## Undergraduate Courses in Mathematics and Statistics

Below are listings for Undergraduate Courses offered through the Department of Mathematics. The authoritative source for course information is the Marshall University Catalog.

View the Mathematics upper-division Undergraduate Course Offering (PDF) schedule for future semesters.

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100 Level Math and Statistics Courses

200 Level Math and Statistics Courses

300 Level Math and Statistics Courses

400 Level Math and Statistics Courses

### 100 Level Math and Statistics Courses

- MTH 100 – Preparation for College Mathematics A
- A mastery-based course that will prepare students for quantitative reasoning courses in their majors.

PR: Math ACT of 18 or below.

*3 Credit Hours* - MTH 102 – Preparation for College Mathematics B
- A mastery-based course that will prepare students for College Algebra.

PR: Math ACT of 18 or below.

*4 Credit Hours* - MTH 102B – Abridged Preparaaton for College Mathematics B
- An abridged mastery-based course that will prepare students for College Algebra.

PR: MTH 100 or MTH 121 or MTH 121B; and permission of the Math Department.

*1 Credit Hours* - MTH 121 – Concepts and Applications of Mathematics (CT)
- Critical thinking course for non-science majors that develops quantitative reasoning skills. Topics include logical thinking, problem-solving, linear modeling, beginning statistics and probability, exponential and logarithmic models, formula use, and financial concepts.

PR: ACT Math 19 or MTH099.

*3 Credit Hours* - MTH 121B – Concepts and Applications of Mathematics with Algebra Review (CT)
- A quantitative reasoning skills course for non-science majors. Topics include logical thinking, problem solving strategies, beginning statistics and probability, exponential and logarithms modeling, formula use, with basic algebra review.

PR: ACT Math 17-18 or MTH100.

*4 Credit Hours* - MTH 122 – Plane Trigonometry
- A study of the trigonometric functions, graphs of the trigonometric functions, identities, equations, inverse trigonometric functions, vectors, complex numbers, and applications.

PR: ACT Math 21 or MTH127 or MTH130.

*3 Credit Hours* - MTH 125 – Mathematical Thinking (CT)
- A critical thinking course for non-science majors. Topics include number systems, sequences, modular arithmetic, deductive arguments, linear programming, techniques of problem solving, and history of mathematics.

PR: ACT Math 19 or MTH099 or MTH100.

*3 Credit Hours* - MTH 127 – College Algebra – Expanded Version
- A brief but careful review of the main techniques of algebra. Polynomial, rational, exponential, and logarithmic functions. Graphs, equations and inequalities, sequences.

PR: ACT Math 19 or ACT Math 20 or MTH099 or MTH102.

*5 Credit Hours* - MTH 130 – College Algebra
- Polynomial, rational, exponential, and logarithmic functions. Graphs, equations and inequalities, sequences.

PR: ACT Math 21.

*3 Credit Hours* - MTH 132 – Precalculus with Science Applications
- Functions used in calculus including polynomial, rational, exponential, logarithmic, and trigonometric. Systems of equations and inequalities, conic sections, polar and parametric equations, sequences and series, Binomial Theorem.

PR: ACT Math 24 or MTH127 or MTH130.

*5 Credit Hours* - MTH 140 – Applied Calculus
- A brief survey of calculus including both differentiation and integration with applications. Not to be substituted for Mathematics 229.

PR: ACT Math 24 or MTH127 or MTH130.

*3 Credit Hours* - MTH 140H – Applied Calculus Honors
- A brief survey of calculus including both differentiation and integration with applications. This honors course will also introduce topics from differential equations with applications.

PR: ACT Math 25 or MTH127 or MTH130.

*3 Credit Hours* - MTH 160 – Applied Mathematical Reasoning (CT)
- A critical thinking course in applied mathematical reasoning. Topics include logic, problem solving, linear modeling, beginning statistics and probability, exponential and logarithmic modeling, formula use.

PR: ACT Math 19 or MTH 099.

*5 Credit Hours*

### 200 Level Math and Statistics Courses

- MTH 220 – Discrete Structures
- Sets, relations, directed and undirected graphs, monoids, groups, lattices, Boolean algebra, and propositional logic.

PR: ACT Math 27 or MTH132 or MTH229 or IST131.

*3 Credit Hours* - STA 225 – Introductory Statistics (CT)
- A critical thinking course in applied statistical reasoning covering basic probability, descriptive statistics and fundamental statistical inference procedures. Parameter estimation and hypothesis testing for variety of situations with wide applications.

PR: ACT Math 21 or MTH121 or higher.

*3 Credit Hours* - MTH 229 – Calculus with Analytic Geometry I (CT)
- An introduction to calculus and analytic geometry, emphasizing critical thinking. Limits, derivatives, and integrals of the elementary functions of one variable, including transcendental functions.

PR: ACT Math 27 or MTH 132.

*5 Credit Hours* - MTH 229H – Calculus with Analytic Geometry I (Honors) (CT)
- An introduction to calculus and analytic geometry for honors students, emphasizing critical thinking. Limits, derivatives, and integrals of the elementary functions of one variable, including transcendental functions.

