Mathematics 1 MATH 142 - Calculus II (4 Credits) MATHEMATICS Methods of integration, sequences and series, approximations. Four classroom hours and one laboratory hour per week. Courses Prerequisites: C or better in MATH 141. MATH 111 - Basic College Mathematics (3 Credits) Carolina Core: ARP Basic college algebra; linear and quadratic equations, inequalities, MATH 151 - Calculus Workshop I (1 Credit) functions and graphs of functions, exponential and logarithm functions, Small study group practice in applications of calculus. For elective credit systems of equations. only. Prerequisites: placement through Algebra version of the Mathematics Corequisite: MATH 141. Placement Test. MATH 152 - Calculus Workshop II (1 Credit) MATH 111I - Intensive Basic College Mathematics (4 Credits) MATH 152 is part of a pilot program at UofSC to help at-risk students in An intensive treatment of the topics covered in MATH 111. Calculus I & II. It is for elective credit only. The class will consist of small Prerequisites: placement through Algebra version of the Mathematics study group practice in applications of calculus. Placement Test. Corequisite: MATH 142 MATH 112 - Trigonometry (2 Credits) MATH 170 - Finite Mathematics (3 Credits) Topics in trigonometry specifically needed for MATH 141, MATH 142, Elementary matrix theory; systems of linear equations; permutations and MATH 241. Circular functions, analytic trigonometry, applications combinations; probability and Markov chains; linear programming and of trigonometry. Credit may not be received for both MATH 112 and game theory. MATH 115. Prerequisites: C or better in MATH 111 or MATH 111I or MATH 122, or Prerequisites: C or better in MATH 111 or MATH 111I, or placement placement through Algebra version of the Mathematics Placement Test. through Algebra version of the Mathematics Placement Test. Carolina Core: ARP MATH 115 - Precalculus Mathematics (4 Credits) Topics in algebra and trigonometry specifically needed for MATH 141, MATH 172 - Mathematical Modeling for the Life Sciences (3 Credits) MATH 142, MATH 241. Subsets of the real line, absolute value; Biological modeling with differential and difference equations; techniques polynomial, rational, inverse, logarithmic, exponential functions; circular of model modifications; analytic, numerical, and graphical solution functions; analytic trigonometry. methods; equilibria, stability, and long-term system behavior; geometric Prerequisites: C or better in MATH 111or MATH 111I, or placement series; vectors, matrices, eigenvalues, and eigenvectors. Applications through Precalculus version of the Mathematics Placement Test. principally to population dynamics and compartment models. Prerequisites: C or better in MATH 122 or MATH 141. MATH 116 - Brief Precalculus Mathematics (2 Credits) Essential algebra and trigonometry topics for Calculus, including working Carolina Core: ARP with equations that involve polynomials, rational functions, exponential MATH 174 - Discrete Mathematics for Computer Science (3 Credits) and logarithmic functions, and trigonometric and inverse trigonometric Logic, number theory, sequences, series, recursion, mathematical functions. Intended for students with prior experience in Precalculus, but induction, set theory, enumeration, functions, relations, graphs and trees. not ready for MATH 141. Connections to computers and to programming are emphasized when Prerequisites: C or better in MATH 112 or MATH 115, or placement possible. through Precalculus version of the Mathematics Placement Test. Prerequisites: C or better in MATH 115, MATH 116, MATH 122, or MATH 141, or placement through the pre-calculus version of the MATH 122 - Calculus for Business Administration and Social Mathematics Placement Test. Sciences (3 Credits) Derivatives and integrals of elementary algebraic, exponential, and Carolina Core: ARP logarithmic functions. Maxima, minima, rate of change, motion, work, MATH 198 - Introduction to Careers and Research in the Mathematical area under a curve, and volume. Sciences (1 Credit) Prerequisites: C or better in MATH 111, MATH 111i or MATH 115 or An overview of different areas of mathematical research and career placement through Algebra version of the Mathematics Placement Test. opportunities for mathematics majors. Pass/fail only. Carolina Core: ARP Prerequisites: C or better in MATH 141. MATH 141 - Calculus I (4 Credits) Graduation with Leadership Distinction: GLD: Research Functions, limits, derivatives, introduction to integrals, the Fundamental MATH 221 - Basic Concepts of Elementary Mathematics I (3 Credits) Theorem of Calculus, applications of derivatives and integrals. Four The meaning of number, fundamental operations of arithmetic, the classroom hours