UNCA Catalog: Courses of Instruction
UNCA Catalog: Table of Contents

Mathematics (MATH) and Statistics (STAT)

Associate Professor Peifer (Chair); Professors Dohse, Patch; Associate Professors Gale, Steele; Assistant Professors Atkinson, Boudreaux, Kaplan, MacLean, McClure; Lecturers Kendrick, McClellan, D. Sulock, Whitlock

The science of mathematics is fundamental to many disciplines and an integral part of a liberal arts education. Quantitative skills such as data analysis, problem solving, pattern recognition and mathematical modeling are increasingly vital to contemporary professions. Entry-level mathematics courses introduce students to basic concepts and tools that are essential to education. Upper-level courses provide students with the opportunity to explore mathematical topics in greater depth.

There are four concentrations of study from which to select a Mathematics major: Pure Mathematics, Applied Mathematics, Statistics, and Mathematics with Teacher Licensure. The requirements for each of these programs are listed below.

Concentration in Pure (Theoretical) Mathematics

This area consists of a traditional Mathematics major. It serves well as a strong liberal arts major. With appropriate selection of the major options, it will give the student an adequate preparation for graduate study in mathematics.

1. Required courses in the major--38-39 hours, including MATH 191, 192, 280, 291, 365, 381, 461, 480, 491; and an additional 12-13 hours chosen from STAT 225 and Mathematics and Statistics courses numbered above 300. These latter hours must include one course from MATH 366, 462, 492.
2. Required courses outside the major--9-11 hours, consisting of CSCI 201, and one of the sequences: CHEM 111-132-144, ECON 101-102, PHYS 221-222.
3. Other departmental requirements--Satisfactory performance on a comprehensive Mathematics exam and the satisfactory presentation of one seminar in MATH 480. Satisfactory completion of this course fulfills the oral competency requirement.

Concentration in Applied Mathematics

This program of study is designed for students planning a career in industry where training in problem solving and interdisciplinary work is essential, or for students planning to pursue a graduate degree in an applied mathematics field. Students in this program are strongly encouraged to minor in a science or social science.

1. Required courses in the major--38-39 hours, including: MATH 191, 192, 280, 291, 352, 365, 381, 394, 480; MATH 461 or 491; STAT 225 or 425; and an additional 6 hours in Mathematics or Statistics courses numbered above 300. These latter hours must include either MATH 366, 395; or the sequence STAT 425-426.
2. Required courses outside the major--18-20 hours: CSCI 201; and 15-17 hours in an area of specialization in a discipline in which mathematical applications are important. This area of specialization must be approved by the department, and of the 15-17 hours, at least nine must be at the 300-400 level.
3. Other departmental requirements--Satisfactory performance on a comprehensive Mathematics exam and the satisfactory presentation of one seminar in MATH 480. Satisfactory completion of this course fulfills the oral competency requirement.

Concentration in Statistics

This program is designed for students who have an interest in probability and statistics. Graduates may pursue a career in actuarial science, quality control or related fields, or enter a graduate program in statistics, mathematics or a related discipline.

1. Required courses in the major--39 hours, including: MATH 191, 192, 280, 291, 365, 381, 480; STAT 185 or 225; 325, 326, 425, 426; and any Mathematics or Statistics course numbered above 300. Students intending to pursue graduate study are strongly advised to take MATH 491.
2. Required courses outside the major--9 hours, including: CSCI 201; and either ECON 101 and 301; or ECON 102 and 302; or MGMT 220 and 380; or six hours at the 300-400 level approved by the department from disciplines which routinely employ statistical methodology.
3. Other departmental requirements--Satisfactory performance on a comprehensive Mathematics exam and the satisfactory presentation of one seminar in MATH 480. Satisfactory completion of this course fulfills the oral competency requirement.

Mathematics with Teacher Licensure

This area is designed to provide a good background in mathematics for those students planning to teach mathematics at the secondary level. Completing this program also satisfies the requirements for secondary licensure in mathematics. (See the Education listing for additional required professional education courses.)

1. Required courses in the major--39 hours, including MATH 191, 192, 251, 280, 291, 332, 365, 381, 480; STAT 225; two courses from: MATH 394, 461 or 491; and an additional 3 hours in Mathematics or Statistics courses numbered above 300.
2. Required courses outside the major - 31 hours, consisting of CSCI 201; PSYC 101, 318; and EDUC 310, 314, 383, 396, 455, 496. Please see the Education curriculum for more detail.
3. Other departmental requirements--Satisfactory performance on a two-part comprehensive Mathematics exam and the satisfactory presentation of one seminar in MATH 480. Satisfactory completion of this course fulfills the oral competency requirement.

