MATHEMATICS COURSES (MATH)

105 College Algebra with Analytic Geometry I (3) (Prerequisite: Placement scores. The grade of C or higher in Math 105 is required to advance to Math 111 or Math 121.) F, S, SU. The study of real numbers and their operations and properties, order of operations, exponents and roots, linear equations and inequalities in one and two variables, their systems and applications, and introduction to functions and graphs. Earns credit toward graduation but will not satisfy any of the six hours of the Basic Communications (Mathematics and/or Logic) in the General Education Requirements. Credit cannot be given for both Mathematics 105 and 120.

110/110L College Algebra with Modeling and Applications (4:3-3) (Prerequisite: Placement scores or permission of department) F, S. Study of real numbers and their operations and properties; algebraic operations; linear function, linear equations, linear inequalities, linear programming, and linear regression; systems of equations and inequalities and applications; functions and graphs; and data analysis.

111 College Algebra with Analytic Geometry II (3) (Prerequisite: Grade of C or higher in Math 105 or placement scores. The grade of C or higher is required in Math 111 to enroll in any higher numbered mathematics course for which Math 111 is a prerequisite.) F, S, SU. The study of polynomials, their operations and factoring, operations with and simplifying rational expressions, roots and radicals, quadratic equations and inequalities, graphs of non-linear functions and the conic sections; exponents and logarithmic functions. Credit cannot be given for both Mathematics 111 and 121.

112 College Trigonometry with Analytic Geometry (3) (Prerequisite: Grade of C or higher in Math 111 or placement scores) F, S, SU. College trigonometry, to include trigonometric identities as well as the inverse trigonometric functions, parabolas, ellipses, and hyperbolas.

114 Probability and Statistics (3) (Prerequisite: Grade of C or higher in Math 111, Math 121, or placement scores) F, S, SU. Basics of probability, including counting, tree diagrams, conditional probability, binomial and normal distributions, mean, variance, standard deviation, and expected value. Credit can not be given for both Mathematics 114 and 115.

115 Finite Mathematics (3) (Prerequisite: Grade of C or higher in Math 111 or placement scores) As needed. Covers such topics as sets, logic, the real numbers, groups, fields, probability, elementary statistics, and modeling. Credit cannot be given for both Mathematics 114 and 115.

120 Introduction to Mathematical Modeling and Problem Solving I (3) (Recommended for non-math and non-science majors) (Prerequisite: Placement scores) The study of algebraic operations, linear functions, data analysis, and simple linear regression in an application setting, Credit cannot be given for both Mathematics 105 and 120.

121 Introduction to Mathematical Modeling and Problem Solving II (3) (Recommended for non-math and non-science majors) (Prerequisite: Grade of C in Math 120 or placement scores) The study of algebra and polynomial functions and operations to include linear and nonlinear functions, data analysis, basic statistics, and linear regression in an applications setting. Credit cannot be given for both Mathematics 111 and 121.

140 Calculus for Business (3) (Prerequisite: Grade of C or higher in Math 111 or Math 121 or Math 180 or placement scores) F, S, SU. Topics include limits, derivatives, applications of the derivative, exponential and logarithmic functions, definite integrals, and applications of the definite integral. This course cannot be used in place of Mathematics 201 for any reason, and it is not a sufficient prerequisite for Mathematics 202.

170 Survey of Mathematics for Early Childhood and Elementary Teachers I (3) (Prerequisite: Grade of C or higher in Math 111 or placement scores) F, S, SU. Origin and development of the real numbers. Emphasis on precision of mathematical language as well as computational algorithms. Mathematics 170 is for students seeking South Carolina Teacher Certification in early childhood education or elementary education and is not open to other majors.

180 Pre-Calculus (3) (Prerequisite: Minimum score of 540 on the Quantitative Section of the SAT or permission of the department) F, S. Emphasis on analytic geometry and elementary functions. Includes lines and conic sections. Credit can not be given for Math 180 and either Math 105, 111, or Math 112.

201 Calculus I (3) (Prerequisite: Grade of C or higher in either Math 112 or Math 180 or placement scores or permission of department) F, S, SU. The first of a three-course sequence covering an introduction to the analysis of real-valued functions of one real variable. Topics include the limit of a function, continuity, the derivative, and applications.

202 Calculus II (3) (Prerequisite: Grade of C or higher in Math 201 or qualifying AP score) F, S, SU. Continuation of Calculus I, the course covers the integral, techniques of integration, the exponential function, the logarithm function, and applications.

