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## Math Undergraduate

This provides brief undergraduate course descriptions, as in the Course Catalog. For more detailed Mathematics course outlines, see "Useful Information" or "Information for Faculty".

## Definition of Prefixes

- COP - Computer Programming
- MAA - Mathematics, Analysis
- MAC - Mathematics, Calculus and Pre-Calculus
- MAD - Mathematics, Discrete
- MAE - Mathematics, Applied Education
- MAP - Mathematics, Applied
- MAS - Mathematics, Algebraic Structures
- MAT - Mathematics, General
- MGF - Mathematics, General and Finite
- MHF - Mathematics, History and Foundations
- MTG - Mathematics, Topology and Geometry
- STA - Statistics

F-Fall semester offering; S-Spring semester offering; SS-Summer semester offering; V-Variable; D-offered only when demand is sufficient.

## Undergraduate Courses

**MAA 3200**Introduction to Advance Mathematics(3). Topics include: naive set theory, functions, cardinality, sequences of real numbers and limits. Emphasis on formal proofs. Prerequisite: MAC 2313. (F)**MAA 4211**Advanced Calculus (3). An intense study of the foundations of calculus. Topics may include: the real number system, continuity, differentiation, Riemann-Stieltjes integration, and series of functions. Note: The student must complete MAA 3200 before attempting this course. Prerequisites: MAC 2313, MAS 3105 and MAA 3200. (S)**MAA 4212**Topics in Advanced Calculus (3). A sequel to MAA 4211. Topics may include: theory of integration; analysis in several variables; and Fourier series. Prerequisite: MAA 4211.**MAA 4402**Complex Variables (3). An introduction to complex variables, beginning with the algebra and geometry of the complex number system. Topics include: complex functions; analytic functions; Cauchy's theorem and its consequences; Taylor and Laurent series; residue calculus; evaluation of real integrals and summation of series; conformal mapping. Prerequisites: MAC 2313, and MAP 2302 or MAA 4211. (F)**MAA 4504**Functional Analysis (3). Metric spaces, Banach spaces, L • p spaces, Hahn Banach theorem, Hilbert spaces, contractions, fixed point theorems and applications to differential equations and numerical analysis. Prerequisites: MAC 2313, MAS 3105.**MAC 1105**College Algebra (3). Operations on polynomials, rational expressions, radicals; lines, circles; inverse functions, exponential and logarithmic functions; systems of equations and inequalities. Prerequisite: Grade of C or higher in MAT 1033 or an appropriate score on placement exam for students with no prior college-level coursework in mathematics.**MAC 1114**Trigonometry (3). Trigonometric functions, identities, conditional equations, polar coordinates, vectors, polar graphs, complex numbers, DeMoivre's Theorem, conic sections. Student cannot receive credit for both this course and MAC 1147 Precalculus Algebra and Trigonometry. Prerequisite: Grade of C or higher in College Algebra. (F,S,SS)**MAC 1140**Precalculus Algebra : Polynomial, rational, exponential and logarithmic functions: zeros of polynomials; conic sections; determinant and Cramer's rule; sequences and series; induction; binomial theorem. Prerequisites: Grade of C or higher in MAC 1105 or an appropriate score on placement exam for students with no prior college-level coursework in mathematics.