Declaration of Major

Declaring a major in Mathematics requires a student to complete a Declaration of Major form that must be signed by the department chair. In addition, before declaring a major a student must satisfy the LANG 102 and Library Research requirements.

Minor in Mathematics

21 hours in Mathematics or Statistics: MATH 191, 192, 291, and at least nine semester hours at the 300 level or above, with no more than one credit in MATH 381 or one credit in MATH 480.

Mathematics Assistance Center

The Mathematics Assistance Center is operated by a professional staff to help students in their courses. Students are welcome to drop in at any time to obtain help on topics ranging from basic mathematics through calculus. They may use the center to work on their homework or to meet in study groups. The center also offers independent study programs for students not prepared for MATH 155.

Courses in Mathematics

155 Nature of Mathematics (4)

Topics from symbolic logic, set theory, plane and solid geometry, fractals, probability, statistics, mathematical modeling, theories of voting, network theory, mathematics in art and music, and financial mathematics are explored with an emphasis on problem solving using scientific calculators and computer spreadsheets. Fall and Spring.

158 Structure of Mathematics II (3)

Intuitive and deductive study of points, lines, planes, curves, surfaces, parallelism and similarity; linear, angular, area and volume measurement. Prerequisite: permission of the instructor. Fall and Spring.

The following courses may not be taken out of sequence: MATH 163, 164, 191, 192 and 291. (MATH 167 may replace 163 and 164.)

163 Applied Algebra (4)

A study of algebraic, exponential and rational functions and their applications. Topics will include graphing, the solving of equations, and mathematical modeling. (Students may not receive credit for both MATH 163 and 167). Fall and Spring.

164 Trigonometry (2)

A study of trigonometric functions, identities, equations and their applications. Topics will include complex numbers and polar coordinates. Prerequisite: MATH 163. (Students may not receive credit for both MATH 164 and 167.) Fall and Spring.

167 Precalculus (4)

The topics are identical to those covered in MATH 163 and MATH 164. This course is primarily for students who need to take Calculus I but do not have a sufficient mathematics background to do so. Prerequisites: the equivalent of two years of high school algebra and satisfactory performance on the mathematics placement exam. (Students may not receive credit for both MATH 167 and 163, or for both MATH 167 and 164.) Fall and Spring.

191 Calculus I (4)

An introduction to limits, continuity, derivatives and integrals, with emphasis on the calculus of polynomial, rational and algebraic functions; a balanced presentation of the theory and application of differential and integral calculus. Prerequisites: MATH 163 and 164; or MATH 167; or four years of high school mathematics, including algebra, geometry and trigonometry; and satisfactory performance on the mathematics placement exam. Fall and Spring.

192 Calculus II (4)

The calculus of exponential, logarithmic and trigonometric functions, the Mean Value Theorem, indeterminate forms, improper integrals and infinite series. Prerequisite: MATH 191. Fall and Spring.

211 Structure of Mathematics I (3)

An intuitive development of the real number system emphasizing problem solving, set theory, arithmetic properties of the real numbers, topics from number theory, and basic algebraic structures. This course is designed for elementary licensure students. Prerequisite: 30 semester hours (sophomore standing). Corequisite: MATH 212. Fall and Spring.

212 Structure of Mathematics I: Laboratory and Field Experience (1)

Laboratory experiences designed to address how children learn mathematics. Field experience in the elementary schools is included. The activities parallel the topics addressed in MATH 211. Corequisite: MATH 211. Fall and Spring.

215 Structure of Mathematics II (3)

A continuation of Math 211. A study of topics from descriptive statistics, probability, and an intuitive and deductive study of geometry, including points, lines, planes, curves, surfaces, parallelism and similarity; linear, angular, area and volume measurement. Prerequisite: MATH 211. Corequisite: MATH 216. Fall and Spring.

216 Structure of Mathematics II: Laboratory and Field Experience (1)

Laboratory Experiences designed to address how children learn mathematics. Field experience in the elementary schools is included. The activities parallel the topics addressed in MATH 215. Corequisite MATH 215. Fall and Spring.