203 Calculus III (3) (Prerequisite: Grade of C or higher in 202 or qualifying AP score) F, S, SU. Continuation of Calculus II, the course covers sequences, infinite series, improper integrals, and applications.

212 Introduction to FORTRAN (3) (Prerequisite: Eligibility to take 111 [or higher] or permission of department) (Same as Computer Science 212) F, S, SU. A study of programming to include input and output procedures, arithmetic and logical operations, DO loops, branching procedures, arrays, declaration statements, and subroutines. Application of these ideas by writing, running, and correcting programs.

230 Discrete Mathematics (3) (Eligibility to take 202 or permission of department) S, SU. Propositional and predicate logic, methods of proof, sequences and summations, recursion, combinatorial circuits, algorithm analysis, set theory, counting techniques, Boolean algebras, and other related topics.

240 Concrete Math (3) (Prerequisite: 202 and 230) As needed. Major topics covered include sums, recurrences, integer functions (mod, floor, ceiling), elementary number theory, binomial coefficients, discrete probability. Additional topics may be chosen from generating functions (solving recurrences, convolutions), special numbers (e.g., Stirling, Bernoulli, Fibonacci), and asymptotics (0 notation, manipulation, and summation formulas).

270 Survey of Mathematics for Early Childhood and Elementary Teachers II (3) (Prerequisite: 170) F, S, SU. Continuation of Mathematics 170. More emphasis on problem-solving. Mathematics 270 is for students seeking South Carolina Teacher Certification in early childhood education and elementary education and is not open to other majors.

301 Ordinary Differential Equations (3) (Prerequisite or Corequisite: 203) S. General first-order differential equations and second-order linear equations with applications. Introduction to power series solutions and numerical methods.

304 Linear Algebra (3) (Prerequisite: 202) F, S, SU. Introduction to the algebra of finite-dimensional vector spaces. Topics covered include finite-dimensional vector spaces, matrices, systems of linear equations, determinants, change of basis, eigenvalues, and eigenvectors.

305 Linear Programming (3) (Prerequisite: 304 and one course from 212 or Computer Science 226) S. Introduction to the theoretical, computational, and applied aspects of the subject. Topics covered include the mathematical model of linear programming, convex sets and linear inequalities, the simplex method, duality, the revised simplex method, and several of the many applications. Computer solutions for several problems will be required.

306 Multivariable Calculus (3) (Prerequisite: 203 and 304 or permission of the department) F, S. Vectors and vector calculus; the calculus of real-valued functions of several variables; topics include partial derivatives, gradients, extrema problems, multiple integrals, iterated integrals, line integrals, and Green's Theorem, as time permits.

310 Mathematical Models and Applications (3) (Prerequisite: 202) AS. Introduction to the theory and practice of building and studying mathematical models for various real world situations that may be encountered in the physical, social, life, and management sciences.

311 Transition to Higher Mathematics (3) (Prerequisite: C or higher in 203 or qualifying AP score and C or higher in either 230 or 304) F, S. This course is principally devoted to understanding and writing mathematical proofs with correctness and style. Elements of mathematical logic such as Boolean logical operators, quantifiers, direct proof, proof by contrapositive, proof by contradiction, and proof by induction are presented. Other material consists of topics such as elementary set theory, elementary number theory, relations and equivalence relations, equivalence classes, the concept of a function in its full generality, and the cardinality of sets.

312 Probability and Statistics for Science and Math (3) (Prerequisite: 230 or 114 and 202 or permission of the department) F. Descriptive statistics, elementary probability, random variables and their distributions, expected values and variances, sampling techniques, estimation procedures, hypothesis testing, decision making, and related topics from inferential statistics.

315 History of Mathematics (3) (Prerequisite: 202) SU. Origins of mathematics and the development of Egyptian and Babylonian, Pythagorean, Greek, Chinese and Indian, and Arabic mathematics as well as mathematics of the Middle Ages and modern mathematics. The development of the calculus, geometry, abstract algebra, analysis, mathematical notation, and basic mathematical concepts will be emphasized as well as the personalities of mathematics and their contributions to the subject.

317 Number Theory (3) (Prerequisite or Corequisite: 202) AF. Introduction to the elementary aspects of the subject with topics including divisibility, prime numbers, congruencies, Diophantine equations, residues of power, quadratic residues, and number theoretic functions.

