## Courses in the Mathematics Curriculum at SC State University

**M 150. Quantitative Reasoning—Mathematics. 3(3, 0).**

A study of how mathematics is used to formulate problems and solve applications problems within the context of the real-world and other disciplines. Quantitative reasoning skills are developed and experience is gained in applying these skills and the methodology of mathematics to analyze quantitative information to make decisions and predictions. Topics include sets, number properties and theory, arithmetic review, consumer mathematics, estimation, measurement, basic geometry, and elementary statistics and probability. Technology is used and writing is emphasized.

Prerequisite: None. (F, S)

**M 151. Quantitative Reasoning—Algebra. 3(3, 0).**

A study of how algebra is used to formulate problems and solve applications problems within the context of the real world and other disciplines. Quantitative reasoning skills are developed and experience is gained in applying these skills and the methodology of algebra to analyze quantitative information to make decisions and predictions. Topics include operations with polynomials, solutions of inequalities and linear, quadratic, radical and rational equations, operations with exponents, simplifying expressions and basic concepts of functions. Technology is used and writing is emphasized.

Prerequisite: M150 or Consent of the Instructor. (F, S)

**M 152. Quantitative Reasoning—Precalculus. 3(3, 0).**

A study of how precalculus is used to formulate problems and solve applications problems within the context of the real world and other disciplines. Quantitative reasoning skills are developed and experience is gained in applying these skills and the methodology of precalculus to analyze quantitative information to make decisions and predictions. Topics include absolute value and inequalities, polynomial, rational, linear, logarithmic, exponential, and trigonometric functions; polar coordinates, solution of triangles, and the conic sections. Technology is used and writing is emphasized.

Prerequisite: M151 or Consent of the Instructor. (F, S)

**M 153. Quantitative Reasoning—Calculus. 3(3, 0).**

A study of how calculus is used to formulate problems and solve applications problems within the context of the real world and other disciplines. Quantitative reasoning skills and the methodology of calculus to analyze quantitative information to make decisions and predictions. Topics include functions, limits, continuity, the derivative, and techniques and applications of differentiation. Technology is used and writing is emphasized.

Prerequisite: M152 or Consent of the Instructor. (F, S)

**M 154. Quantitative Reasoning Business Calculus. 3(3, 0).**

A study of how calculus is used to formulate problems and solve applications problems within the context of the real world and other disciplines. Quantitative reasoning skills are developed and experience is gained in applying these skills and the methodology of calculus to analyze quantitative information to make decisions and predictions. Topics include functions, limits, continuity, the derivative, antiderivative, and techniques and applications of differentiation and integration with emphasis on business and economics. Technology is used and writing is emphasized.

Prerequisite: M152 or Consent of the Instructor. (F, S)

**M 155. Introduction to Mathematical Modeling. 3(3, 0).**

A study of mathematical models and how they are used to analyze quantitative information to make decisions and predictions. Topics include percentage change, formulas, statistics, statistical inference, probability and odds, and linear, exponential, and logarithmic functions. The course emphasizes problem solving by means of numerical or geometrical representations of real world phenomena, determining how to solve a problem, formulating alternatives, and predicting outcomes. Writing assignments and the use of technology are an integral part of the course. A written project using student generated data is required.

Prerequisite: M150 or Consent of the Instructor. (F, S)

**M 158. Calculus I. 4(4, 0).**

A study of how calculus is used to formulate and solve application problems in science and engineering. Topics in this course are as follows: Limits, Differentiation and Related Rates, Differentiation Rules, Maximum/Minimum, Optimization Problems, Definite and Indefinite Integrals, Logarithmic, Exponential and Inverse Trigonometric Functions, Differentiation and Integration of Transcendental Functions, Elementary Differential Equations. Emphasis is on science and engineering applications of calculus.

Prerequisite: M152 or Consent of the Instructor. (F, S)

**M 163. Calculus II. 3(3, 0).**

The definite and indefinite integral; techniques of integration; differentiation and integration of transcendental functions; applications of integration.

