Mathematics (MATH)

University Directory
University Courses

MATH 205 MINING MANAGEMENT MATH I

MATH 021 BASIC ALGEBRA
(3-0) 3 credits. Prerequisite: Appropriate mathematics placement. This course prepares students for college level mathematics. Topics generally include: basic properties of real numbers, exponents and radicals, rectangular coordinate geometry, solutions to linear and quadratic equations, inequalities, polynomials and factoring. Students may also be introduced to functions and systems of equations. Note: This is remedial level course and no credit for MATH 021 will be granted for graduation.

MATH 101 INTERMEDIATE ALGEBRA
(3-0) 3 credits. Prerequisite: MATH 021 or appropriate mathematics placement. Basic properties of real numbers, linear equations and inequalities, quadratic equations, systems of equations, polynomials and factoring, rational expressions and equations, and radical expressions and equations, and an introduction to functions such as polynomial, exponential and logarithmic functions. May not be used for credit toward a baccalaureate degree, but may be used toward the associate degree.

MATH 102/102L COLLEGE ALGEBRA
(3-1) 4 credits. Prerequisite: MATH 101 or appropriate mathematics placement. Corequisite: MATH 102L. Equations and inequalities; polynomial functions and graphs; exponents, radicals, binomial theorem, zeros of polynomials; systems of equations; exponential, logarithmic, and inverse functions, applications and graphs. Other topics selected from sequences, series, and complex numbers. This course may not be used for credit toward an engineering or science degree (except for interdisciplinary science, chemistry, and associate of arts).

MATH 115 PRECALCULUS
(5-0) 5 credits. Prerequisite: MATH 101 or appropriate mathematics placement. A preparatory course for the calculus sequence. Topics include: polynomial, rational, exponential, logarithmic and trigonometric functions and their graphs; systems of equations, inequalities and complex numbers. May not be used for credit toward an engineering or science degree (except for interdisciplinary science, chemistry, and associate of arts).

MATH 120 TRIGONOMETRY
(3-0) 3 credits. Prerequisite: MATH 102 “C” or better, or an acceptable score on the COMPASS Placement Examination. Topics include: trigonometric functions, equations, and identities; inverse trigonometric functions; exponential and logarithmic functions, and applications of these functions. This course may not be used for credit toward an engineering or science degree (except for interdisciplinary science, chemistry, and associate of arts).

MATH 123 CALCULUS I
(4-0) 4 credits. Prerequisite: MATH 115 with a minimum grade of “C” or appropriate mathematics placement or permission of instructor. Students who are initially placed into MATH 102 or below must complete MATH 102 and MATH 120 with grades of “C” or better before enrolling in MATH 123. Students who are placed in MATH 120 should consult their advisor to determine whether their placement score was sufficiently high to allow concurrent registration in MATH 123. The study of limits, continuity, derivatives, applications of the derivative, antiderivatives, the definite and indefinite integral, and the fundamental theorem of calculus.

MATH 125 CALCULUS II
(4-0) 4 credits. Prerequisite: MATH 120 completed with a minimum grade of “C” or appropriate score on departmental Trigonometry Placement Examination and MATH 123 completed with a minimum grade of “C.” A continuation of the study of calculus, including the study of sequences, series, polar coordinates, parametric equations, techniques of integration, applications of integration, indeterminate forms, and improper integrals.

MATH 140 THE NATURE OF MATHEMATICS
(3-0) 3 credits. Prerequisites: MATH 102 (College Algebra) or MATH 115 completed with a “C” or better or an acceptable score on the Algebra Placement Examination, and ENGL 101. The intent of this course is to give the student an appreciation for the mathematical approach to problem solving and an overall perspective of the role of mathematics in the history of technology and society. Major themes in mathematics are explored from several points of view: the mathematics involved, the historical development of ideas, and the utilization of these ideas in other fields of endeavor.

MATH 225 CALCULUS III
(4-0) 4 credits. Prerequisite: MATH 125 completed with a minimum grade of “C.” A continuation of the study of calculus, including an introduction to vectors, vector calculus, partial derivatives, and multiple integrals.

