MATH 1101 - Fundamentals of College Mathematics
An introductory course in the study of linear and elementary quadratic equations designed to help students develop critical thinking skills in the area of mathematics. The course emphasizes the importance of algebraic principles, applications, and problem solving. Students may enroll concurrently in MATH 1102.
Credit: 3
MATH 1102 - Fundamentals of Mathematics Laboratory
Co-requisite: MATH 1101.
A mathematics lab to be taken concurrently with MATH 1101, the course provides supplementary individual and small group instruction and supervised practice with fundamental algebra skills to help students succeed in MATH 1101. Students enrolled in MATH 1102 must be enrolled concurrently in MATH 1101.
Repeatable for up to 2 credits.
Credit: 1
MATH 1105 - Intermediate Algebra
Prerequisite: An ACT Math score of at least 18, an SAT Quantitative score of at least 450, a grade of C- or better in MATH 1101, or an appropriate score on the math placement test.
An intermediate algebra course connecting the real world to mathematics. Topics include: factoring polynomials and solving equations by factoring, rational expressions and equations, graphing functions, systems of equations, absolute value equations, inequalities, radical expressions and functions, quadratic equations and their graphs, and quadratic formula. Students may enroll concurrently in MATH 1106.
Credit: 3
MATH 1106 - Intermediate Algebra Laboratory
Co-requisite: MATH 1105.
A mathematics lab to be taken concurrently with MATH 1105, the course provides supplementary individual and small group instruction and supervised practice with intermediate algebra skills to help students succeed in MATH 1105.
Repeatable for up to 2 credits.
Credit: 1
MATH 1115 - Survey of Mathematics
Prerequisite: MATH 1105 or an appropriate score on a placement test.
A general survey course that emphasizes reasoning skills, real-life math applications, and non-routine problem solving through individual and team assignments. Topics may include: inductive and deductive reasoning, logic, sequences, systems of numeration, geometry, metric system conversion analysis, personal finance, permutations and combinations, and an introduction to probability, plus individual topics of choice to prepare students for courses in their major or pursue self-interests.
Credit: 3
MATH 1116 - Problem Solving
Prerequisite: An ACT Math score of at least 21, an SAT Quantitative score of at least 510, a grade of C- or better in MATH 1105, or an appropriate score on the math placement test.
This course is designed to improve students’ problem-solving skills by investigating both traditional and non-traditional mathematics problems. Reasoning, reflection upon the problem-solving process, and the elements of effective thinking will be emphasized. Students will write and present their ideas both orally and visually. There will also be real-world applications of mathematical problem solving to games and puzzles, the infinite, and the arts. This course will be taught in the style of inquiry-based learning.
Credit: 3
MATH 1120 - Mathematics in the Modern World
Prerequisite: An ACT Math score of at least 21, an SAT Quantitative score of at least 510, a grade of C- or better in MATH 1105, or an appropriate score on the math placement test.
This course takes a mathematical approach to understanding contemporary issues and explores ways to apply mathematics in everyday life. Students will evaluate and interpret quantitative data through means such as functions, modeling, probability, and statistics and will use the results to form opinions and make decisions. Topics and applications may include the arts and entertainment, biological and health sciences, business and economics, education, environmental science, geography, personal finance, physical science, politics, and sports.
Credit: 3
MATH 1123 - Statistics
This course provides an introduction to descriptive and inferential statistics. Topics include describing, summarizing, and displaying data; using sample statistics to estimate population parameters; evaluating hypothesis using confidence levels with application to the physical and social sciences; logically drawing conclusions based on statistical procedures; and quantifying the possibility of error and bias.
Credit: 3
MATH 1130 - Pre-Calculus I
Prerequisite: An ACT Math score of at least 21, an SAT Quantitative score of at least 510, a grade of C- or better in MATH 1105, or an appropriate score on the math placement test.
This course covers mathematical topics that prepare students for higher-level mathematics courses. Topics include: functions and their properties, polynomial and rational functions and their graphs, transformation method of graphing functions, exponential and logarithmic functions and equations, right-triangle trigonometry, an introduction to trigonometric functions and their graphs, solving systems of inequalities, and solving systems of equations. Optional topics: matrices, determinants and Cramer’s rule, linear programming, fundamental counting principle, permutations and combinations, and an introduction to probability.
Credit: 3
MATH 1140 - Pre-Calculus II
Prerequisite: A grade of C- or better in MATH 1130 or advisor approval.
