number sense, numeration, and numerical operations. Selected assessment and instructional activities will be designed for implementation with elementary students during field placement experiences (CI/SPE 3000). Prerequisite: MAT 2030. (Same as CI 3030.) MAT 3110. Introduction to Modern Algebra/(3).F;S. Topics covered include sets, functions, equivalence relations, groups, rings, integral domains, fields and homomorphisms of these structures. Prerequisite: MAT 2240 or permission of the instructor. (WRITING) MAT 3130. Introduction to Differential Equations/(3).F;S. A theory of ordinary differential equations with applications and classical methods for their solutions including series and Laplace transform techniques. Some numerical methods and differential equations software might be introduced. Prerequisite: MAT 2130, with MAT 2240 recommended. MAT 3220. Introduction to Real Analysis I/(3).F. A treatment of the calculus of real valued functions of real variables including sequences, limits of function, continuity and differentiation. Prerequisite: MAT 2130 or permission of the instructor. (WRITING) MAT 3250. A Study of the Integers/(2).S. A study of the integers beginning with the Peano postulates and including the Fundamental Theorem of Arithmetic, Diophantine equations, congruences, Fermat's and Wilson's theorems, perfect numbers, Euler's theorem. Fermat's conjecture and the Goldbach conjecture. Emphasis will be on the historical as well as the theoretical development of the subject. Prerequisite: MAT 3110 or permission of the instructor. MAT 3310. Applications of Mathematics/(3).F. A survey of problems in the physical, engineering, biological and management sciences in which undergraduate level mathematics is applied in the formulation and solution. The course offers an opportunity for students to bring all of their mathematical background to bear on some specific real-world problems. Prerequisites: MAT 2130 and 2240 or permission of instructor. (WRITING; SPEAKING; NUMERICAL DATA; COMPUTER) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 3500. Independent Study/(1-3).F;S. MAT 3520. Instructional Assistance/(1).F;S. A supervised experience in the instructional process on the university level through direct participation in a classroom situation. Grading will be on a satisfactory/unsatisfactory basis only. Prerequisite: junior or senior standing. May be repeated for a total credit of three semester hours. MAT 3530-3549. Selected Topics/(1-4).On Demand. MAT 3610. Introduction to Geometry/(3).F;S. A study of the development of Euclidean geometry including both the synthetic and the metric approach. Topics to be considered include parallelism and similarity, measurements, ruler and compass constructions, and consideration of at least one non-Euclidean geometry. Prerequisite: MAT 1120. (SPEAKING) MAT 3910. Introduction to the Logic and Structure of Mathematics I/(4).F. To be included are topics from abstract algebra, geometry, number theory, mathematical logic, trigonometry and an intuitive approach to calculus. Prerequisite: Junior or senior standing or permission of instructor. (SPEAKING) MAT 3915. Investigating Geometry with Technology/(2).F. Investigations of topics in geometry set in technological environments. The course will emphasize explorations and mathematical reasoning. Prerequisite: Junior or senior standing or permission of instructor. (COMPUTER) MAT 3920. Introduction to the Logic and Structure of Mathematics II/(4).S. This course is an extension of 3910. Prerequisite: MAT 3910 or permission of the instructor. (SPEAKING) MAT 3940. Computer Algebra for Learning Mathematics/(2).S. An introduction to computer algebra systems such as Derive, Maple V, and Mathematica. The course will emphasize the use of symbolic algebra as a tool in learning and doing mathematics through the interplay of numeric, graphic and symbolic calculations. Prerequisite: Junior or senior standing or permission of instructor. MAT 4010. Undergraduate Seminar/(1-3).On Demand. (Permission to register must be given by the department chairman.) (WRITING) MAT 4015. Senior Seminar for Mathematics Majors in Education/(3).F;S. The course will address mathematics content and pedagogy issues of importance to secondary mathematics teachers. Class discussions, group activities, written assignments, and oral presentations will be integral parts of the course. The course will use a problem-solving approach to real world applications of a number of mathematics concepts commonly found in the high school mathematics curriculum. Open to seniors the semester prior to student teaching and to juniors by permission of instructor. (WRITING; SPEAKING; NUMERICAL DATA) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 4220. Introduction to Real Analysis II/(3).S. A continuation of MAT 3220, including the Riemann integral, infinite series, and sequences and series of functions. Prerequisite: MAT 3220. (SPEAKING) MAT 4310. Numerical Methods/(3).S. Development and application of numerical methods. Topics covered include computer