## Course Descriptions for (MATH) 1XX through 6XX

**For more information, see Bulletin.sc.edu's Mathematics page. **

**111 — Basic College Mathematics (3)** Basic college algebra; linear and quadratic equations, inequalities, functions and graphs of functions, exponential and logarithm functions, systems of equations. Credit may not be received for both MATH 111 and 115.**Prerequisites:** placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/

**111 I - Intensive Basic College Mathematics (4) **An intensive treatment of the topics covered in MATH 111.**Prerequisites:** placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/

**112 - Trigonometry (2) **Topics in trigonometry specifically needed for MATH 141, 142, 241. Circular functions, analytic trigonometry, applications of trigonometry. Credit may not be received for both MATH 112 and 115**Prerequisites:** C or better in MATH 111 or 111L, or placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/

**115 - Precalculus Mathematics (4) **Topics in algebra and trigonometry specifically needed for MATH 141, 142, 241. Subsets of the real line, absolute value; polynomial, rational, inverse, logarithmic, exponential functions; circular functions; analytic trigonometry. Credit may not be received for both MATH 111 and 115 or both MATH 112 and 115.**Prerequisites:** C or better in MATH 111 or 111L, or placement through Precalculus version of the Mathematics Placement Test: http://assess.math.sc.edu/

**116 - Brief Precalculus Mathematics (2)** Essential algebra and trigonometry topics for Calculus, including working with equations that involve polynomials, rational functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. Intended for students with prior experience in Precalculus, but not ready for MATH 141.**Prerequisites:** C or better in MATH 115, or placement through Precalculus version of the Mathematics Placement Test: http://assess.math.sc.edu/

**122 - Calculus for Business Administration and Social Sciences (3)** Derivatives and integrals of elementary algebraic, exponential, and logarithmic functions. Maxima, minima, rate of change, motion, work, area under a curve, and volume.**Prerequisites:** C or better in MATH 111 or 111L, or placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/

**141 - Calculus I (4) **Functions, limits, derivatives, introduction to integrals, the Fundamental Theorem of Calculus, applications of derivatives and integrals.**Prerequisites:** C or better in MATH 112, 115, 116, or placement through Precalculus version of the Mathematics Placement Test: http://assess.math.sc.edu/

**142 - Calculus II (4) **Methods of integration, sequences and series, approximations.**Prerequisites:** C or better in MATH 141.

**151 - Calculus Workshop I (2)** Small study group practice in applications of calculus. For elective credit only.**Prerequisites:** Concurrent registration in MATH 141

**152 - Calculus Workshop II** **(2)** Small study group practice in applications of calculus. For elective credit only.**Prerequisites:** Concurrent registration in MATH 142

**170 - Finite Mathematics (3)** Elementary matrix theory; systems of linear equations; permutations and combinations; probability and Markov chains; linear programming and game theory.**Prerequisites:** C or better in MATH 111, 111L, or 112, or placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/

**172 - Mathematical Modeling for the Life Sciences (3) **Biological modeling with differential and difference equations; techniques of model modifications; analytic, numerical, and graphical solution methods; equilibria, stability, and long-term system behavior; geometric series; vectors, matrices, eigenvalues, and eigenvectors. Applications principally to population dynamics and compartment models.**Prerequisites:** Concurrent registration in MATH 142

**174 - Discrete Mathematics for Computer Science (3)** Induction, complexity, elementary counting, combinations and permutations, recursion and recurrence relations, graphs and trees; discussion of the design and analysis of algorithms–with emphasis on sorting and searching.**Prerequisites:** C or better in any 100-level MATH course or placement through either version of the Mathematics Placement Test: http://assess.math.sc.edu/

**198 - Introduction to Careers and Research in the Mathematical Sciences. (1) **An overview of different areas of mathematical research and career opportunities for mathematics majors. Pass/fail only.**Prerequisites:** C or better in MATH 141.