Prerequisite: M 153 or Consent of the Instructor. (F, S)

**M 168. Calculus II.4 (4, 0).**

A study of how calculus is used to formulate and solve application problems in science and engineering. Topics in this course are as follows: Differential Equations (Slope Fields and Euler’s Method, First-Order Linear Differential Equations), Area of Plane Regions, Volume-of Solids, Arc Length, Surface of Revolution, Work, Moments, Center of Mass, Fluid Pressure, Fluid Force, Integration by Parts, Trigonometric Integrals, Partial Fractions, Improper Integrals, Sequences and Series, Convergence, Alternating Series, Ratio and Root Test, Taylor Series, Power Series, Parametric and Polar Coordinates, Kepler’s Laws.

Prerequisite: M 158. (F, S)

**M 207. Foundations of Geometry. 3(3, 0).**

Theorems and concepts more advanced than those of high school geometry. Geometry of the triangle, circle, plane, and solid figures, with proofs by coordinate methods.

Prerequisite: M 151 or Consent of the Instructor. (F, S)

**M 208. Introduction to Statistics. 3(3, 0).**

Descriptive statistical measures, discrete/continuous random variables, probability/sampling distributions, statistical inference to include hypothesis testing, point/ interval estimation, correlation, and regression. A calculator is required.

Prerequisite: M 152 or Consent of the Instructor. (F, S)

**M 210. Finite Mathematics. 3(3, 0).**

Matrix algebra, elements of linear programming, simplex method, sets basic counting principles, basic statistics and probability concepts, Markov chains, elementary game theory. The emphasis will be on problem formulation and application.

Prerequisite: M 151 or Consent of the Instructor. (F,S)

**M 214. Mathematics for the Managerial, Military, and Social Sciences. 3(3, 0).**

Review of arithmetic and algebra with emphasis on applications. An introduction to selected topics in finite mathematics including matrix algebra, systems of linear equations, graphical solution of max-min problems in two variables, the simplex method.

Prerequisite: M 151 or Consent of the Instructor. (F, S)

**M 215. Logic, Sets, and Proofs. 3(3, 0).**

An introduction to the language of logic and set theory, elementary set theory, properties of the real number system, symbolic logic and its relationship to theory, algorithms and their complexity, set counting methods and recurrence relations. Special attention will be given to proof of the various theorems and properties.

Prerequisite: M 151 or Consent of the Instructor. (F, S)

**M 237. Calculus III. 3(3, 0).**

Parametric equations, polar coordinates, vectors in the plane and three dimensions, techniques of integration, and application of the integral.

Prerequisite: M 163. (F, S)

**M 238. Calculus IV. 3(3, 0).**

Infinite series, partial derivatives, maxima and minima of functions of several variables, and application of line, surface, and volume integrals.

Prerequisite: M 237. (S)

**M 250. Linear Algebra for Science and Engineering. 3(3,0).**

The course will cover the following fundamental topics: two- and three-dimensional vectors. Do not cross-product with applications in physics and engineering; Matrices and their elementary properties, Linear systems and determinants, Matrix Decomposition, eigenvalues eigenfunctions.

Prerequisites: M 153 or M 158.

**M 278. Calculus III. 4(4, 0).**

A study of how calculus is used to formulate and solve application problems in science and engineering. Topics in this course are as follows: Partial Derivatives, Differentials, Chain Rule, Directional Derivatives and Gradient, Maximum/Minimum, Applications of Minimum/Maximum, Lagrange Multipliers, Iterated Integrals, Change of Variables, Center of Mass and Moment of Inertia, Surface Area, Triple Integrals and Applications, Vector Fields, Line Integrals, Conservative Vector Fields, Green’s Theorem, Parametric Surfaces, Surface Integrals, Divergence Theorem, Stokes Theorem.

Prerequisite: M 168. (F, S)

**M 301. Introduction to Mathematical Logic. 3(3, 0).**

The sentential and predicate calculus, logical inference and proof theory.

Prerequisite: M 153 or M 158.

**M 303. Introduction to Number Theory 3(3, 0).**

A study of the properties of the integers with theorems on primes, divisibility, congruencies, Diophantine equations, and continued fractions.