This course is a continuation of MATH 1130 and covers further mathematical topics that prepare students for higher level mathematics courses. Course topics include: a complete development of trigonometry including trigonometric functions and their identities; solving trigonometric equations, applications of trigonometry to vectors; polar coordinates, and polar form of complex numbers; rectangular form and polar form of conic sections; matrices and matrix formulation of solution of systems of equations; determinants and Cramer’s rule; introduction to sequences and series; and the binomial theorem.
Credit: 3
MATH 1150 - Pre-Calculus I and II Accelerated
Prerequisite: A grade of A in MATH 1105, a grade of C or better in MATH 1130, an ACT Math score of at least 24, an SAT Quantitative score of at least 570, or an appropriate score on a placement test.
A course for well-qualified students who are prepared to complete the pre-calculus sequence in one term. The course includes all the topics covered in Pre-Calculus I, MATH 1130, and Pre-Calculus II, MATH 1140, but is presented in one term.
Credit: 3
MATH 1234 - Introduction to Cryptology
Prerequisite: An ACT Math score of at least 21, an SAT Quantitative score of at least 510, a grade of C- or better in MATH 1105, or an appropriate score on the math placement test.
This course gives an historical introduction to cryptology, the science of making and breaking secret codes. It begins with the oldest recorded codes, taken from hieroglyphic engravings, and ends with the encryption schemes used to maintain privacy during internet credit card transactions. Since secret codes are based on mathematical ideas, each new encryption method discussed in this course leads to the study of new mathematical ideas and results. Topics covered include basic modular arithmetic, primes and divisors, permutations, and elementary statistics. This course will also cover the social and historical aspects associated to cryptology.
Credit: 3
MATH 2007 - Mathematics Across the Ages
Prerequisite: An ACT Math score of at least 24, an SAT Quantitative score of at least 570, a grade of C- or better in MATH 1130, or an appropriate score on the math placement test.
A survey of the historical development of mathematical thought from ancient times to the present. Possible topics include: Babylonian, Egyptian, Greek, Chinese, Hindu, and Arabian mathematics; European mathematics in the middle-ages and the Renaissance; and the development of calculus, number theory, abstract algebra, non-Euclidean geometry, set theory, and information theory.
Credit: 3
MATH 2214 - Calculus I
Prerequisite: An ACT Math score of at least 26, an SAT Quantitative score of at least 620, a grade of C- or better in MATH 1140 or 1150, or an appropriate score on the math placement test.
A course in single variable calculus which emphasizes limit, continuity, derivative, and integral. Primary focus is on the derivative with an introduction to the integral and elementary applications of the integral. Differentiation topics include: chain rule, implicit differentiation, curve sketching, and maxima and minima problems. Integration topics include: fundamental theorem of calculus, method of substitution, area between curves, and volumes of revolution.
Credit: 3
MATH 2215 - Calculus II
Prerequisite: MATH 2214 or advisor approval.
A continuation of Calculus I, completing the development of the integral. Integration topics include: integration by parts, trigonometric substitution, method of partial fractions, length of curves, surfaces, and volumes of revolutions. Other topics include: infinite series, tests of convergence; power series, radius of convergence, and Taylor’s series. Other topics may include calculus of conic sections, vector algebra, and scalar and vector product.
Credit: 3
MATH 2216 - Calculus III
Prerequisite: MATH 2215.
A course in calculus of several variables. The course begins with vector algebra, scalar and vector product, and elementary applications of vectors. Emphasis is placed on differentiation and integration of functions of several variables with peripheral focus on limits and continuity. Differentiation topics include: partial derivative, directional derivative, chain rule formula, gradient, maxima and minima problems, Lagrange multipliers, divergence, and curl. Integration topics include: iterated integrals in rectangular, polar, and spherical coordinates; line integrals; Green’s theorem; divergence theorem; and Stoke’s theorem.
Credit: 3
MATH 2220 - Proof Writing
Prerequisite: An ACT Math score of at least 24, an SAT Quantitative score of at least 570, a grade of C- or better in MATH 1130, or an appropriate score on the math placement test.
An introduction to proof writing and mathematical logic covering sentential and first order logic, introduction to sets, introduction to formal proofs, and practical proof writing for a working mathematician.
Credit: 3
MATH 2326 - Mathematics for Decision-Making
Prerequisite: MATH 1123; MATH 1130 or higher.