**221 - Basic Concepts of Elementary Mathematics I (3)** The meaning of number, fundamental operations of arithmetic, the structure of the real number system and its subsystems, elementary number theory. Open only to students in elementary or early childhood teacher certification.**Prerequisites:** C or better in MATH 111/111I, or by placement through Algebra version of the Mathematics Placement Test: http://assess.math.sc.edu/, or consent of the department

**222 - Basic Concepts of Elementary Mathematics II (3) **Informal geometry and basic concepts of algebra. Open only to students in elementary or early childhood teacher certification.**Prerequisites:** grade of C or better in MATH 221, or consent of the department

**241 - Vector Calculus (3) **Vector algebra, geometry of three-dimensional space; lines, planes, and curves in space; polar, cylindrical, and spherical coordinate systems; partial differentiation, max-min theory; multiple and iterated integration, line integrals, and Green’s theorem in the plane.**Prerequisites:** C or better in MATH 142, or consent of the department

**242 - Elementary Differential Equations (3)** Ordinary differential equations of first order, higher order linear equations, Laplace transform methods, series methods; numerical solution of differential equations. Applications to physical sciences and engineering.**Prerequisites:** C or better in MATH 142, or consent of the department

**300 - Transition to Advanced Mathematics (3) **Rigor of mathematical thinking and proof writing via logic, sets, and functions. Intended to bridge the gap between lower-level (computational-based) and upper-level (proof-based) mathematics courses.**Prerequisites:** C or better in MATH 142, or consent of the Undergraduate Director

**344 - Applied Linear Algebra (3) **General solutions of systems of linear equations, vector spaces and subspaces, linear transformations, singular value decompositions, and generalized inverse.**Prerequisites:** C or better in MATH 142, or consent of the Undergraduate Director

**344L - Applied Linear Algebra Lab (1) **Computer based applications of linear algebra for science and engineering students. Topics include numerical analysis of matrices, direct and indirect methods for solving linear systems, and least squares method (regression). Typical applications include practical issues related to discrete Markov porcesses, image compression, and linear programming.**Prerequisites:** C or better or concurrent enrollment in MATH 344

**374 - Discrete Structures (3) **Propositional and predicate logic; proof techniques; recursion and recurrence relations; sets, combinatorics, and probability; functions, relations, and matrices; algebraic structures.**Prerequisites:** C or better in both MATH 142 and CSCE 146

**399 - Independent Study (3-9) **Contract approved by instructor, advisor, and department chair is required for undergraduate students.

**401 - Conceptual History of Mathematics (3) **Topics from the history of mathematics emphasizing the 17th century to the present. Various mathematical concepts are discussed and their development traced. For elective or Group II credit only.**Prerequisites:** C or better in MATH 122, or 141, or consent of the Undergraduate Director

**499 - Undergraduate Research (1-3) **Research on a specific mathematical subject area. The specific content of the research project must be outlined in a proposal that must be approved by the instructor and the Undergraduate Director. Intended for students pursuing the B.S. in Mathematics with Distinction. (Pass-Fail grading only.)

**511 - Probability (3) **Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities, moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate, and bivariate normal distributions.**Prerequisites:** C or higher or concurrent enrollement in MATH 241 or consent of the Undergraduate Director

**514 - Financial Mathematics I (3) **Probability spaces. Random variables. Mean and variance. Geometric Brownian Motion and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage arguments. Options pricing and the Black-Scholes formula.**Prerequisites:** C or higher or concurrent enrollement in MATH 241 or consent of the Undergraduate Director

**515 - Financial Mathematics II (3) **Convex sets. Separating Hyperplane Theorem. Fundamental Theorem of Asset Pricing. Risk and expected return. Minimum variance portfolios. Capital Asset Pricing Model. Martingales and options pricing. Optimization models and dynamic programming.**Prerequisites:** C or better in MATH 514 or STAT 522 or consent of the Undergraduate Director

**520 - Ordinary Differential Equations (3) **Differential equations of the first order, linear systems of ordinary differential equations, elementary qualitative properties of nonlinear systems.**Prerequisites:** C or better in MATH 344 or 544; or consent of the Undergraduate Director

**521 - Boundary Value Problems and Partial Differential Equations (3) **Laplace transforms, two-point boundary value problems and Green’s functions, boundary value problems in partial differential equations, eigenfunction expansions and separation of variables, transform methods for solving PDE’s, Green’s functions for PDE’s, and the method of characteristics.**Prerequisites:** C or better in MATH 520 or MATH 241 and 242 or consent of the Undergraduate Director

**522 - Wavelets (3) **Basic principles and methods of Fourier transforms, wavelets, and multiresolution analysis; applications to differential equations, data compression, and signal and image processing; development of numerical algorithms. Computer implementation.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**523 - Mathematical Modeling of Population Biology (3) **Applications of differential and difference equations and linear algebra modeling the dynamics of populations, with emphasis on stability and oscillation. Critical analysis of current publications with computer simulation of models.**Prerequisites:** C or better in MATH 142, BIOL 301, or MSCI 311 recommended