and one laboratory hour per week. structure of the real number system and its subsystems, elementary Prerequisites: C or better in Math 112, MATH 115, or MATH 116, or number theory. Open only to students in elementary or early childhood placement through Precalculus version of the Mathematics Placement teacher certification. Test. Prerequisites: C or better in MATH 111 or MATH 111I or placement Carolina Core: ARP through Algebra version of the Mathematics Placement Test. 2 Mathematics MATH 222 - Basic Concepts of Elementary Mathematics II (3 Credits) MATH 490 - Mathematics Internship (1-3 Credits) Informal geometry and basic concepts of algebra. Open only to students Academic counterpart to a professional work experience in which in elementary or early childhood teacher certification. mathematics plays a central role. Introduction to the uses of problem Prerequisites: C or better in MATH 221. formulation and problem solving in a working environment. Introduction to career possibilities for a student trained in mathematics. Restricted to MATH 241 - Vector Calculus (3 Credits) MATH major with 3.0 or better GPA and completion of at least 60 credits. Vector algebra, geometry of three-dimensional space; lines, planes, and Prerequisites: C or better in MATH 241, MATH 300 and at least one 500 curves in space; polar, cylindrical, and spherical coordinate systems; level MATH course; CSCE 145 or CSCE 206 and one of the following STAT partial differentiation, max-min theory; multiple and iterated integration, courses STAT 509, STAT 512, STAT 515. line integrals, and Green’s theorem in the plane. Prerequisites: C or better in MATH 142. MATH 499 - Undergraduate Research (1-3 Credits) Research on a specific mathematical subject area. The specific content MATH 242 - Elementary Differential Equations (3 Credits) of the research project must be outlined in a proposal that must be Ordinary differential equations of first order, higher order linear equations, approved by the instructor and the Undergraduate Director. Intended for Laplace transform methods, series methods; numerical solution of students pursuing the B.S. in Mathematics with Distinction. Pass-Fail differential equations. Applications to physical sciences and engineering. grading only. Prerequisites: C or better in MATH 142. Graduation with Leadership Distinction: GLD: Research MATH 300 - Transition to Advanced Mathematics (3 Credits) MATH 511 - Probability (3 Credits) Rigor of mathematical thinking and proof writing via logic, sets, and Probability and independence; discrete and continuous random variables; functions. Intended to bridge the gap between lower-level (computational- joint, marginal, and conditional densities, moment generating functions; based) and upper-level (proof-based) mathematics courses. laws of large numbers; binomial, Poisson, gamma, univariate, and Prerequisites: C or better in MATH 142. bivariate normal distributions. Prerequisites: C or better in MATH 241. MATH 344 - Applied Linear Algebra (3 Credits) General solutions of systems of linear equations, vector spaces Corequisite: MATH 241. and subspaces, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, singular value Cross-listed course: STAT 511 decomposition, and generalized inverse. MATH 344L is an optional MATH 514 - Financial Mathematics I (3 Credits) laboratory course where additional applications will be discussed. Probability spaces. Random variables. Mean and variance. Geometric Prerequisites: C or better in MATH 142. Brownian Motion and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage arguments. Options pricing and the MATH 344L - Applied Linear Algebra Lab (1 Credit) Black-Scholes formula. Computer based applications of linear algebra for science and Prerequisites: C or better in MATH 241. engineering students. Topics include numerical analysis of matrices, direct and indirect methods for solving linear systems, and least squares Cross-listed course: STAT 522 method (regression). Typical applications include practical issues MATH 515 - Financial Mathematics II (3 Credits) related to discrete Markov processes, image compression, and linear Convex sets. Separating Hyperplane Theorem. Fundamental Theorem programming. Credit not allowed for both MATH 344L and 544L. of Asset Pricing. Risk and expected return. Minimum variance Prerequisite or Corequisite: C or better or concurrent enrollment in portfolios. Capital Asset Pricing Model. Martingales and options pricing. MATH 344. Optimization models and dynamic programming. MATH 374 - Discrete Structures (3 Credits) Prerequisites: C or better in MATH 514 or STAT 522. Propositional and predicate logic; proof techniques; recursion and Cross-listed course: STAT 523 recurrence relations; sets,