PR: ACT Math 30

*5 Credit Hours* - MTH 230 – Calculus with Analytic Geometry II
- Applications of the integral, techniques of integration, and infinite series. A study of conic sections, polar coordinates, and parametric equations.

PR: MTH229 or IST230.

*4 Credit Hours* - MTH 231 – Calculus with Analytic Geometry III
- Vectors, curves, and surfaces in space. Derivatives and integrals of functions of more than one variable. A study of the calculus of vector-valued functions.

PR: MTH230.

*4 Credit Hours* - MTH 280-283 – Special Topics
- Courses on special topics not listed among the current course offerings.

PR: Permission of instructor.

*1 to 4 Credit Hours*

### 300 Level Math and Statistics Courses

- MTH 300 – Introduction to Higher Mathematics
- A transition between elementary calculus and higher mathematics with emphasis on techniques of proofs.

PR: MTH230.

*4 Credit Hours* - STA 326 – Applied Statistical Methods
- Use of statistical packages; introduction to descriptive, probability and sampling distributions; forecasting, inferences concerning one and two samples; simple and multiple regression, analysis of variance and covariance.

PR: C or better in MTH 225.

*3 Credit Hours* - MTH 329 – Elementary Linear Algebra
- Systems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications.

PR: ACT Math 27 or MTH132 or MTH229 or IST131.

*3 Credit Hours* - MTH 331 – Linear Algebra
- Vector spaces, matrices and determinants, linear transformations, eigenvalues and eigenvectors, and applications.

PR or CR: MTH300.

*4 Credit Hours* - MTH 335 – Differential Equations
- First and second-order ordinary differential equations. Applications include vibrations and electrical circuits. Laplace transform, approximate solutions, orthogonal functions, Fourier series; partial differential equations including heat, wave, and Laplace equations.

PR: MTH231.

*4 Credit Hours* - STA 345 – Applied Probability and Statistics
- Statistical methods in scientific/engineering research, with emphasis on applications. Probability modeling, experimental design/survey sampling, estimation/hypothesis testing procedures, regression, ANOVA/factor analysis. Implementation using statistical software such as Excel/SAS.

PR: MTH230 or IST230.

*3 Credit Hours* - MTH 360 – Introduction to Complex Variables
- An introductory survey of complex numbers, analytic functions, properties of elementary functions, integrals, series, residues and poles, with a focus on practical applications.

PR: MTH 231.

*3 Credit Hours* - MTH 361 – Vector Calculus
- A course in n-dimensional calculus: the derivative, the integral, and applications. Coordinate-free methods are emphasized.

PR: MTH 231.

*3 Credit Hours*

### 400 Level Math and Statistics Courses

- MTH 400 – Structure of Algebra
- Informal development of modern elementary algebra. Recommended for pre-service middle school teachers and for elementary and secondary in-service teachers. May not be used for either a 5-12 mathematics specialization or for a degree offered by the Department of Mathematics.

PR: MTH130.

*3 Credit Hours* - MTH 401 – Structure of Modern Geometry
- Informal development of geometry with an exploration of probability and statistics. Recommended for pre- service middle school teachers and for elementary and secondary in-service teachers. May not be used for either a 5-12 mathematics specialization or for a degree offered by the Department of Mathematics.

PR: MTH130 or MTH127.

*3 Credit Hours* - MTH 404 – Mathematics Methods and Materials
- Content and content-specific pedagogy for secondary mathematics education majors.

PR: CI470 and Admitted to Teacher ED 5.

*3 Credit Hours* - MTH 405 – History of Mathematics
- A study of the history of mathematics from the time of the ancient Greeks to the end of the nineteenth century.

PR: MTH300.

*3 Credit Hours* - MTH 411 – Mathematical Modeling
- Students work in teams to construct mathematical models of various real-world situations. Problems to be modeled are drawn from diverse areas of application and use a wide range of undergraduate mathematics.

PR: MTH231.

*3 Credit Hours* - STA 412 – Regression Analysis
- Topics in determining regression models; deriving parameter estimates using calculus; detailed coverage of tests of assumptions and remedial procedures (transformations and weighted least- squares); multiple and polynomial regression; tests and corrections for autocorrelation.

PR: One previous course in statistics and some familiarity with calculus and linear algebra, or permission of instructor.

*3 Credit Hours* - STA 413 – Experimental Designs
- Principles of experimentation; analysis of variance and covariance; latin square and related designs; factorial designs, response surface; robustness; nested and split-plot designs.

PR: One previous course in statistics and some familiarity with calculus and linear algebra, or permission of instructor

*3 Credit Hours* - MTH 415 – Partial Differential Equations
- Elementary partial differential equations. Heat Equation, Laplace’s Equation, separation of variables, Fourier series, vibrating strings, eigenvalue problems, finite differences, Bessel functions, Legendre polynomials.

PR: MTH331 and MTH335.

*3 Credit Hours* - MTH 416 – Advanced Differential Equations
- Differential equations are studied qualitatively. Topics include the existence and uniqueness of solutions and the behavior of solutions including stability of nonlinear systems, periodic solutions, and approximation using pertubation methods.