**524 - Nonlinear Optimization (3) **Descent methods, conjugate direction methods, and Quasi-Newton algorithms for unconstrained optimization; globally convergent hybrid algorithm; primal, penalty, and barrier methods for constrained optimization. Computer implementation of algorithms.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**525 - Mathematical Game Theory (3) **Two-person zero-sum games, minimax theorem, utility theory, n-person games, market games, stability.**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344, or consent of the Undergraduate Director

**526 - Numerical Linear Algebra (4) **Matrix algebra, Gauss elimination, iterative methods; overdetermined systems and least squares; eigenvalues, eigenvectors; numerical software. Computer implementation. Credit may not be received for both MATH 526 and MATH 544.**Prerequisites:** Concurrent enrollment in or C or better in MATH 142 or consent of the Undergraduate Director

**527 - Numerical Analysis (3) **Interpolation and approximation of functions; solution of algebraic equations; numerical differentiation and integration; numerical solutions of ordinary differential equations and boundary value problems; computer implementation of algorithms.**Prerequisites:** C or better MATH 520 or in both MATH 242 and 344, or consent of the Undergraduate Director

**531 - Foundations of Geometry (3) **The study of geometry as a logical system based upon postulates and undefined terms. The fundamental concepts and relations of Euclidean geometry developed rigorously on the basis of a set of postulates. Some topics from non-Euclidean geometry.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**532 - Modern Geometry (3) **Projective geometry, theorem of Desargues, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**533 - Elementary Geometric Topology (3) **Topology of the line, plane, and space, Jordan curve theorem, Brouwer fixed point theorem, Euler characteristic of polyhedra, orientable and non-orientable surfaces, classification of surfaces, network topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**534 - Elements of General Topology (3) **Elementary properties of sets, functions, spaces, maps, separation axioms, compactness, completeness, convergence, connectedness, path connectedness, embedding and extension theorems, metric spaces, and compactification.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**540 - Modern Applied Algebra (3) **Finite structures useful in applied areas. Binary relations, Boolean algebras, applications to optimization, and realization of finite state machines.**Prerequisites:** MATH 241

**541 - Algebraic Coding Theory (3) **Error-correcting codes, polynomial rings, cyclic codes, finite fields, BCH codes**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344 or consent of the Undergraduate Director

**544 - Linear Algebra (3) **Vectors, vector spaces, and subspaces; geometry of finite dimensional Euclidean space; linear transformations; eigenvalues on theoretical concepts, logic, and meethods.**Prerequisites:** C or better in MATH 300, or consent of the Undergraduate Director

**544L - Linear Algebra Lab (1) **Computer-based applications of linear algebra for mathematics students. Topics include numerical analysis of matrices, direct and indirect methods for solving linear systems, and least squares method (regression). Typical applications include theoretical and practical issues related to discrete Markov’s processes, image compression, and linear programming.**Prerequisites:** Prereq or coreq: C or better or concurrent enrollment in MATH 544.

**546 - Algebraic Structures I (3) **Permutation groups; abstract groups; introduction to algebraic structures through study of subgroups, quotient groups, homomorphisms, isomorphisms, direct product; decompositions; introduction to rings and fields.

**Prerequisites:**C or better in MATH 544 or consent of the Undergraduate Director

**547 - Algebraic Structures II (3) **Rings, ideals, polynomial rings, unique factorization domains; structure of finite groups; topics from: fields, field extensions, Euclidean constructions, modules over principal ideal domains (canonical forms).**Prerequisites**: C or higher in MATH 546 or consent of the Undergraduate Director

**550 - Vector Analysis (3) **Vector fields, line and path integrals, orientation and parametrization of lines and surfaces, change of variables and Jacobians, oriented surface integrals, theorems of Green, Gauss, and Stokes; introduction to tensor analysis.**Prerequisites:** C or higher in MATH 241 or consent of the Undergraduate Director

**551 - Introduction to Differential Geometry (3) **Parametrized curves, regular curves and surfaces, change of parameters, tangent planes, the differential of a map, the Gauss map, first and second fundamental forms, vector fields, geodesics, and the exponential map.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**552 - Applied Complex Variables (3) **Complex integration, calculus of residues, conformal mapping, Taylor and Laurent Series expansions, applications.**Prerequisites:** C or better in MATH 241 or consent of the Undergraduate Director