MATH 241 MATHEMATICS OF FINANCE
(3-0) 3 credits. Prerequisites: MATH 102 or permission of instructor. Topics include simple and compound interest including annuities, amortization, sinking funds, valuation of bonds, depreciation and capitalized cost.

MATH 281 INTRODUCTION TO STATISTICS
(3-0) 3 credits. Prerequisite: MATH 102 or MATH 115. A study of descriptive statistics including graphs, measures of central tendency and variability and an introduction to probability theory, sampling and techniques of statistical inference with an emphasis on statistical applications. Individuals may apply at most 4 credits toward a degree from the following list of courses: MATH 281, IENG/MATH 381, MATH 441/442.

MATH 291 INDEPENDENT STUDY
1 to 5 credits. Prerequisite: Permission of instructor. Includes directed study, problems, readings, directed readings, special problems and special projects. Students complete individualized plans of study which include significant one-on-one student-teacher involvement. The faculty member and students negotiate the details of the study plans. Enrollments are usually 10 or fewer students. Meeting depending upon the requirements of the topic. May be repeated to a total of five (5) credit hours.

MATH 292 TOPICS
1 to 5 credits. Includes current topics, advanced topics and special topics. A course devoted to a particular issue in a specified field. Course content is not wholly included in the regular curriculum. Guest artists or experts may serve as instructors. Enrollments are usually 10 or fewer students with significant one-on-one student/teacher involvement. May be repeated to a total of five (5) credit hours.

MATH 315 LINEAR ALGEBRA
(4-0) 4 credits. Prerequisite: MATH 225 and MATH 321 or permission of instructor. Course topics include: the theory and applications of systems of linear equations, matrices, determinants, vector spaces, linear transformations and applications.

MATH 321 DIFFERENTIAL EQUATIONS
(4-0) 4 credits. Prerequisite: MATH 125 with a minimum grade of “C.” Selected topics from ordinary differential equations including development and applications of first order, higher order linear and systems of linear equations, general solutions and solutions to initial-value problems using matrices. Additional topics may include Laplace transforms and power series solutions. MATH 225 and 321 may be taken concurrently or in either order. In addition to analytical methods this course will also provide an introduction to numerical solution techniques.

MATH 353 LINEAR OPTIMIZATION
(3-0) 3 credits. Prerequisites: MATH 321 or MATH 315 or permission of instructor. Convex sets and functions, linear inequalities and combinatorial problems; topics in linear programming from fundamental theorems of simplex method through sensitivity analysis, duality, transportation, and assignment problems.

MATH 354 NON-LINEAR OPTIMIZATION
(3-0) 3 credits. Prerequisite: MATH 225. Numerical methods for constrained and unconstrained problems. Emphasis on algorithms such as simplex method, direct search methods, conjugate gradient methods, shortest-path problems, and integer programming.

MATH 373 INTRODUCTION TO NUMERICAL ANALYSIS
(3-0) 3 credits. Prerequisite: MATH 321 and CSC 150 or permission of instructor. This course is an introduction to numerical methods. Topics include elementary discussion of errors, polynomial interpolation, quadrature, non-linear equations, and systems of linear equations. The algorithmic approach and efficient use of the computer will be emphasized. Additional topics may include: calculation of eigenvalues and eigenvectors, numerical differentiation and integration, numerical solution of differential equations.

MATH 381 INTROTO PROB AND STAT
(3-0) 3 credits. Prerequisite: MATH 125 and prerequisite or corequisite: MATH 225. Introduction to probability theory, discrete and continuous distributions, sampling distributions and the Central Limit Theorem with general principles for statistical inference and applications of random sampling to hypothesis testing, confidence limits, correlation, and regression. This course is cross-listed with IENG 381. Individuals may apply at most 4 credits toward a degree from the following list of courses: MATH 281, IENG/MATH 381, MATH 441/442.

MATH 382 PROBABILITY THEORY AND STATISTICS II
(3-0) 3 credits. Prerequisite: MATH 381. Review of general principles of statistical inference, linear regression and correlation, multiple linear regression, ANOVA, and statistical design of experiments. This course is cross-listed with IENG 382.

