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Undergraduate Course Descriptions

Degrees and Courses

MATH 015 PRE-ALGEBRA (3-0-0)(F,S). Fundamental algebraic skills needed for MATH 25. Review of arithmetic (fractions, negative numbers, and percents), an introduction to graphing, and an introduction to variables, simplifying
algebraic expressions, and solving linear equations.

MATH 025 ELEMENTARY ALGEBRA (3-0-0). Brief review of arithmetic operations and their properties. Positive integer exponents, variables, algebraic expressions, solution of linear equations, definition of absolute value. Expansion of product of two binomials, factorization of quadratics, solution of quadratic equations by factoring. Two-dimensional Cartesian coordinate
systems, slope, equations of lines, solution of 2-by-2 linear systems. Simple“word problems.”

MATH 108 INTERMEDIATE ALGEBRA (4-0-4). Radicals, negative and rational exponents, completing the square, quadratic formula. Linear and quadratic inequalities (including absolute value); simple systems of equations and inequalities. Multiplication of polynomials; basic factorization techniques. Manipulation of rational expressions, compound fractions, rationalization of
denominator (or numerator). Introduction to the concept of function, graphs of functions and equations. Introduction to exponential and logarithmic expressions. Math 108 is NOT a Core course, and cannot be taken for credit after any MATH course numbered MATH 143 or higher. PREREQ: MATH 25 or satisfactory placement score.

MATH 123 QUANTITATIVE REASONING (3-0-3)(DLM). Survey of quantitative reasoning topics including deductive and inductive reasoning, benchmarks, and sense of scale. Topics will be applied in a conceptual way to interpretation of graphical information, descriptive and inferential statistics, elementary probability, and exponential growth. PREREQ: MATH 25 or satisfactory placement score.

MATH 143 COLLEGE ALGEBRA (3-0-3)(DLM). Emphasis on the concept of functions as mathematical entities; domain, range, algebraic operations, composition, inverses, graphing. Polynomial functions, division of polynomials, roots, factor theorem, complex numbers, fundamental theorem of algebra. Rational functions and asymptotes. Logarithmic and exponential functions. Multi-level algebraic manipulation of functional expressions – e.g. difference quotients. Conic sections and other topics from analytic geometry as time permits. Mathematical modeling based on Business and Science applications using algebraic functions will be prominent. Credit cannot be granted for both MATH 143 and MATH 147. PREREQ: MATH 108 or satisfactory placement score.

MATH 144 ANALYTIC TRIGONOMETRY (2-0-2). Right-triangle and circular function approaches to trigonometry. Trigonometric identities. Graphs of trigonometric functions; amplitude, frequency, phase shift. Inverse trigonometric functions and their graphs. Polar coordinates, polar representations of complex numbers. Credit cannot be granted for both MATH 144 and MATH 147. PREREQ: MATH 143 or satisfactory placement score.

MATH 147 PRECALCULUS (5-0-5). A single course equivalent to College Algebra (MATH 143) plus Analytic Trigonometry (MATH 144). Credit cannot be granted for both MATH 143 and MATH 147, nor for both MATH 144 and MATH 147. PREREQ: MATH 108 or satisfactory placement score.

MATH 157 STRUCTURE OF ARITHMETIC FOR TEACHERS (4-0-4)(F,S). Number systems from whole numbers through the reals: numeration, number operations, algorithms, and properties. Includes an integrated materials component which makes use of physical models and technology. PREREQ: MATH 108 or satisfactory placement score.

MATH 160 SURVEY OF CALCULUS (4-0-4)(DLM). A survey of the essentials of calculus, intended mainly for students in business and social sciences; emphasis on applications to such areas. Basic concepts and computational techniques for functions, derivatives, and integrals, with emphasis on polynomial, rational, exponential and logarithmic functions. Very brief introduction to calculus of functions of several variables. MATH 160 cannot be taken for credit after MATH 170. PREREQ: MATH 143 or satisfactory placement score.

MATH 170 CALCULUS I (4-0-4)(DLM). Definitions of limit, derivative and integral. Computation of the derivative, including logarithmic, exponential and trigonometric functions. Applications of the derivative, approximations, optimization, mean value theorem. Fundamental Theorem of Calculus, brief introduction to applications of the integral and to computations of antiderivatives. Intended for students in engineering, mathematics and the sciences. PREREQ: MATH 143 and MATH 144, or MATH 147, or satisfactory placement score.

MATH 175 CALCULUS II (4-0-4). A continuation of MATH 170. Applications of the integral, symbolic and numerical techniques of integration. Sequences and series, with an emphasis on power series and approximations, convergence and error bounds. Separable differential equations. Parametric curves in the plane and polar coordinates. Includes use of mathematical software such as Maple or Mathematica. PREREQ: MATH 170.