Prerequisite: M 153 or M158. (F)

**M 305. Introduction to Modern Geometry. 3(3, 0).**

Transformation groups, invariants, affine and projective geometry.

Prerequisite: M 153 or 158. (F)

**M 306. Modern Algebra. 3(3, 0).**

An axiomatic treatment of the basic algebraic systems, including groups, rings, integral domains, and fields.

Prerequisite: M 153 or M158, M 215. (S)

**M 309. Introduction to Statistical Methods and Data Analysis I. 3(3, 0).**

Techniques of describing data; exploratory data analysis; random variables and probability distributions; statistical inferences about population means; categorical data and inferences about variances; linear regression and correlation; multiple comparisons; an introduction to the analysis of variance; throughout the focus is on computer solutions.

Prerequisite: M 152 or Consent of the Instructor. (F, S)

**M 310. Introduction to Statistical Methods and Data Analysis II. 3(3, 0).**

The general linear model; multiple regression; the relationship between regression and analysis of variance; analysis of variance for some fixed, random, and mixed effects models; the analysis of covariance; data description and management; computer packages are used through the course.

Prerequisite: M 309. (S)

**M 314. Linear Algebra. 3(3, 0).**

This course covers vectors and linear spaces, operations on matrices, determinants, linear systems of equations, linear subspaces, linear transformations and canonical forms.

Prerequisite: M163 or M168, M 215. (F, S)

**M 315 Discrete Mathematics. 3(3, 0).**

An introduction to computer-based mathematics including recursion, algorithms and their complexity, graph theory and the theory of formal languages.

Prerequisite: M 215. (F, S)

**M 350. Applied Mathematics. 3(3, 0).**

This course stresses the application of mathematics to problems drawn from engineering, physical, chemical and biological fundamentals. Course topics include the following: Advanced topics from fourier analysis, partial differential equations, boundary value problems, signal processing and wavelet analysis.

Prerequisite: M 237 or M 278.

**M 403. Differential Equations. 3(3, 0).**

Ordinary differential equations with applications; series solutions; solution by Laplaces transform; numerical methods.

Prerequisite: M 237 or M278. (F)

**M 404. Introduction to Real Analysis I. 3(3, 0).**

Advanced topics from the theory of functions of one variable; includes the real number system, Bolzano-Weierstrss Theorem, Heine-Borel Theorem; theory of limits; continuity, uniform continuity, differentiability, sequences of functions, theory of Riemann integration.

Prerequisite: M 238 or M 278. (F)

**M 405. Introduction to Real Analysis 11. 3(3, 0).**

Advanced topics from the theory of functions of several variables: includes a review of partial differentiations, general theorems of partial differentiation, transformations and mappings; Jacobians, Implicit Functions Theorem; multiple integrals.

Prerequisite: M 404. (S)

**M 406. Introduction to Complex Analysis. 3(3, 0).**

The algebra of complex numbers, analytic functions, the geometry of elementary functions, power series, and contour integration.

Prerequisite: M 237 or M 278. (S)

**M 407. Mathematical Models and Applications. 3(3, 0).**

Introduction to theory and practices of building and studying mathematical models for various real-world situations that may be encountered in management, life, social and physical sciences.

Prerequisite: M163 or M 168, CS 161 or CS 160. (S)

**M 408. Introduction to Probability. 3(3,0).**

Probability as a mathematical system, probability spaces and their properties, conditional probability; random variables (discrete and continuous and their distributions), functions of random variables. Chebyshev’s inequality, regression and multivariate distributions; limit theorems and special distributions; introduction to stochastic processes.

Prerequisite: M 208, M 237 or M 278. (F)

**M 409. Mathematical Statistics. 3(3, 0).**

Sampling, point and interval estimates, testing hypotheses, the power of a test, regression, analysis of variance and some nonparametric methods.