**MAC 1147**Precalculus Algebra and Trigonometry: Polynomial and rational functions and their graphs. Trigonometric functions and their graphs, inverse trig functions, trig identities and conditional equations, solving right and oblique triangles. The conic sections, systems of equations, sequence and series, mathematical induction and the binomial theorem. Prerequisite: Grade of C or higher in MAC 1105 or an appropriate score on placement exam for students with no prior college-level coursework in mathematics.**MAC 2233**Calculus For Business (3). A one semester introduction to the basic notions of calculus. Specific topics include: Differential Calculus using polynomial, exponential and logarithmic functions, and its application to optimization; integral calculus with area and probability applications. Prerequisite: Grade of C or higher in MAC 1140 or an appropriate score on placement exam for students with no prior college-level coursework in mathematics.**MAC 2311**Calculus I (4). Introduction to derivatives, differentiation formulas, differentials, applications of the derivative; introduction to antiderivatives. Prerequisite: Grade of C or higher in MAC 1140 and MAC 1114 or in MAC 1147 or an appropriate score on placement exam for students with no prior college-level coursework in mathematics.**MAC 2312**Calculus II (4). Riemann sums, techniques of integration, applications of the integral, improper integrals, infinite series, Taylor series, polar and parametric functions. Prerequisite: MAC 2311, with a grade of C or better. (F,S,SS)**MAC 2313**Multivariable Calculus (4). This course deals with the differential and integral calculus of real valued multivariable functions. The topics include: directional and partial derivatives, gradients, and their applications; differential calculus of vector valued functions; multiple, iterated, line, and surface integrals. Prerequisite: MAC 2312 or equivalent with a grade of C or better. (F,S,SS)**MAD 1100**Mathematics for Information Technology (3). Introduction to discrete mathematical structures with emphasis on applications to information technology: binary numbers, logic, sets, functions, recursion, combinatorics, graph theory, Boolean algebra. Prerequisite: Grade of C or better in College Algebra.**MAD 2104**Discrete Mathematics (3). Sets, functions, relations, permutations, and combinations, propositional logic, matrix algebra, graphs and trees, Boolean algebra, switching circuits. Prerequisites: Grade of C or better in MAC 1105**MAD 3305**Graph Theory (3). An introduction to the study of graphs. Topics include the following: paths and circuits, connectedness, trees, shortest paths, networks, planar graphs, the coloring of graphs, and directed graphs. Applications of graphs to computer science will be discussed. Prerequisites: COP 2210 or CGS 2420 and either MAS 3105 or MAD 2104. (F,S,SS)**MAD 3401**Numerical Analysis (3). Basic ideas and techniques of numerical analysis. Topics include: finite differences, interpolation, solution of equations, numerical integration and differentiation, applications, introduction to applied linear algebra. This course will make extensive laboratory use of the computer facility. Prerequisites: COP 2210 or CGS 2420 and MAC 2312. (F,S,SS)**MAD 3512**Theory of Algorithms (3). Strings, formal languages, finite state machines, Turing machines, primitive recursive and recursive functions, recursive unsolvability. Prerequisite: MAD 2104. Computer Science majors must also take COT 3420. (F,S,SS)**MAD 4203**Introduction to Combinatorics (3). A survey of the basic techniques of combinatorial mathematics. Topics will include the Pigeonhole Principle, Binomial Coefficients, Inclusion-Exclusion, Recurrence Relations, and Generating Functions. Prerequisites: MAC 2313 or both MAC 2312 and MAD 2104. (SS)**MAE 3893**Mathematics Education Seminar (1). Provides students committed to Mathematics Education an early teaching experience and it will provide other students a low pressure opportunity to try out teaching. Prerequisite: MAC 2311.**MAE 3894**Early Teaching Experience (1). The goal of this course is to provide early in the program a unique opportunity for math education students to experience the tastes, the challenges, and the rewards involved in the teaching of math. Prerequisite: MAC 2311.**MAP 2302**Differential Equations (3). An introduction to differential equations and their applications, based upon a knowledge of calculus. Topics to include: initial value problems of the first order, numerical solutions, systems of differential equations, linear differential equations, Laplace transforms, series solutions. Prerequisite: MAC 2312 with a grade of C or better. (F,S,SS)**MAP 3103**Mathematical Modeling and Applications (3). A course to provide an understanding of the use of mathematical models in the description of the real world. Basic principles in the philosophy of formal model building as well as specific models will be considered. Prerequisites: MAS 3105 and either MAC 2313 or MAP 2302. (D)**MAP 3104**Topics in Mathematical Modeling (3). A sequel to MAP 3103. In-depth study of techniques listed for MAP 3103. Prerequisite: MAP 3103. (D)**MAP 4104C**Topics in Mathematical Modeling (4). This course is an introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. We will discuss formulation of the problem, derivation of the solution, and interpretation of the results. This course consists of 3 hours regular lecture and 1 hour lab. Prerequisite: MAC 2313, MAP 2302 and MAS 3105.**MAP 4315**Nonlinear Dynamics with Applications to Sciences (3). The use of mathematics in order to solve real-world problems in all areas of science. Among other topics, the course will also give a first introduction into the chaos theory. Prerequisites: MAC 2313 and/or MAP 2302 and/or MAS 3105, or permission of the instructor.**MAP 4401**Advanced Differential Equations (3). A second course in differential equations. Topics may include: Bessel functions and other special functions arising from classical differential equations, Sturm-Liouville problems, partial differential equations, transform techniques. Prerequisites: MAP 2302 and MAC 2313. (S)**MAS 3105**Linear Algebra (3). An introduction to the topics in linear algebra most often used in applications. Topics include: matrices and their applications; simultaneous linear equations and elementary operations; linear dependence; vector spaces; rank and inverses; inner products and 'best' approximations; numerical solutions of simultaneous linear equations; eigenvalues and eigenvectors; iterative methods for calculating eigenvalues; and systems of linear equations. Prerequisite: MAC 2312. (F,S,SS)**MAS 4203**Number Theory (3). Topics to be discussed are selected from the following: congruence's, Diophantine equations, distribution of primes, primitive roots, quadratic reciprocity, and classical theorems of number theory. Prerequisites: MAA 3200 or MAS 3105 or MTG 3212 (SS).**MAS 4301**Algebraic Structures (3). An introduction to abstract mathematical structures of modern algebra. Fundamental concepts of groups, rings, and fields will be studied. Note: the student must complete MAA 3200 before attempting this course. Prerequisites: MAS 3105 and MAA 3200. (S)**MAS 4302**Topics in Algebraic Structures (3). A sequel to Algebraic Structures. Topics may include: a continuation of the study of groups, rings and/or fields; polynomial domains; Euclidean domains; and Galois theory. Prerequisite: MAS 4301. (D)**MAS 4310**Introduction to Algebraic Geometry (3). Introduction to the theory of affine and projective algebraic varieties over algebraically closed ground field. Various examples are discussed. Prerequisites: MAS 4301, MAA 4402.**MAT 2949**Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Co-op program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus I and COP 2210.**MAT 3905**Independent Study (VAR). Individual conferences, assigned readings, and reports on independent investigations.**MAT 3930**Special Topics (VAR). A course designed to give groups of students an opportunity to pursue special studies not otherwise offered.**MAT 3949**Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Co-op Program. Limited to students admitted to the Co-op Program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus II and COP 2212.**MAT 4905**Independent Study (VAR). Individual conferences, assigned readings, and reports on independent investigations.**MAT 4930**Special Topics (VAR). A course designed to give groups of students an opportunity to pursue special studies not otherwise offered.**MAT 4943**Mathematical Sciences Internship (VAR). A special program to encourage students to get on-the-job experience in computer sciences, statistics, or mathematics in an industrial enterprise, governmental agency or other organization. Requirements: minimum grade of 'B' or higher in all courses in the major area, and approval by Departmental Internship Committee. Application is required at least one term in advance of registration for this course.**MAT 4949**Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Co-op Program. Limited to students admitted to the Co-op Program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus II, a statistics course, and COP 2120.**MAP 4412**Introduction to Fourier Analysis (3). Abstract measure theory, L • p spaces, Fourier transform in L • 2, Plancherel theorem, Fourier transform of distributions, fundamental solutions of differential equations, application wavelets. Prerequisites: MAC 2313, MAS 3105.**MGF 1106**- Finite Mathematics (3). Study of concepts and applications involving finite mathematical processes such as sets, combinatorial techniques, formal logic, discrete probability, linear systems, matrices, linear programming. Prerequisite: Working knowledge of high school algebra. (F,S,SS)**MGF 1107**- The Mathematics of Social Choice and Decision Making (3). Voting systems and their desirable properties. Weighted voting systems, fair division procedures, apportionment methods and game theory.**MHF 1202**Sets, Logic, and Writing (3). Intuitive set theory, introduction to symbolic logic, the relationship between them and their applications to problem-solving, involving writing as a crucial tool in the course. Prerequisite: permission of Undergraduate Studies. (SS)**MHF 3404**History of Mathematics (3). Development of mathematical thought through the ages. Topics may include equation solving, trigonometry, astronomy, and calculus. Prerequisite: MAC 2312. (V)**MHF 4102**Axiomatic Set Theory (3). Axioms of set theory, order and well-foundedness, cardinal numbers, ordinal numbers, axiom of choice, special topics. Prerequisites: MAA 3200 or permission of instructor. (S, alternate years)**MHF 4302**Mathematical Logic (3). A study of formal logical systems and their applications to the foundations of mathematics. Topics to be selected from the following: definition of mathematical proofs; set theory; analysis formalized with the predicate calculus; theorem of Godel and Church; recursive function theory; and idealized computers. Prerequisite: MAA 3200 or MAD 3512. (S, alternate years)**MHF 4401**Topics in the History of Modern Mathematics (3). Riemannian geometry, relativity and other topics at discretion of instructor. Prerequisites: MAA 3200 or MAD 3512. (S, alternate years)

