### Course Descriptions

#### Math 105: College Algebra I (3)

(Prerequisite: Placement Scores. A grade of C or higher in Mathematics 105 is required to advance to Mathematics 111 or Mathematics 121). F, S, SU.

The study of real numbers and their operations and properties; order of operations including exponents and roots; linear equations and inequalities in one and two variables, their systems and applications; introduction to functions and graphs; and the study of polynomials and their operations. Earns credit toward graduation

but will not satisfy any of the six hours of Mathematics in the General Education Requirements. Credit cannot be given for both Mathematics 105 and Mathematics 110.

#### Math 110: College Algebra with Applications (3)

(Prerequisite: Placement scores or permission of department; Prerequisite/Corequisite: Mathematics 110L).

Study of real numbers and their operations and properties; linear functions, equations, and inequalities; systems of equations; introduction to functions and graphs; and the study of polynomials and their operations. Earns credit toward graduation but will not satisfy any of the six hours of Mathematics in the General Education Requirements. Credit cannot be given for both Mathematics 110 and Mathematics 105.

#### Math 110L: College Algebra with Modeling (1:3)

(Prerequisite/Corequisite: Mathematics 110)

Study of algebraic operations, properties of the real number system, data analysis, and problem solving skills to complete a variety of assigned projects and activities involving word problems, linear modeling, and linear programming.

#### Math 111: College Algebra II (3)

(Prerequisite: Grade of C or higher in Mathematics 105 or Mathematics 110 and 110L or placement scores. The grade of C or higher is required in Mathematics 111 to enroll in any higher numbered mathematics course for which Mathematics 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.

#### Math 121: Introduction to Mathematical Modeling and Problem Solving (3)

(Recommended for non-math and non-science majors)

(Prerequisite: Grade of C or higher in Mathematics 110 and 110L or placement scores or permission of the department.)

The study of algebra and polynomial functions and operations to include linear and nonlinear functions, data analysis, basic statistics, and linear regression in applications setting. Credit cannot be given for both Mathematics 111 and 121.

#### Math 132: College Trigonometry with Analytic Geometry (3)

(Prerequisite: Grade of C or higher in Mathematics 111 or placement scores) F, S, SU.

College trigonometry, to include trigonometric identities as well as the inverse trigonometric functions, parabolas, ellipses, and hyperbolas. Credit toward graduation cannot be earned for both Mathematics 137 and Mathematics 132.

#### Math 134: Probability and Statistics (3)

(Prerequisite: Grade of C or higher in Mathematics 111 or Mathematics 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.

#### Math 137: Pre-Calculus (3)

(Prerequisite: A grade of C or higher in Mathematics 111, placement scores, or permission of the department.)

A complete treatment of plane trigonometry, including the trigonometric functions, trigonometric identities, and solutions to and applications of right and arbitrary triangles; properties of functions, including their composition, inversion, and piecewise definition; techniques of graphing functions, including polynomial, rational, algebraic, exponential, and logarithmic functions; and other pre-calculus topics as time permits. Credit toward graduation cannot be earned for both Mathematic 137 and Mathematics 132.

#### Math 140: Applied Calculus (3)

(Prerequisite: Grade of C or higher in Mathematics 111 or Mathematics 121 or Mathematics 137 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. Credit toward graduation cannot be earned for both Mathematics 140 and 201.

#### Math 170: Survey of Mathematics for Early Childhood and Elementary Teachers I (3)

(Prerequisite: Grade of C or higher in Mathematics 111 or placement scores) F, S, SU.

Origin and development of the real numbers. Emphasis on the precision of Mathematical language as well as computational procedures and algorithms involving whole numbers and integers. The study of algebraic concepts (patterns, relations, and functions) and the role of Mathematical structures in the use of equalities, equations, and inequalities are emphasized. Mathematics 170 is for students seeking South Carolina Teacher Licensure in early childhood education or in elementary education or a B.G.S. in Educational studies.

#### Math 201: Calculus I (3)

(Prerequisite: Grade of C or higher in either Mathematics 132 or Mathematics 137 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. Credit toward graduation cannot be earned for both Mathematics 140 and 201.

#### Math 201L: Calculus I Workshop (1:3)

(Corequisite: Mathematics 201) F, S, SU.

Intensive calculus workshop for students enrolled in Mathematics 201. Students work collaboratively in small groups on problems that emphasize the key ideas of calculus. The workshop will also introduce students to technology that can automate and help visualize calculus concepts. Assessed as S (Satisfactory) or U (Unsatisfactory).

#### Math 202: Calculus II (3)

(Prerequisite: Grade of C or higher in Mathematics 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.

#### Math 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.

#### Math 212: Introduction to FORTRAN (3)

(Prerequisite/Corequisite Mathematics 201 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.

#### Math 222: Problem Solving in the Sciences using Software (3)

(Prerequisite: Grade of C or higher in 201 or placement scores.)

Provides students from diverse areas of science an introduction to software currently available to solve problems in the sciences with the aid of computers. Packages include, but are not limited to, Maple, Matlab, SAS, and SPSS. Skills that pertain to the practical implementation of solutions to applied problems in the use of these software packages will be presented. Problems from the sciences that require elementary concepts from calculus, algebra, and statistics will be considered. Appropriate presentation of solutions containing computational and graphical components together with documentation will be emphasized.

#### Math 230: Discrete Mathematics I (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.

#### Math 235: Mathematics for the Middle School Teacher (3)

(Prerequisite: Grade of C or higher in Mathematics 230) F.