251 Discrete Mathematics (3)

Introductory logic and Boolean algebra, mathematical induction, recursion and difference equations, combinatorics, graph theory and modeling. Prerequisite: MATH 191. Spring.

280 Introduction to the Foundations of Mathematics (3)

Set theory, functions and relations, the structure of the real number system, deductive logic and the nature of proof, and axiomatic systems. Pre- or corequisite: MATH 192. Fall and Spring.

291 Calculus III (4)

Functions of several variables, with emphasis on partial differential and multiple integration; introduction to vector analysis; may include an introduction to line and surface integrals. Prerequisite: MATH 192. Fall and Spring.

332 Geometry (3)

Euclidean geometry and the fifth postulate; hyperbolic and elliptic geometries, the consistency of non-Euclidean geometries, and projective geometry. Prerequisites: MATH 280, 291. Odd years Fall.

341 Numerical Analysis (CSCI 381) (3)

Methods for numerically solving mathematical problems: polynomial approximation, approximation theory, numerical differentiation and integration, numerical methods in matrix algebra and differential equations, numerical solution of non-linear equations. Prerequisites: MATH 291; proficiency in any programming language; or permission of instructor. Even years Spring.

352 Introduction to Mathematical Models (3)

The focus of this course is to teach students the application of mathematical techniques to real world problems. Content includes: difference equations, stability analysis and chaos, Markov processes and basic probability theory. Students will be expected to use personal computers for their projects. Prerequisite: MATH 291; or permission of instructor. Odd years Spring.

365 Linear Algebra I (3)

Study of the theory and applications of systems of linear equations, vector spaces, matrices, linear transformations, determinants and eigen-vectors. Specific topics include inner product spaces, Gram-Schmidt orthogonalization and the diagonalization of matrices. Prerequisite: MATH 192. Fall and Spring.

366 Linear Algebra II (3)

An in-depth treatment of topics from MATH 365. Other topics include applications of eigen-values and eigen-vectors; Jordan Canonical form, the Hamilton-Cayley theorem, quadratic forms and linear programming. Prerequisites: MATH 280, 365. Odd years Spring.

368 Theory of Numbers (3)

Divisibility, prime numbers, congruences, linear and non-linear Diophantine equations, quadratic residues, representations as sums, and continued fractions. Prerequisite: MATH 280. Odd years Spring.

381 Problems in Mathematics (1)

This course meets once per week for the purpose of discussing and solving a variety of mathematical problems and concepts not normally covered in traditional courses. Problem-solving methods will be discussed. Topics may include, for example, number theory, coding theory, geometry, probability and optimization. The course may be repeated for credit. Prerequisite: MATH 291 and at least junior standing; or permission of instructor. Fall.

391 Advanced Calculus (3)

Topics in Vector Calculus, including Implicit Function Theorem, Gradient Fields, Green's Theorem, Divergence Theorem and Stokes' Theorem. Prerequisite: MATH 291; or permission of instructor. (MATH 365 is recommended.) Even years Spring.

394 Differential Equations (3)

Existence and uniqueness of solutions of differential equations; separable, homogeneous, and exact equations; the Laplace transform; elementary numerical and infinite series methods; Fourier series; and various applications. Prerequisite: MATH 291. Fall and Spring.

395 Partial Differential Equations (3)

First and second order partial differential equations, their derivations, methods of solution, and applications to the physical sciences. Prerequisites: MATH 291, 394. Even years Spring.

398 Complex Variables (3)

Complex numbers and their geometrical representation, analytic functions of a complex variable, integration, power series and the calculus of residues. Prerequisite: MATH 291. Even years Fall.

431 Topology (3)

Metric spaces, topological spaces, separation axioms, connectedness and compactness. Prerequisites: MATH 280, 291; or permission of instructor. Odd years Spring.

461 Abstract Algebra I (3)

An introduction to the algebraic structures: groups, rings, integral Domains and fields. Basic facts about group and ring homomorphisms are included. Prerequisites: MATH 280, 291, or permission of instructor. Every year.

462 Abstract Algebra II (3)

An in-depth study of one or more of the ideas introduced in MATH 361; e.g., the Sylow theorems for group or elementary Galois theory of fields. Prerequisite: MATH 461. Odd year Spring.

480 Mathematics Seminar (1)

Seminar in which students read background papers, participate in discussions, and lead one seminar. Prerequisites: MATH 291 and at least junior standing; or permission of instructor. Spring.