MATH 187 DISCRETE AND FOUNDATIONAL MATHEMATICS I (4-0-4)(F,S,SU). An introduction to the language and methods of reasoning used throughout mathematics and computer science. Emphasis on proof writing, including mathematical induction. Content drawn from propositional and predicate logic; elementary set theory; functions and relations; and basic principles of elementary number theory, combinatorial enumeration, and graph theory. PREREQ: MATH 144 or MATH 147 or satisfactory placement score.

MATH 211 GEOMETRY FOR THE CLASSROOM (3-0-3)(F). Activity-based treatment of geometry designed to extend preservice teachers’ understanding of geometry and its connections to other areas of mathematics. Topics may include: constructions, conjectures and proofs, dynamic geometry technology, transformations. It is recommended that this course be taken prior to MATH 311. PREREQ: MATH 147.

MATH 254 APPLIED STATISTICS WITH COMPUTERS (3-0-3)(DLM). Pre-calculus treatment of descriptive statistics, confidence intervals, hypothesis testing, simple linear regression, correlation, introduction to probability. Emphasis on reasoning, problem solving, communicating ideas, and applications to a wide variety of disciplines. Use of computer statistics packages to handle computations. Carries no credit after MATH 360 or MATH 361. PREREQ: MATH 108 or satisfactory placement score.

MATH 257 GEOMETRY AND PROBABILITY FOR TEACHERS (4-0-4)(F,S)(DLM). Probability, statistics, geometric concepts, principles, and measurement. Includes the use of physical materials and technology. PREREQ: MATH 157. MATH 261 STATISTICS FOR THE CLASSROOM (3-0-3)(S). Activity-based treatment of statistics designed to extend preservice teachers’ understanding of statistics and its connections to other areas of mathematics. Topics may include: simulations, hypothesis testing, dynamic statistical software and technology. It is recommended that this course be taken prior to MATH 361. PREREQ: MATH 147.

MATH 275 MULTIVARIABLE AND VECTOR CALCULUS (4-0-4). Vector algebra and geometry, functions of several variables, partial and directional derivatives, gradient, chain rule, optimization, multiple and iterated integrals. Parametric curves and surfaces, vector fields, divergence and curl, line and surface integrals, Green’s, Stokes’ and divergence theorems. Use of software such as Maple or Mathematica for visualization, exploration and solutions of“real-world” problems. PREREQ: MATH 175.

MATH 287 COMMUNICATION IN THE MATHEMATICAL SCIENCES (3-0-3)(F/S) (CID). Integrates mathematics content with the opportunity to develop proof writing and communication skills important in the mathematical sciences. Content is drawn from discrete and foundational math and elementary analysis. Introduction to and engagement with written and verbal communication practices characteristic to mathematical sciences. Introduction to and use of technologies that support communication in the mathematical sciences. PREREQ: MATH 187.

MATH 291 PUTNAM PRACTICE I (1-0-1)(F/S). Solving problems from previous Putnam examinations and related problems. May be repeated once for credit. (Pass/Fail.)

MATH 298 MATHEMATICS EDUCATION SEMINAR I (1-0-1)(S). This seminar is intended for Mathematics, Secondary Education majors in their first two years of the program. Topics will rotate. The focus of the seminar will be on building connections between areas and levels of mathematics, across university courses as well as with K-12 mathematics. May be repeated for credit.

MATH 301 INTRODUCTION TO LINEAR ALGEBRA (3-0-3)(F,S). Linear algebra from a matrix perspective with applications from the applied sciences. Topics include the algebra of matrices, methods for solving linear systems of equations, eigenvalues and eigenvectors, matrix decompositions, vector spaces, linear transformations, least squares, and numerical techniques. PREREQ: MATH 175.

MATH 305 INTRODUCTION TO ABSTRACT ALGEBRA AND NUMBER THEORY (3-0-3). Division algorithm. Greatest common divisor and Euclidean algorithm. Solving linear modular equations, Chinese Remainder Theorem, Primitive roots, solving modular quadratic equations. Introduction to group theory: motivation, definitions and basic properties. Finite cyclic groups, permutation groups, isomorphisms, Lagrange’s Theorem. PREREQ: MATH 187.

MATH 307 (COMPSCI 367) CRYPTOLOGY I (4-0-4)(F). Introduction to modular arithmetic. The study of: the RSA, El-Gamal, Diffie-Hellman, and Blum-Blum- Shrub public key cryptosystems, authentication and digital signatures, anonymity protocols. Protocol failures for these systems. Cross-listed with COMPSCI 367 and COMPSCI 567; credit may be received for only one of these three courses. PREREQ: MATH 170 and MATH 187.