Prerequisite: M 408. (S)

**M 410. Numerical Analysis I. 3(3, 0).**

A study of numerical methods for solving linear systems of equations, solution of transcendental equations and polynomial equations. Error analysis, convergence of numerical algorithms and iterative methods. Numerical methods of evaluating definite integrals. Approximate methods of solving systems of equations.

Prerequisite: CS 161 or CS 160, M 163 or M 168. (F)

**M 411. Numerical Analysis II. 3(3, 0).**

A study of numerical methods for solving boundary value problems in ordinary differential equations. Error analysis and convergence of numerical algorithms. Interpolation and numerical differentiation. Smoothing of data and method of least square. Solution of systems of differential equations.

Prerequisite: M 410/CS 402. (F)

**M 412. Operations Research. 3(3, 0).**

Linear programming, transportation and assignment problems, non-linear programming, network analysis, dynamic programming, queuing theory, and Markov processes.

Prerequisite: M 208 or M 309, M 314. (S)

**M 490. Problem Solving in Mathematics. 3(3, 0).**

Students will engage in extensive experiences and practice in solving mathematical problems. The experiences will serve as a backdrop for an in-depth examination of research into the learning of mathematical concepts.

Prerequisites: M 207, M 208 or M 309, and M 237 or M 278 or Consent of the Instructor. (F)

**M 498. Mathematics Research Study. 3(3, 0).**

Provides an opportunity for the student to do independent reading and research under the supervision of a staff member. The students may elect to read in the following areas: number theory, theory of equations, Boolean algebra, convexity and inequalities, vector and tensor analysis, differential geometry, elementary topology, linear spaces, probability, statistics, and boundary value problems.

Prerequisite: M 238 or M 278 or Consent of the Instructor. (F)

**MATHEMATICS EDUCATION**

**M Ed 104. Geometry for Elementary School Teachers. 3(3, 0).**

A modern view of geometry for pre-service elementary school teachers. The course is concerned with elementary geometric ideas and proofs, and some practical geometric applications. Pre-clinical experiences are required (twenty to forty hours).

Prerequisite: M 150. (F, S)

**M Ed 300. Mathematics for Elementary School Teachers. 3(3, 0).**

Designed primarily for prospective elementary school teachers. The study of new approaches and course content. Emphasis is placed on efficiency in performing mathematical computations and the understanding of elementary mathematical procedures. Pre-clinical experiences are required (twenty to forty hours).

Prerequisite: M 150 and MED 104. (F, S)

**M Ed 308F. Principles of Learning Secondary Materials and Methods. 3(3, 0).**

The purpose of this course is to enable prospective teachers of secondary school mathematics to re-examine and to become thoroughly competent in present-day course content and teaching methods of secondary school mathematics. M 237 or M 278. Junior Standing or Consent of the Instructor. (F, S)

**MIDDLE LEVEL EDUCATION**

### M Ed 320. The Mathematics Education in Middle School 3(3,0).

This course prepares candidates to create and sustain an inclusive and supportive learning environment in which all students can engage in learning. They will develop skills in using reflective practice to adapt behavior to assist all students in learning. Candidates will be able to design and implement instruction and assessment that assist students in developing critical thinking skills. They will develop a variety of learning experiences to integrate content knowledge into the planning, implementation, and assessment of instruction. Candidates will be able to create opportunities that enable students to demonstrate skill in the content area. They will be able to use a variety of approaches for teaching students to construct meaning from the text and experiences in the content area. They will be able to reflect on their own teaching in light of research, theories and best practice and demonstrate an understanding of the purposes and characteristics of different kinds of curricula and related resources that are consistent with student learning. Candidates will learn to work with teachers in other content areas to connect important ideas, concepts, and skills within other disciplines. They will also establish criteria and develop strategies for assessment that allow all students to understand what they know and can do in light of their instructional experiences. They will learn to work harmoniously with parents, teachers, administrators and the community and to embrace technology as an essential tool for teaching and learning. Finally this course will provide opportunities for observing and participating in various school and classroom settings that include a wide rate of instructional and administrative elements. They will have opportunities for interacting with students of varying socio-economic, racial and ethnic backgrounds, and those with special learning needs and diverse learning styles.