489 Professional Internship (1-3)

Semesterlong internship involving mathematical/statistical work with participating public agencies, nonprofit organizations or commercial institutions. A written report and oral presentation are required upon completion of the project. Prerequisites: minimum grade-point average of 2.5 overall and in the department, MATH 291, at least junior standing, and permission of instructor. (Grading S/U.) May be repeated for a total of three hours credit. See department chair.

491 Analysis I (3)

The real number system, limits, sequences and functions, continuity, derivatives, mean value theorems and integration. Prerequisites: MATH 280, 291; or permission of instructor. Fall.

492 Analysis II (3)

Sequences and series of functions. Further topics may include, for example, introduction to metric spaces, Lebesgue measure and integration, and functions of more than one variable. Prerequisite: MATH 491. Even years Spring.

499 Undergraduate Research in Mathematics (1-3)

Independent research under the supervision of a faculty mentor. An IP grade may be awarded at the discretion of the instructor. Can be repeated for a total of 3 hours credit. Prerequisites: MATH 280, 291. See department chair.

171-4, 271-4, 371-4, 471-4 Special Topics in Mathematics (1-4)

Courses not otherwise included in the catalog listing but for which there may be special needs. May be repeated for credit as often as permitted and as subject matter changes. See department chair.

Courses in Statistics

185 Introductory Statistics (4)

Introduction to the principal statistical methods for investigating the stochastic elements of organization. The focus of the course includes: understanding the methods; selection of methods appropriate to a process; interpretation of results. Major topics include: descriptive statistics, discrete and continuous probability distributions; sampling; statistical inference and regression methods. Computer-based assignments will be used for selected areas. Fall and Spring.

225 Introduction to Calculus-Based Statistics (4)

Organization and display of data; measures of central tendency and dispersion; alternative for-mulations of probability; distributions of random variables; the Central Limit Theorem; statistical inference, confidence intervals and hypothesis tests; contingency table analysis; analysis of variance; and linear correlation and regression. Prerequisite: MATH 192. Fall and Spring.

321 Exploratory Data Analysis and Nonparametric Statistics (3)

Course focuses on the initial statistical techniques used to analyze data and the measures taken if assumptions for standard statistical procedures do not hold. Content may include, but is not limited to: graphical data analysis, assessing normality and transformations, nonparametric statistical inferences, identification of outliers, topics in simple regression, and introduction to time series analysis. Prerequisite: 3 to 4 hours in any other Statistics course. Even years Fall.

325 Introduction to Regression Models (3)

Estimation and inference for regression models. Topics include: least squares estimation; models comparisons; estimation of validity of model assumptions and remedial measures; simple linear, multiple linear, non-linear and logistic regression; and dummy variables. Prerequisite: three to four hours in any other Statistics course. Odd years Fall.

326 Introduction to Analysis of Variance Models (3)

Design, estimation and inference for ANOVA and related models. Topics include: single factor and multiple factor ANOVA; fractional factorial, split-plot, and repeated measures designs, examination of validity of model assumptions and remedial measures; and analysis of covariance. Prerequisite: three to four hours in any other Statistics course. Even years Spring.

327 Applied Multivariate Analysis (3)

Methods of multivariate analysis, including canonical correlation, clustering, discriminant analysis, factor analysis, multivariate analysis of variance, multiple regression and principal components analysis. Prerequisites: three to four hours in any other Statistics course, and MATH 365. Odd years Spring.

425 Introduction to Probability Theory (3)

Various formulations of probability, the structure of probability spaces, combinatorial analysis, discrete and continuous random variables, joint distributions, the Central Limit Theorem, moment generating functions and characteristic functions. Prerequisite: MATH 291. Even years Fall.

426 Introduction to Mathematical Statistics (3)

Sampling distributions of statistics, properties of statistics, general principles of statistical inference, linear statistical models, some non-parametric statistics, Bayesian statistics, and an introduction to statistical decision theory. Prerequisite: STAT 425. Odd years Spring.

499 Undergraduate Research in Statistics (1-3)

Independent research under the supervision of a faculty mentor. An IP grade may be awarded at discretion of instructor. May be repeated for a total of 3 hours credit. See department chair.

171-4, 271-4, 371-4, 471-4 Special Topics in Statistics (1-4)

Courses not otherwise included in the catalog listing but for which there may be special needs. May be repeated for credit as often as permitted and as subject matter changes. See department chair.

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