MATH 391 INDEPENDENT STUDY
1 to 5 credits. Prerequisite: Permission of instructor. Includes directed study, problems, readings, directed readings, special problems and special projects. Students complete individualized plans of study which include significant one-on-one student-teacher involvement. The faculty member and students negotiate the details of the study plans. Enrollments are usually 10 or fewer students. Meeting depending upon the requirements of the topic. May be repeated to a total of five (5) credit hours.

MATH 392 TOPICS
1 to 5 credits. Includes current topics, advanced topics and special topics. A course devoted to a particular issue in a specified field. Course content is not wholly included in the regular curriculum. Guest artists or experts may serve as instructors. Enrollments are usually 10 or fewer students with significant one-on-one student/teacher involvement. May be repeated to a total of five (5) credit hours.

MATH 402 COMMUNICATING MATHEMATICS
(1-0) 1 credit. Prerequisite: MATH 498. The student will produce a word-processed technical report of research conducted in MATH 498 and give a department colloquium talk summarizing her or his work. Department faculty member(s) will provide guidance in the production of the technical report and in the preparation for the colloquium talk.

MATH 413 ABSTRACT ALGEBRA I
(3-0) 3 credits. Prerequisites: CSC 251 or permission of instructor. Introduction to the theory and applications of algebraic structures including groups, rings, and fields.

MATH 421 COMPLEX ANALYSIS
(3-0) 3 credits. Prerequisite: MATH 225. The algebra of complex numbers; complex functions; contour integration and Cauchy integral theorems; Taylor and Laurent series and the residue theorem; the evaluation of real definite integrals; elementary mapping problems.

MATH 423/424 ADVANCED CALCULUS I and ADVANCED CALCULUS II
(4-0) 4 credits each. Prerequisite: MATH 225 or permission of instructor. Prerequisite for MATH 424 is MATH 423. A theoretical treatment of Calculus that covers: limits; continuity and differentiability of functions of a single variable and of several variables; convergence of sequences and series; integration; and applications

MATH 424 ADVANCED CALCULUS II
(4-0) 4 credits each. Prerequisite: MATH 225 or permission of instructor. Prerequisite for MATH 424 is MATH 423. A theoretical treatment of Calculus that covers: limits; continuity and differentiability of functions of a single variable and of several variables; convergence of sequences and series; integration; and applications.

MATH 431 DYNAMICAL SYSTEMS
(3-0) 3 credits. Prerequisites: MATH 315 or permission of instructor. This course is a study of both discrete and continuous dynamical systems. Topics include analysis of planar autonomous systems, stability analysis, bifurcation, chaos, and strange attractors. In addition, this course may include the study of Van der Pol’s equation, Lorenz equations, Duffing’s equation, Hamiltonian systems, and Poincare maps.

MATH 432 PARTIAL DIFFERENTIAL EQUATIONS
(3-0) 3 credits. Prerequisites: MATH 225 and MATH 321. Fourier series, partial differential equations, Frobenius series, Bessel functions, and transform methods.

MATH 441 ENGINEERING STATISTICS I
(2-0) 2 credits. Prerequisite: MATH 225. An introduction to the core ideas in probability and statistics. Computation of probabilities using, for instance, counting techniques and Bayes’ rule. Introduction to discrete and continuous random variables, joint and conditional distributions, expectation, variance and correlation, random sampling from populations, hypothesis tests and confidence intervals, and least squares. This course is the first in a sequence of two (2) twocredit mini-courses in probability and statistics offered in a single term, the second being MATH 442. Individuals may apply at most 4 credits toward a degree from the following list of courses: MATH 281, IENG/MATH 381, MATH 441/442.