Topics include the development of the set of real numbers, problem solving, elementary number theory, rational and irrational numbers, decimals, percents, relations and functions. Mathematics 235 is for students seeking South Carolina Teacher Licensure in middle school education with a Mathematics area of concentration and is not open to other majors.

#### Math 270: Survey of Mathematics for Early Childhood and Elementary Teachers II (3)

(Prerequisite: Grade of C or higher in Mathematics 170 or 201) F, S, SU.

Continuation of Mathematics 170. The study of rational numbers (fractional, decimal and percentage forms), of elementary concepts in probability, of data analysis (collecting, organizing, and displaying data), and of appropriate statistical methods are the major components of the course with additional emphasis on problem-solving. Mathematics 270 is for students seeking South Carolina Teacher Licensure in early childhood education and in elementary education or a B.G.S. in Educational Studies.

#### Math 301: Ordinary Differential Equations (3)

(Prerequisite: Grade of C or higher in 202 or permission of the department.) S.

General first-order differential equations and second-order linear equations with applications. Other topics may include Mathematical models, computational methods, dynamical systems, aspects of higher-order linear equations, Laplace transforms, and an introduction to partial differential equations.

#### Math 304: Linear Algebra (3)

(Prerequisite: Grade of C or higher in Mathematics 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.

#### Math 305: Linear Programming (3)

(Prerequisites: 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.

#### Math 306: Multivariable Calculus (3)

(Prerequisite: Grade of C or higher in Mathematics 203 or permission of the department, Mathematics 304 recommended. A student with a grade of B or higher in Mathematics 202 may, with permission of the department, take Mathematics 203 concurrently with Mathematics 306 instead of as a prerequisite.) 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.

#### Math 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.

#### Math 311: Transition to Higher Mathematics (3)

(Prerequisites: Grade of C or higher in Mathematics 203 or qualifying AP score; Mathematics 230 or 304 is recommended) 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.

#### Math 312: Probability and Statistics for Science and Mathematics (3)

(Prerequisites: 230 or 134 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.

#### Math 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, mathematics notation, and basic mathematics concepts will be emphasized as well as the personalities of mathematicians and their contributions to the subject.

#### Math 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.

#### Math 318: Combinatorics and Graph Theory (3)

(Prerequisite: 203) Offered 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.

#### Math 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.

#### Math 332: Discrete Mathematics II (3)

(Prerequisite: Grade of C or higher in either 230 or 311 or permission of department) Offered as needed.

Major topics covered include sums, recurrences, relations and functions including integer functions (mod, floor, ceiling), elementary number theory, binomial coefficients, discrete probability, and graphs. Additional topics may be chosen from generating functions (solving recurrences, convolutions), special numbers (e.g., Stirling, Bernoulli, Fibonacci), and asymptotics (O notation, manipulation, and summation formulas).

#### Math 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.

#### Math 370: Intuitive Geometry (3)

(Prerequisite: Grade of C or higher in Math 202 or 270) F, S, SU.

Continuation of Mathematics 270. Intuitive development of geometric shapes in two- and three-dimensional space. Concepts of congruence, parallelism, perpendicularity, symmetry, transformations, measurement (English and metric systems as well as estimation skills), right angle trigonometry, and coordinate geometry are considered. Mathematics 370 is for students seeking South Carolina Teacher Licensure in early childhood education or in elementary education or a B.G.S. in Educational Studies.

#### Math 375: Fundamental Skills of Mathematics (3)

Offered in 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.

#### Math 405: Abstract Algebra (3)

(Prerequisite: Grade of C or higher in Mathematics 311 or both Mathematics 306 and grade of C or higher

in Mathematics 230 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.

#### Math 407: Real Analysis I (3)

(Prerequisite: Grade of C or higher in Mathematics 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.

#### Math 409: Complex Analysis I (3)

(Prerequisite: Grade of C or higher in Mathematics 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.

#### Math 411: Topology I (3)

(Prerequisite: Grade of C or higher in Mathematics 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.

#### Math 420: Mathematical Probability (3)

(Prerequisite: 306 and a grade of C or higher in Mathematics 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.

#### Math 422: Nonlinear Optimization (3)

(Prerequisite: 306) AS.

Nonlinear optimization topics including derivatives, partial derivatives, onedimensional 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.

#### Math 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.

#### Math 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.

#### Math 497: Special Studies (3), (2), or (1)

(Prerequisite: Permission of department) S.

Open only to juniors or seniors with a grade point average of 3.0 or higher in their major courses. A maximum of three semester hours may be earned. All individual research projects are reviewed by three faculty members from two different disciplines. May be taken for credit (three hours) towards the Honors degree by special arrangement.

#### Math 499: Mathematics Capstone Course (3)

(Prerequisite: A grade of C or higher in Mathematics 230 or 311, at least 24 hours of mathematics required for the major; and permission of the department; should be taken 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.

#### Math 502: Geometry for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 508: Linear Algebra for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 509: Abstract Algebra for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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 semi-groups, 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.

#### Math 511: Discrete Mathematics for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 515: History of Mathematics for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 516: Calculus for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 518: Probability and Statistics for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.

#### Math 520: AP Calculus AB Certification for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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 six 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.

#### Math 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.

#### Math 530: Special Topics in Mathematics for Teachers (3)

(Prerequisite: Bachelor’s degree plus eligibility for licensure 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.