**554 - Analysis I (3) **Least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform continuity, differentiation, Riemann integral and fundamental theorem of calculus.**Prerequisites:** C or better in MATH 300 and either at last one of 511, 520, 534, 550, or 552, or consent of the Undergraduate Director

**555 - Analysis II (3) **Riemann-Stieltjes integral, infinite series, sequences and series of functions, uniform convergence, Weierstrass approximation theorem, selected topics from Fourier series or Lebesgue integration.**Prerequisites:** C or better in MATH 554 or consent of the Undergraduate Director

**561 - Introduction to Mathematical Logic (3) **Syntax and semantics of formal languages; sentential logic, proofs in first order logic; Godel’s completeness theorem; compactness theorem and applications; cardinals and ordinals; the Lowenheim-Skolem-Tarski theorem; Beth’s definability theorem; effectively computable functions; Godel’s incompleteness theorem; undecidable theories.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**562 - Theory of Computation (3) **Basic theoretical principles of computing as modeled by formal languages and automata; computability and computational complexity.**Prerequisites:** C or better in CSCE 350 or MATH 344 or 544 or 574 or consent of the Undergraduate Director

**570 - Discrete Optimization (3) **Discrete mathematical models. Applications to such problems as resource allocation and transportation. Topics include linear programming, integer programming, network analysis, and dynamic programming.**Prerequisites:** C or better in MATH 344 or 544, or consent of the Undergraduate Director

**574 - Discrete Mathematics I (3) **Mathematical models; mathematical reasoning; enumeration; induction and recursion; tree structures; networks and graphs; analysis of algorithms.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**575 - Discrete Mathematics II (3) **A continuation of MATH 574. Inversion formulas; Polya counting; combinatorial designs; minimax theorems; probabilistic methods; Ramsey theory; other topics.**Prerequisites:** C or better in MATH 574 or consent of the Undergraduate Director

**576 - Combinatorial Game Theory (3) **Winning in certain combinatorial games such as Nim, Hackenbush, and Domineering. Equalities and inequalities among games, Sprague-Grundy theory of impartial games, games which are numbers.**Prerequisites:** C or better in MATH 344, 544, or 574, or consent of the Undergraduate Director

**580 - Elementary Number Theory (3) **Divisibility, primes, congruences, quadratic residues, numerical functions. Diophantine equations.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**587 - Introduction to Cryptography (3) **Design of secret codes for secure communication, including encryption and integrity verification: ciphers, cryptographic hashing, and public key cryptosystems such as RSA. Mathematical principles underlying encryption. Code-breaking techniques. Cryptographic protocols.**Prerequisites**: C or better in CSCE 145 or in MATH 241, and in either CSCE 355 or MATH 574, or consent of the Undergraduate Director

**590 - Undergraduate Seminar (1-3) **A review of literature in specific subject areas involving student presentations. Content varies and will be announced in the Master Schedule of Classes by suffix and title. Pass-fail grading. For undergraduate credit only.**Prerequisites:** consent of instructor

**599 - Topics in Mathematics (1-3) **Recent developments in pure and applied mathematics selected to meet current faculty and student interest.**602 - An Inductive Approach to Geometry (3) **This course is designed for middle-level pre-service mathematics teachers. This course covers geometric reasoning, Euclidean geometry, congruence, area, volume, similarity, symmetry, vectors, and transformations. Dynamic software will be utilized to explore geometry concepts.

**Prerequisites:**C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**603 - Inquiry Approach to Algebra (3) **This course introduces basic concepts in number theory and modern algebra that provide the foundation for middle level arithmetic and algebra. Topics include: algebraic reasoning, patterns, inductive reasoning, deductive reasoning, arithmetic and algebra of integers, algebraic systems, algebraic modeling, and axiomatic mathematics. This course cannot be used for credit towards a major in mathematics.**Prerequisites:** C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**650 - AP Calculus for Teachers (3) **A thorough study of the topics to be presented in AP calculus, including limits of functions, differentiation, integration, infinite series, and applications. (Not intended for degree programs in mathematics.)** Prerequisites**: current secondary high school teacher certification in mathematics and a C or better in at least 6 hours of calculus, or consent of the Undergraduate Director