318 Combinatorics and Graph Theory (3) (Prerequisite: 203) As Needed. In combinatorial theory the course will discuss the basic counting principles, arrangements, distributions of objects, combinations, and permutations. Considerable attention will be given to ordinary and exponential generating functions. Also to be covered will be the standard counting techniques of recurrence, inclusion-exclusion, Burnside's Theorem, and Polya's Enumeration Formula. In graph theory the course will cover the basic theory of graphs. Also covered will be graph isomorphism, planar graphs, Euler and Hamiltonian circuits, trees, and graph colorings.

330 Special Topics in Mathematics I (3) (Prerequisite: Permission of the department) In-depth study of an area of interest in mathematics. Different areas of study will be offered.

345 Plane Geometry (3) (Prerequisite: 230 or 311 or 370 or permission of the department) F. Topics include the elements of plane geometry, up to and including congruence, parallelism and similarity, area and volume, ruler and compass constructions, other geometries and transformations. This course includes topics from the history of mathematics.

370 Intuitive Geometry (3) (Prerequisite: 270) F, S, SU. Continuation of Mathematics 270. Intuitive development of geometric figures in plane and in space. Consideration of congruence, parallelism, perpendicularity, symmetry, and measurement. Mathematics 370 is for students seeking South Carolina Teacher Certification in early childhood education or elementary education and is not open to other majors.

375 Fundamental Skills of Mathematics (3) S. An apprenticeship offered in the freshman mathematics program. Each student will work under the careful supervision of a mathematics faculty member who will assign outside reading as well as evaluate performance in both oral and written examinations.

405 Abstract Algebra (3) (Prerequisite: 311 or permission of the department) F. Introduction to the terminology and basic properties of algebraic structures, such as groups, rings, and fields. The course includes topics from the history of mathematics.

407 Real Analysis I (3) (Prerequisite: 311 or permission of the department) S. At the intermediate-level covers the following topics: Cauchy sequences and the construction of real numbers, sequences and series of real numbers, the real line as a metric space, continuity and uniform continuity, derivatives of real-valued functions of one real variable, spaces of continuous functions, Lebesgue measure and the Lebesgue integral, and Fourier series.

409 Complex Analysis I (3) (Prerequisite: 311 or permission of the department) AS. Complex numbers and functions, derivatives and integrals of complex functions, the Cauchy integral theorem and its consequences, residue theory, and conformal mapping. Additional topics as time permits.

411 Topology I (3) (Prerequisite: 311 or permission of the department) As Needed. Introduction to Point Set Topology including discussion of limit points, continuity, compactness, connectedness, metric spaces, locally compact spaces, locally connected spaces, and the Baire Category Theorem.

420 Mathematical Probability (3) (Prerequisite: 306 and either 230 or 311) AS. Introduction to probability theory to include the topics of probability spaces, conditional probability and independence, combinatorial theory, random variables, special discrete and continuous distributions, expected value, jointly distributed random variables, order statistics, moment generating functions and characteristic functions, Law of Large Numbers, and the Central Limit Theorem.

422 Nonlinear Optimization (3) (Prerequisite: Math 306) AS. Nonlinear optimization topics including derivatives, partial derivatives, one-dimensional search techniques, multi-dimensional search techniques, both unconstrained and constrained optimization techniques including LaGrange Multipliers and Kuhn-Tucker Conditions, and specialized techniques. Emphasis is on optimization theory, numerical algorithms with error analysis, and solving applied problems.

425 Numerical Analysis (3) (Prerequisite: 203 and one of 212 or Computer Science 226) (Same as Computer Science 425) F. Techniques and types of errors involved in computer applications to mathematical problems. Topics include techniques for solving equations, systems of equations, and problems in integral calculus. Computer solutions for several problems will be required.

430 Special Topics in Mathematics II (3) (Prerequisite: Permission of the Department) In-depth study of an area of interest in mathematics. Different areas of study will be offered.

497 Special Studies (3), (2), or (1) (Prerequisite: Permission of department) S. Open only to juniors or seniors with a GPA of 3.0 or higher in their major courses. A maximum of 3 semester hours may be earned. All individual research projects are reviewed by three faculty members from two different disciplines.

499 Mathematics Capstone Course (3) (Prerequisite: At least 24 hours of mathematics required for the major; should be taken the semester of graduation or the semester before graduation) F, S. This course will include review and integration of the concepts from the core courses required for the mathematics major as well as an in-depth exploration in some advanced mathematics area. Requirements will include an internal exam and completion of a capstone mathematics project sponsored by a faculty member and approved by the Department of Mathematics.