MATH 308 (COMPSCI 368) CRYPTOLOGY II (4-0-4)(S). Introduction to groups, fields, polynomial rings and Lucas numbers. The study of: the Elliptic Curve, LUC, and NTRU public keys cryptosystems, authentication and digital signatures, anonymity protocols. Cross-listed with COMPSCI 368 and COMPSCI 568; credit may be received for only one of these three courses. PREREQ: MATH 170 and MATH 187.

MATH 311 FOUNDATIONS OF GEOMETRY (3-0-3)(S). Euclidean, non- Euclidean, and projective geometries from an axiomatic point of view. PREREQ: MATH 175 and MATH 187.

MATH 314 FOUNDATIONS OF ANALYSIS (3-0-3)(F/S). The real number system, completeness and compactness, sequences, continuity, foundations of the calculus. PREREQ: MATH 175 and MATH 287.

MATH 333 DIFFERENTIAL EQUATIONS WITH MATRIX THEORY (4-0-4). Use of differential equations to model phenomena in sciences and engineering. Solution of differential equations via analytic, qualitative and numerical techniques. Linear and nonlinear systems of differential equations. Introduction to matrix algebra, determinants, eigenvalues, and solutions of linear systems. Laplace transforms. PREREQ: MATH 175.

MATH 360 ENGINEERING STATISTICS (3-0-3)(F,S). Calculus based survey of statistical techniques used in Engineering. Data collection and organization, basic probability distributions, sampling, confidence intervals, hypothesis testing, process control, simple regression techniques, design of experiments. Emphasis on examples and applications to engineering, including product reliability, robust design and quality control. PREREQ: MATH 175.

MATH 361 PROBABILITY AND STATISTICS I (3-0-3)(F,S). Calculus-based treatment of probability theory, random variables, distributions, conditional probability, central limit theorem, descriptive statistics, estimation, tests of hypotheses,
and regression. Differs from MATH 360 by providing more thorough coverage of theoretical foundations and wider variety of applications drawn from natural and social sciences as well as engineering. PREREQ: MATH 175.

MATH 365 INTRODUCTION TO COMPUTATIONAL MATHEMATICS (3-0-3)(S). Uses Matlab and Maple software packages from a problem-oriented perspective with examples from the applied sciences. Matrix computations, solving linear systems, interpolation, optimization, least squares, discrete Fourier analysis, dynamical systems, computational efficiency, and accuracy.
Emphasis on critical thinking and problem solving using both numerical and symbolic software. PREREQ: MATH 175.

MATH 370 TECHNOLOGY IN THE SECONDARY MATHEMATICS CLASSROOM (3-0-3)(S). Essential skills and techniques for using technology in teaching and learning mathematics, problem solving, and mathematical thinking and reasoning. Mathematical topics selected from areas such as algebra, probability, statistics, and geometry. PREREQ: 6 credits of upper-division mathematics.

MATH 387 DISCRETE AND FOUNDATIONAL MATHEMATICS II (4-0-4)(S)(Odd years). A continuation of MATH 187, exploring more advanced topics in logic, set theory, and discrete mathematics. Proof techniques in predicate logic; diagonalization arguments in logic, set theory and computer science; ordered sets; mathematical methods in cryptography; advanced techniques of combinatorial enumeration; selected topics in graph theory. PREREQ: MATH 187.

MATH 400 MATHEMATICS SECONDARY EDUCATION CAPSTONE SEMINAR (1-0-1)(F/S)(FF). Provides support for students as they develop into professional educators. Explores lesson planning, collecting and analyzing assessment data, and reflective practices. PREREQ: MATH 490. COREQ: ED-CIFS 484 or ED-CIFS 485.

MATH 401 SENIOR THESIS IN THE MATHEMATICAL SCIENCES (1-0-1)(F/S)(FF). Independent mathematical work in an active and modern subject area of the mathematical sciences, guided by an official research faculty member in the department of mathematics and culminating in a written thesis presented in an appropriate public forum. PREREQ: One of MATH 403, 405, 411, 414, 426, 433, 436, 456, 462, 465, 471 or 480.

MATH 403 LINEAR ALGEBRA (3-0-3)(S). Concepts of linear algebra from a theoretical perspective. Topics include vector spaces and linear maps, dual vector spaces and quotient spaces, eigenvalues and eigenvectors, diagonalization, inner product spaces, adjoint transformations, orthogonal and unitary transformations, Jordan normal form. PREREQ: MATH 187 and one of MATH 301 or MATH 333.

MATH 405 ABSTRACT ALGEBRA (3-0-3)(F)(Odd years). Topics in group theory, ring theory and field theory with emphasis on finite and solvable groups, polynomials and factorization, extensions of fields. PREREQ: MATH 301 and MATH 305.