A course developing the quantitative skills necessary for the effective formulation and solution of problems in business, management, economics, and the social and life sciences. Topics include: probability and probability distributions, functions and their graphs, differentiation and its application to max-min problems, linear programming, network models, project management with PERT-CPM, and simulation.
Credit: 3
MATH 3000 - Proof Writing in Mathematics
Prerequisite: A C- or higher in WC&IL II or HON 1000; and MATH 1130 or higher or a score of 570+ in SAT Mathematics or a score of 24+ in ACT Mathematics or an appropriate score on the placement test.
An introductory upper division course in proof writing and mathematical logic which covers sentential logic and first order logic and will include the methodology of writing proofs in mathematics and communicating these proofs effectively to an audience. The course will examine logic from both the syntactic and semantic perspectives. Topics include an introduction to proof methods and the deductive calculus, tautologies and validities, the soundness and completeness theorems, translation of English sentences into logic, inference rules such as universal and existential instantiation and generalization, mathematical induction, and the presentation of a theorem with lemmas and corollaries for publication.
Credit: 3
MATH 3110 - Foundations of Mathematical Logic and Applications
Prerequisite: CSCI 1301, MATH 2220, 3301, or consent of instructor. (May be taken concurrently).
A course in mathematical logic covers proof theory, model theory, and the theory of decidability. Topics include sentential logic, First order logic, deductive calculus, completeness and soundness theorems, model theory, isomorphisms, compactness theorem, and Godel’s incompleteness theorem, applications to theoretical computer science, and complexity theory.
Credit: 3
MATH 3220 - College Geometry
Prerequisite: MATH 2215.
This course provides geometry content and process for those planning to become secondary math teachers. The course is also appropriate for other mathematics majors. Included are activities and discussions in inductive and deductive reasoning in Euclidean geometry, classical geometry with constructions, transformations, dynamical geometry software, non-Euclidean geometries, three-dimensional geometry, spatial reasoning, and miscellaneous topics.
Credit: 3
MATH 3234 - Mathematical Cryptology
Prerequisite: MATH 2214 (Calculus I) or higher or consent of instructor.
This course gives a mathematical introduction to cryptology, the art and science of making and breaking secret codes. It begins with the oldest recorded codes and ends with the encryption schemes used to maintain privacy during internet credit card transactions. Topics covered include the classical monoalphabetic ciphers and their cryptanalysis; polyalphabetic ciphers and their cryptanalysis; perfect cipher systems; and public-key cryptology, including Diffi-Hellman key exchange, RSA, Knapsack codes, and anonymity. The mathematical subjects include permutations, modular arithmetic, statistics, recurrence relations, and elementary number theoretic results.
Credit: 3
MATH 3240 - Math Concepts for Elementary Teachers
Prerequisite: MATH 1115.
A review of the central concepts, tools of inquiry, and structures of the discipline of mathematics so that elementary teachers can create learning experiences that make aspects of the subject matter meaningful for students.
Credit: 3
MATH 3301 - Discrete Mathematics
Prerequisite: MATH 1130, 2220, or consent of instructor.
This course focuses on the theory and application of mathematical principles critical to the computing sciences. Students study and apply key concepts in topics such as set theory, combinatorics, language and grammars, propositional and quantifier logic, Boolean functions and circuit design, growth of functions and big-O notation, time complexity of algorithms, mathematical induction and program correctness, recursive definitions and recursive algorithms, and solving recurrence relations.
Credit: 3
MATH 3302 - Elementary Number Theory
Prerequisite: MATH 2215; or MATH 2214 and 3301. Undergraduate standing.
Topics covered include prime and composite integers; factorization; divisibility; number theoretic functions; Diophantine equations; congruence of integers; quadratic reciprocity; mathematical inductions; cryptography; Pythagorean triples; and real, complex and p-adic numbers.
Credit: 3
MATH 3305 - Linear Algebra
Prerequisite: MATH 2214 or higher except MATH 2326 or consent of instructor.
Elementary linear algebra with applications in the sciences and to computers and economics. Topics include: systems of linear equations; matrix theory, determinants and eigenvalues; geometry of Euclidean n-space; abstract vector spaces, bases, linear independence, and spanning sets; linear transformations, null space, and range; diagonalization of matrices; eigenvalues and eigenvectors of symmetric matrices; quadratic forms, inner products; and orthonormalization.
Credit: 3
MATH 3307 - Differential Equations
Prerequisite: MATH 2214 or higher except MATH 2326/3301. Recommended: MATH 3305.