**MTG 1204**Geometry for Education (3). Introduction for teachers to basic concepts of Euclidean geometry with ideas and activities adaptable to classroom. Students study and analyze pattern, learning and enhancing analytic, creative and visualization skills.**MTG 3212**College Geometry (3). A study of the basic structure of Euclidean geometry together with topics from advanced Euclidean geometry and non-Euclidean geometry. Prerequisite: Calculus II or permission of the instructor. (S)**MTG 4254**Differential Geometry (3). Hypersurfaces in Rn. Geodesics and curvature. Parametrisation of surfaces, abstract manifolds. Integration, surfaces with boundary, Stokes Theorem. Isometries and intrinsic geometry. Gauss-Bonnet Theorem. Prerequisites: MAC 2311, MAS 3105, MAP 2302 or permission of the instructor.**MTG 4302**Topology (3). An introductory course in topology requiring a prerequisite knowledge of calculus. Topics to be discussed will be selected from the following: topological spaces, metric spaces, continuity, completeness, compactness, separation axioms, products spaces, subspaces, convergence, and homotopy theory. Prerequisites: MAC 2313, MAS 3105, and MAA 3200. (D)**STA 4603-STA 4604**Mathematical Techniques of Operations Research I and II (3-3) . An introduction to those topics in mathematics associated with studies in operations research. Topics include the following: linear programming and related topics, dynamic programming, queuing theory, computer simulation, network analysis, inventory theory, decision theory, integer programming. Prerequisites: MAS 3105 and either STA 3033 or STA 3322. (D)