MATH 406 NUMBER THEORY (3-0-3)(S). Quadratic residues, Representing numbers as sums of squares, Continued fractions, Diophantine equations Including Pell’s equation, arithmetic functions and Mobius Inversion, the distribution of prime numbers, primality testing, factoring natural numbers. PREREQ: MATH 305.

MATH 411 INTRODUCTION TO TOPOLOGY (3-0-3)(F)(Even years). Sets, metric and topological spaces, product and quotient topology, continuous mappings, connectedness and compactness, homeomorphisms, fundamental group, covering spaces. PREREQ: MATH 314.

MATH 414 ADVANCED CALCULUS (4-0-4)(F). Introduction to fundamental elements of analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: infinite series, sequences and series of function, uniform convergences, theory of integration, implicit function theorem and applications. PREREQ: MATH 275, MATH 301, and MATH 314.

MATH 426 COMPLEX VARIABLES (3-0-3)(S)(Odd years). Complex numbers, functions of a complex variable, analytic functions, infinite series, infinite products, integration, proofs and applications of basic results of complex analysis. Topics include the Cauchy integral formulas, the residue theorem, the Riemann mapping theorem and conformal mapping. PREREQ: MATH 275.

MATH 433 ORDINARY DIFFERENTIAL EQUATIONS (3-0-3)(S)(Odd years). Theory of linear and nonlinear ordinary differential equations and their systems, including Dynamical systems theory. Properties of solutions including existence, uniqueness, asymptotic behavior, stability, singularities and boundedness. PREREQ: MATH 333.

MATH 436 PARTIAL DIFFERENTIAL EQUATIONS (3-0-3)(S)(Even years). Theory of partial differential equations and boundary value problems with applications to the physical sciences and engineering. Detailed analysis of the wave equation,
the heat equation, and Laplace’s equation using Fourier series and other tools. PREREQ: MATH 333.

MATH 456 LINEAR PROGRAMMING (3-0-3)(SU)(On Demand). Linear optimization problems and systems of linear inequalities. Algorithms include simplex method, two-phase method, duality theory, and interior point methods. Programming assignments. PREREQ: MATH 301.

MATH 462 PROBABILITY AND STATISTICS II (3-0-3)(F). Provides a solid foundation in the mathematical theory of statistics. Topics include probability theory, distributions and expectations of random variables, transformations of random variables, moment-generating functions, basic limit concepts and brief introduction to theory of estimation and hypothesis testing: point estimation, interval estimation and decision theory. PREREQ: MATH 275, MATH 301, and MATH 361.

MATH 464 MATHEMATICAL MODELING (3-0-3)(F). Introduction to mathematical modeling through case studies. Deterministic and probabilistic models. Optimization. Examples will be drawn from the physical, biological, and social
sciences. PREREQ: MATH 361 or PERM/INST.

MATH 465 NUMERICAL ANALYSIS I (3-0-3)(F). Approximation of functions, solutions of equations in one variable and of linear systems. Polynomial, cubic spline, and trigonometric interpolation. Optimization. Programming assignments. PREREQ: MATH 301 or MATH 333.

MATH 471 DATA ANALYSIS (3-0-3)(S)(Even years). Provides an application of the various disciplines in statistics to data analysis, introduction to statistical software, demonstration of interplay between probability models and statistical inference. Topics include introduction to concepts of random sampling and statistical inference, goodness of fit tests for model adequacy, outlier detection, estimation and testing hypotheses of means and variances, analysis of variance, regression analysis and contingency tables. PREREQ: MATH 361.

MATH 480 SENIOR PROJECT (3-4 credits)(Offered on demand). Research on a mathematical problem in the form of a thesis, or work on an applied problem which could be provided by local industry. PREREQ: Senior standing.

MATH 488 SENIOR OUTCOMES ASSESSMENT (0-0-0)(F,S). Required to graduate. Senior Mathematics and Applied Mathematics students will take an outcome assessment examination. Senior Mathematics Secondary Education students will submit a portfolio and should take MATH 488 during their student teaching. (Pass/Fail.) PREREQ: Senior standing.

MATH 490 MATHEMATICS IN SECONDARY SCHOOLS (3-0-3)(F). Objectives, content, and methods of secondary school mathematics programs. PREREQ: MATH 370 and six hours of mathematics completed at or above the 300-level or PERM/INST.

MATH 491 PUTNAM PRACTICE II (1-0-1)(F/S). Solving problems from previous Putnam examinations and related problems. May be repeated once for credit. (Pass/Fail.)

MATH 498 MATHEMATICS EDUCATION SEMINAR II (1-0-1)(F). This seminar is intended for Mathematics, Secondary Education majors in their last two years of the program. Topics will rotate. The focus of the seminar will be on building connections between areas and levels of mathematics, across university courses (particularly upper-division courses) as well as with K-12 mathematics. May be repeated for credit. PREREQ: Upper-division standing.