MATH 442 ENGINEERING STATISTICS II
(2-0) 2 credits. Prerequisite: MATH 441. In part, covers topics from MATH 441 in more depth including additional standard distributions used to model real-world phenomena, additional standard hypothesis tests and confidence intervals. Other topics include building multiple regression models, parameter estimation, and reliability. Selected non-parametric and computer-intensive methods may also be covered. This course is the second in a sequence of two (2) two-credit minicourses in probability and statistics offered in a single term, the first being MATH 441. Individuals may apply at most 4 credits toward a degree from the following list of courses: MATH 281, IENG/MATH 381, MATH 441/442.

MATH 451 MATH MODELING
(3-0) 3 credits. Prerequisites: MATH 321 or permission of instructor. The primary goal of this course is to present the mathematical formulation and analysis utilized in scientific modeling. Applications from both Science and Engineering will be covered. The types of models will include deterministic and stochastic models. Topics may include: epidemiology, biomass, elasticity, heat flow, electrical circuits, mechanical vibrations and optimization.

MATH 471 NUMERICAL ANALYSIS I
(3-0) 3 credits. Prerequisite: MATH 373 or CSC 372. Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, numerical methods for solving linear systems.

MATH 486 STATISTICAL QUALITY AND PROCESS CONTROL
(3-0) 3 credits. Prerequisites: IENG 381 or MATH 441 or permission of instructor. This course covers the development of statistical methods for application to problems in quality and process control. Statistical topics include: basics of processes and variability, statistically controlled processes, variable and attribute control charts, moving averages, individual trend and others, process capability, sampling plans for attributes and variables. This course is crosslisted with IENG 486.

MATH 491 INDEPENDENT STUDY
1 to 3 credits. Prerequisite: Permission of instructor. Includes directed study, problems, readings, directed readings, special problems and special projects. Students complete individualized plans of study which include significant one-on-one student-teacher involvement. The faculty member and students negotiate the details of the study plans. Enrollments are usually 10 or fewer students. Meeting depending upon the requirements of the topic. May be repeated to a total of three (3) credit hours.

MATH 492 TOPICS
1 to 6 credits. Includes current topics, advanced topics and special topics. A course devoted to a particular issue in a specified field. Course content is not wholly included in the regular curriculum. Guest artists or experts may serve as instructors. Enrollments are usually 10 or fewer students with significant one-on-one student/teacher involvement. May be repeated to a total of six credit hours.

MATH 498 UNDERGRADUATE RESEARCH/SCHOLARSHIP
(1-0) 1 credit. Prerequisite: Permission of instructor. Includes senior project, and capstone experience. Independent research problems/projects or scholarship activities. The plan of study is negotiated by the faculty member and the student. Contact between the two may be extensive and intensive. Does not include research courses which are theoretical.

MATH 685 STATISTICAL APPROACHES TO RELIABILITY
(4-0) 4 credits. Prerequisite: MATH 441 or permission of instructor. This course covers the development of statistical methods for application to problems in reliability engineering. Statistical topics include: basics of reliability and lifetesting, probabilistic reliability, patterns of failures, probability concepts and distributions in reliability, analysis of reliability data, prediction and modeling, reliability measurements and problems. This course is cross-listed with ME 685.

MATH 687 STATISTICAL DESIGN AND ANALYSIS OF EXPERIMENTS
(3-0) 3 credits. Prerequisite: MATH 381 or MATH 441 and MATH 442 or permission of instructor. Sampling distribution and inference for normal distribution parameters, single and multifactor experiments, ANOVA, randomized blocks, Latin square and related designs, simple and multiple regression, analysis of covariance. Use of computer subroutines.

MATH 691 INDEPENDENT STUDY
1 to 3 credits. Prerequisite: Permission of instructor. Student should have obtained permission of an instructor in the Department of Mathematics and Computer Science prior to registering for this course. Directed independent study of a topic or field of special interest. This may involve readings, research, laboratory or fieldwork, and preparation of papers, as agreed to in advance, by student and instructor. May be repeated to a total of six credit hours.

MATH 692 TOPICS
1 to 3 credits. Lecture course or seminar on a topic or field of special interest, as determined by the instructor. May be repeated to a total of six credit hours.

Contact: South Dakota School of Mines and Technology
http://sdmines.sdsmt.edu/sdsmt/directory/courses/math