502 Geometry for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. Accelerated training in methods of proof, Euclidean, non-Euclidean, transformational, and finite geometries, plus constructions. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

508 Linear Algebra for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. Matrices, vector spaces, and linear transformations. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

509 Abstract Algebra for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. Review of real and complex numbers, sets, functions, induction, and well ordering. Introduction to semigroups, groups, rings, homomorphism, and isomorphism. Elementary theory of groups, elementary theory of rings. As time permits, topics will include factor groups, quotient rings, cyclic groups, finite groups, abelian groups, polynomial rings, division rings, and fields. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses.

511 Discrete Mathematics for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. Study of propositional and predicate logic, set theory, combinatorics and finite probability, relations, functions, Boolean Algebras, simplification of circuits, and other selected topics in discrete mathematics. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

515 History of Mathematics for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. General survey of the history of mathematics with special emphasis on topics that are encountered in high school or college (undergraduate) mathematics courses. The course will cover the mathematics of ancient times, beginning with the Egyptians, Babylonians, and Greeks, and continue to the present. Particular attention will be given to the contributions of selected mathematicians. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

516 Calculus for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) F, S, SU. Full development of limits, derivatives, and integrals. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Concentration is on concepts and applications. Occasionally will be offered in the Fall and/or Spring Semester.

517 Abstract Algebra and Linear Algebra for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major or permission of the department) SU. This course will examine the basic concepts and results of abstract algebra and linear algebra. The course will address such topics as the division algorithm, greatest common divisor, least common multiple, prime factorization, modular arithmetic, simultaneous equations, matrices, binary operations, groups, examples of groups, group properties, subgroups, finite groups, permutation groups, LaGrange's Theorem, linear spaces, the span and independence of a set of vectors, and basis. Applications will be given throughout. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

518 Probability and Statistics for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major or permission of the department) SU. Survey of areas of probability theory to include selected topics from sample spaces; combinatorial theory; random variables and their distributions; conditional probability; joint and marginal distributions; expected values and variances; and the Central Limit Theorem. Survey of descriptive and inferential statistics to include selected topics from the use of tables, graphs, and formulas; sampling techniques; estimation and confidence intervals; hypothesis testing; decision making; and correlation and regression. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

519 Logic and Geometry for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major or permission of the department) SU. This course will include a discussion of mathematical language, logic, and sets; an introduction to Euclid and the Elements: axiomatic systems, modern geometry; the postulates of Hilbert, Birkhoff, and School Mathematics Study Group (SMSG); neutral geometry, i.e., geometry based on Euclid's first four postulates; the basics for non-Euclidean geometry including models for hyperbolic geometry and elliptic geometry. With written departmental approval, seniors may take courses numbered 500-599 for either undergraduate or graduate credit. Designation of credit as undergraduate or graduate must be made at registration. Freshmen, sophomores, and juniors may not take 500-level courses. Occasionally will be offered in the Fall and/or Spring Semester.

520 AP Calculus AB Certification for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics, or permission of department, or permission of State Department of Education.) SU. Study of the topics covered in the AP Calculus AB course and how a teacher should cover these topics. There are essentially 6 main areas: function theory, definitions of limits and derivatives, differentiation techniques, applications of the derivative, the definite integral and techniques of integration, and applications of the integral.

521 AP Calculus BC Certification for Teachers (3) (Prerequisite: 520 or the equivalent, or permission of State Department of Education, or permission of department) SU. Study of topics covered in the AP Calculus BC course and how a teacher should cover these topics. In addition to all subject matter covered in Mathematics 520, which will be reviewed during the course, the following topics will be emphasized: the calculus of vector functions and parametrically defined functions; polar coordinates; integration by parts, partial fractions, and trigonometric substitution; L'Hopital's rule; improper integrals; convergence of sequences of numbers and functions; series of real numbers; power series; Taylor polynomials and error approximation.

530 Special Topics in Mathematics for Teachers (3) (Prerequisite: Bachelor's degree plus eligibility for certification in mathematics or science, or senior status as a mathematics major, or permission of department) SU. A topic of interest to secondary mathematics teachers will be logically and rigorously covered.

799 Mathematics: Seminar Practicum Capstone (3) (Prerequisite: 12 hours in specialty core; Corequisite: Education 768) SU. This course is designed to integrate and extend the subject matter covered in the preceding four specialty area courses. A special course will involve the identification and completion of one or more projects involving the specialty and education core and/or exploration of a related topic. The project(s) should be designed so that they can be used in an appropriate professional setting.

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