A course in ordinary differential equations utilizing concepts and techniques from Calculus I and II and linear algebra. Emphasis is on solution to higher-order linear equations. First order topics include: separation of variables, exact equations, integrating factors, and homogenous and non- homogenous systems with applications to networks. Higher order topics include: a detailed study of solutions to second order linear equations by reduction of order, variation of parameters, and series solutions; linear independence of solutions, the Wronskian, general solution to linear homogenous and non-homogenous equations, and linear equations with constant coefficients and the Laplace transform method.
Credit: 3
MATH 3316 - Problem Solving for Mathematics Teaching
Prerequisite: MATH 2214.
This course is designed to improve students’ problem-solving skills for solving both traditional and non-traditional mathematics problems. Reasoning, communicating mathematics, mathematical representations, and connections between various mathematical topics will be emphasized.
Credit: 3
MATH 3320 - Set Theory
Prerequisite: MATH 2220, 3110, 3301, or consent of instructor.
To provide students with a solid background in set theory and to develop mathematical sophistication in general, this is a course in which covers ZF (Zermelo Frankel axioms) and ZFC (ZF + the axiom of choice), DeMorgan’'s laws, Power Sets, Set Algebra, Zorn’s lemma and other equivalent versions of AC, equivalence relations, well orderings and partial orderings, bijections, Russell’s paradox, cofinality, mathematical induction, transfinite induction, ordinals and cardinals, ordinal and cardinal arithmetic, the continuum hypothesis, and the constructible universe.
Credit: 3
MATH 3460 - Probability
Prerequisite: MATH 2215 or consent of instructor.
Discrete and continuous probability with applications. Topics include: finite sample spaces, combinations and permutations, conditional probability, independent events, discrete random variables, continuous random variables, functions of random variables, higher-dimensional random variables, expectation, variance, correlation coefficient, generating function, reproductive properties, sequences of random variables, law of large numbers, central limit theorem.
Credit: 3
MATH 3470 - Applied Statistics
Prerequisite: MATH 2214 or higher except MATH 2326/3301, or consent of instructor. MATH 1123 is strongly suggested but not required.
This course is an introduction to the mathematical theory of statistics. Topics covered include discrete and continuous distributions, tests of hypotheses, estimation, analysis of variance, regression and correlation, sequential analysis, and rank order statistics.
Credit: 3
MATH 3500 - Numerical Methods
Prerequisite: CSCI 2911; MATH 3305 and 3307*; (*May be taken concurrently.)
The purpose of numerical analysis is two-fold: (1) to find acceptable approximate solutions when exact solutions are either impossible or impractical, and (2) to devise alternate methods of solutions better suited to the capabilities of computers. Topics for this course include elements of error analysis, root finding, numerical solutions of systems of linear equations, polynomial approximation and interpolation, numerical integration and differentiation, and numerical solution of ordinary and partial differential equations. Students should expect to do some computer programming using MATLAB, FORTRAN, PYTHON, or C.
Credit: 3
MATH 3600 - Mathematics for Data Science
Prerequisite: MATH 3305; and MATH 1123 or BIOL 3090 or MATH 3470 or PSY 2100; or consent of instructor
This course presents the mathematics of data science methods to promote effective and efficient application as well as innovation in the field. Topics include the bias-variance trade-off, singular value decomposition, principal component analysis and its application to Google's page rank algorithm, gradient descent, support vector machines, kernels, and neural networks. Additional topics may include metric spaces and K-nearest neighbors, information theory. A programming language such as Python, together with relevant Data Science libraries, like TensorFlow, will be used.
Credit: 3
MATH 3990 - Internship
Prerequisite: At least a 2.7 GPA for undergraduate level.
Internships provide students with applied, experiential learning opportunities so that they can make connections between academic study and the practical application of that study in a professional work environment. Academic internships are supervised by a faculty member and an on-site professional supervisor. All academic internships must be approved in advance by the department or program. Unless stipulated otherwise by the department or program, credit hours are defined by the university's credit hour policy (for example, a 3-credit internship will require a minimum of 120 hours onÂsite). Internships may be repeated for a total of 9 credit hours.
Repeatable for up to 9 Credits.
Credit: 1 to 3
MATH 4210 - Topology
Prerequisite: MATH 2215; and MATH 3310 or higher; or consent of instructor.
An introduction to the basic concepts of topology in the setting of metric spaces and more general topological spaces. Topics include completeness, compactness, connectedness, continuous functions and continuity in terms of nets, Hausdorf spaces, product spaces, metric spaces, Tychonoff thereom, Bolzno-Weierstrass theorem, Stone-Weierstrass theorem, and the Baire category theorem.