PR: MTH300 and MTH335.

*3 Credit Hours* - STA 420 – Nonparametric Methods
- Coverage of a variety of nonparametric or distribution-free methods for practical statistical inference problems in hypothesis testing and estimation, including rank procedures and randomization procedures.

PR: One previous course in statistics and some familiarity with calculus and linear algebra, or permission of instructor

*3 Credit Hours* - STA 422 – Applied Time Series Analysis
- Finding statistical models to represent various time dependent phenomena and processes; coverage of a variety of forecasting techniques, with an emphasis on adaptive, regression, and Box-Jenkins procedures.

PR: MTH230 or permission.

*3 Credit Hours* - STA 425 – Sampling Design and Estimation
- Coverage of the theory and applications of a variety of sampling designs, sample size determination; ration and regression estimated comparisons among the designs.

PR: STA 326 or permission of instructor

*3 Credit Hours* - MTH 427 – Advanced Calculus I
- A rigorous study of the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series.

PR: MTH231 and MTH300. CR: MTH331.

*3 Credit Hours* - MTH 428 – Advanced Calculus II
- A rigorous development of algebra and topology of Euclidean spaces, differentiability and integrability of functions of several variables.

PR: MTH427.

*3 Credit Hours* - MTH 430 – Topology I
- First course in topology. Basics of point-set topology: metric and topological spaces, continuity, connectedness, compactness, products, quotients. Surfaces and simplicial complexes, Euler characteristics.

PR: MTH300.

*3 Credit Hours* - MTH 431 – Topology II
- First course in algebraic topology. Homotopy, fundamental group, simplicial homology.

PR: MTH430 and MTH450.

*3 Credit Hours* - MTH 440 – Graph Theory and Combinatorics
- This course is designed to introduce students in mathematical sciences to the theorems, techniques, and applications of graph theory and combinatorics.

PR: MTH300.

*3 Credit Hours* - MTH 442 – Numerical Linear Algebra
- Direct and iterative methods for numerical solution of linear systems of equations. Eigenvalues and eigenvectors. Error Analysis and norms. Related topics and applications.

PR: MTH331.

*3 Credit Hours* - MTH 443 – Numerical Analysis
- Computer arithmetic, roots of equations, interpolation, linear systems, and numerical differentiation and integration. Analysis of errors in and convergence properties of algorithms. Computer implementation of methods.

PR: MTH331 and a programming language.

*3 Credit Hours* - STA 445 – Probability & Statistics I
- Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments.

PR: MTH231.

*3 Credit Hours* - STA 446 – Probability & Statistics II
- Statistical inference: estimation of parameters, tests of hypotheses. Regression, analysis of variance.

PR: STA445.

*3 Credit Hours* - MTH 448 – Modern Geometries
- Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.

PR: MTH300.

*3 Credit Hours* - MTH 449 – Projective Geometry
- Projective Geometry using both synthetic and algebraic methods.

PR: MTH300.

*3 Credit Hours* - MTH 450 – Modern Algebra I
- Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from number theory.

PR: MTH300 and MTH331.

*3 Credit Hours* - MTH 452 – Modern Algebra II
- Continuation of MTH 450.

PR: MTH450.

*3 Credit Hours* - MTH 455 – Number Theory
- A survey of some basic properties of the integers: divisibility (prime numbers, factorization, perfect numbers), congruences (modular arithmetic, linear and quadratic congruences, the Chinese Remainder Theorem), and Diophantine equations.

PR: MTH300.

*3 Credit Hours* - STA 464 – Statistical Computing
- Introduction to the commonly used statistical computing techniques, procedure and methods, with extensive use of R language and environment, and SAS for statistical computing and graphics.

PR: STA 445 or STA 446

*3 Credit Hours* - STA 466 – Stochastic Processes
- Review of probability theory. Topics include stationary processes, discrete and continuous time Markov chains, Markovian queueing systems, random walks, renewal processes, Brownian motion and Markov Chain Monte Carlo.

PR: MTH 231 and MTH 445

*3 Credit Hours* - STA 470 – Applied Survival Analysis
- Survival and hazard functions, parametric and non-parametric methods, models and inferences for survival data, and regression diagnosis.

PR: 445, or permission.

*3 Credit Hours* - MTH 480-483 – Special Topics
- Courses on special topics not listed among the current course offerings.

PR: Permission of instructor.

*1 to 4 Credit Hours* - MTH 485-488 – Independent Study
- An independent program of study of advanced topics not normally covered in other courses. The topics are chosen upon mutual agreement between the student and the instructor.

PR: Permission of instructor.

*1 to 4 Credit Hours* - MTH 490 – Internship
- A supervised internship in an area of mathematics, applied mathematics, or statistics. By permission only.

PR: MTH 300 and permission

*2 to 12 Credit Hours* - MTH 491 – Senior Seminar
- Capstone experience in reading, doing, writing and speaking mathematics. Students will explore topics related to a theme chosen by the instructor.

*2 Credit Hours*