arithmetic and error, interpolation and approximation, roots of nonlinear equations, and numerical integration. Also covered: solution techniques for either linear systems of equations or ordinary differential equations. Prerequisite: CS 1440 or equivalent; MAT 2130. (NUMERICAL DATA; COMPUTER) (ND Prerequisite: Passing the math placement test or successful completion of MAT 0010.) MAT 4340. Introduction to Operations Research/(3).On Demand. A thorough study of linear programming including duality theory and sensitivity analysis. At least two other topics related to mathematical applications in the management sciences queuing theory, Markov processes, game theory, decision analysis, network analysis, etc. will be covered. Prerequisites: MAT 2240 and either STT 3850 or 4250. [Dual-listed with MAT 5340.] MAT 4400. Senior Research/(1-3).F;S. A research project under the supervision of a mathematics faculty mentor. Written updates of progress will be completed every five weeks. A formal, typeset technical report of the results is to be submitted to the faculty upon completion of the project. Students cannot receive credit for both MAT 4510 and 4400. Prerequisite: one 4000- level mathematics course. (WRITING) MAT 4410. Fractals and Chaos/(3).S. An introduction to fractal geometry and chaos theory. Topics include fractal definition, self-similarity, dimension, generation of fractals, iteration of functions, dynamical systems, chaos definition, and attractors. Prerequisite: MAT 2130 or MAT 2240. MAT 4560. Methods of Applied Mathematics/(3).On Demand. The content may vary depending on the instructor. Suggested topics are: Fourier series; Sturm- Liouville problems; special functions and transforms; partial differential and nonlinear differential equations with applications; numerical methods. Prerequisites: MAT 3130 with MAT 3220 recommended. Knowledge of computers might be helpful. [Dual-listed with MAT 5360.] MAT 4570. Advanced Differential Equations/(3).F.Even-numbered years. Usual topics include: power series solutions; special functions; methods and theory of systems; existence and uniqueness theorems and continuations of solutions; Sturm theory; nonlinear differential equations; numerical methods. Prerequisites: MAT 2240, 3130, with MAT 3220 recommended. [Dual-listed with MAT 5370.] MAT 4580. Partial Differential Equations/(3).On Demand. Topics include: classification and properties of elliptic, hyperbolic, and parabolic equations; separation of variables; Laplace and Fourier transforms; initial and boundary value problems; eigenfunction expansions; solution of Laplace, wave and heat equations; and solitons. Prerequisite: MAT 3130. MAT 3220 recommended. [Dual-listed with MAT 5380.] MAT 4610. Foundations of Geometry/(2).SS. A treatment of projective geometry including both the synthetic and the analytic approach. Also to be considered is a study of the relation of Euclidean, affine and hyperbolic geometrics to projective geometry. Prerequisites: MAT 2240 and 3610. [Dual-listed with MAT 5961.] MAT 4710. Introduction to Topology/(3).F. A study of the basic concepts of general topological space including such topics as compactness, connectedness, product spaces, metric spaces, and continuous functions. Prerequisite: MAT 3110. (SPEAKING) [Dual-listed with MAT 5710.] MAT 4720. Abstract Algebra/(3).F. A study of group theory including quotient groups, the fundamental theorem of finite Abelian groups, and the Sylow theorems. Includes an introduction to rings with emphasis on Euclidean rings and other principal ideal domains. Prerequisite: MAT 3110 or permission of the instructor. (SPEAKING) [Dual-listed with MAT 5210.] MAT 4910. Informal Geometry/(3).F. An informal treatment of all aspects of geometry. The topics considered include congruence, measure of segments and angles, constructions, parallels and parallelograms, similarity, space geometry, areas and volumes, and measurements related to circles. Prerequisite: MAT 3910 or 3920 or permission of the instructor. (SPEAKING) [Dual-listed with MAT 5965.] MAT 4930. Basic Concepts of Probability and Statistics/(3).On Demand. This course examines the concepts underlying the elementary and middle school curriculum in probability and statistics. Probability models will be studied using both mathematical approaches and simulations. Statistics will be presented as a problem solving process involving question formulation, data collection, data analysis and the interpretation of results. Prerequisite: MAT 3910 or 3920 or permission of instructor. [Dual-listed with MAT 5935.] MAT 4990. Numerical Linear Algebra/(3).On Demand. Methods for solving systems of linear equations with an emphasis on large, sparse systems. LU factorization including storage schemes, graph theory, ordering algorithms, and block factorization. Iterative methods including Jacobi, SOR, and conjugate gradient. Eigenvalue methods including power method, QR factorization, and Lanczos methods. Parallel matrix computations. Prerequisite: MAT 4310. (Same as CS 4990/5990.) [Dual-listed with MAT 5390.]