Credit: 3
MATH 4301 - Combinatorics and Graph Theory
Prerequisite: MATH 3301.
This course explains how to reason and model using enumerative combinatorics and applied graph theory. Combinatorial reasoning underlies all analysis of computer systems. Topics covered include generating functions, set partitions, recurrence relations, inclusion-exclusion, trees, graph connectivity, independence, graph coloring, Hamiltonian and Euler circuits and paths, regular expressions and languages, and finite state automata. Additional Topics may include regular Turing machines, Computational Complexity, and the theory of NP Complete Problems along with other theoretical Computer Science topics including advanced Recursion Theory.
Credit: 3
MATH 4330 - Abstract Algebra
Prerequisite: MATH 3305 or consent of instructor. MATH 2220 is strongly suggested but not required
An introduction to algebra as a deductive system. Topics include: complex numbers, well ordering, groups, cyclic groups, permutation groups, rings, equivalence relations, polynomial rings, division algorithm, unique factorization, zeros of polynomials.
Credit: 3
MATH 4440 - Real Analysis
Prerequisite: MATH 2215 or consent of instructor. MATH 2220 is strongly suggested but not required.
An introduction to the theory of real analysis. Topics include: completeness of the real numbers, basic topology of the real numbers, continuous functions and compactness, sequences and series, limits, derivatives, mean value theorems, the Riemann integral, Taylor’s formula, power series, uniform convergence.
Credit: 3
MATH 4450 - Complex Analysis
Prerequisite: MATH 2216, or consent of instructor.
Complex Analysis is the theory and applications of analytic functions of a single complex variable. Topics include: Taylor and Laurent series representation, Cauchy’s integral theorem and formula, residue calculus, harmonic functions, zeros and poles, counting theorem, conformal mappings, linear functional transformations, Schwartz-Christoffel transformation, Laplace’s equation, Poisson’s equation, Neumann problems, and the Fourier representation theorem.
Credit: 3
MATH 4470 - Partial Differential Equations
Prerequisite: MATH 3307
This course explores applications of differential equations. Topics for this course include application of second order linear equations, series solutions of second order linear equations including Euler equations and Bessel’s equation, partial differential equations and Fourier series including heat equation, wave equation, and Laplace’s equation.
Credit: 3
MATH 4471 - Applications of Differential Equations
Prerequisite: MATH 3305, 3307; or consent of instructor.
Topics for this course include systems of first order linear equations, qualitative theory (existence, uniqueness, stability, and periodicity), boundary value problems, and Sturm-Liouville theory.
Credit: 3
MATH 4475 - Modeling and Simulation
Prerequisite: CSCI 2912; MATH 1123 and 2214.
Material includes the advanced study of mathematical techniques, algorithms, and applications applicable to assist and improve decision-making in the management and behavioral sciences. The course focuses on both the techniques and the use of the computer in facilitating application of these techniques.
Credit: 3
MATH 4920 - Math Education Practicum
Prerequisite: MATH 3316, or any other MATH 3000-level class, or consent of instructor.
This course combines the study of mathematics problem-solving with practical classroom experience. Students will investigate the issues of teaching mathematics while gaining practical experience as tutors. Students will follow the progress of their own students in mathematics labs.
Credit: 3
MATH 4940 - Research in Logic or Pure Math
Prerequisite: Senior status as a math major.
Text will vary depending on subject of concentration of each student. Forty percent of the grade will be determined by a final project, 40% by final presentation, and 20% by oral exams so that the Instructor can evaluate students on their preparation, effort, and ability to solve problems independently.
Repeatable for up to 6 credits.
Credit: 1 to 3
MATH 4950 - Research in Applied Mathematics
MATH 4950 Research in Applied Mathematics is an upper-division course for senior students from any major in CNCS. Students work closely with a faculty member in the Department of Mathematics who will guide them in learning advanced topics and doing research in applied mathematics. The topics broadly encompass mathematical modeling, data analysis, numerical implementation, etc. in interdisciplinary studies, depending on students’ majors and needs. There is no prerequisite but MATH 3307 Differential Equation is highly recommended.
Repeatable for up to 6 credits.
Credit: 1 to 3
MATH 4960 - Observation/Participation
Credit: 3
MATH 4980
Secondary math student teaching practicum in math student teaching.
Credit: 3