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## Undergraduate Math Courses

NOTE: PTP* indicates an appropriate score in the Placement Testing Program (PTP) is required.

**102. Intermediate Algebra**. 3 credits. (Does not count toward graduation at UND.) Prerequisite: PTP*. Equations, exponents, quadratic equations, lines, graphs, inequalities. S/U grading only. F,S,SS

**103. College Algebra**. 3 credits. Prerequisite: PTP* or Math 102. Sections meeting 5 days per week are offered for students determined eligible by the Math Department. Polynomial and rational functions, inverse functions, exponential and logarithmic functions, simple conics, systems of equations, determinants, arithmetic and geometric sequences, the Binomial Theorem. F,S,SS

**105. Trigonometry**. 2 credits. Prerequisite: One year of high school geometry and either PTP* or Math 102. Angles, trigonometric functions and their inverses, solving triangles, trigonometric identities. F,S,SS

**107. Precalculus**. 4 credits. Prerequisite: Math 102 or PTP*. Equations and inequalities; polynomial rational, exponential, logarithmic and trigonometric functions; inverse trigonometric functions; algebraic and trigonometric methods commonly needed in calculus. F,S,SS

**112. Transition to Calculus**. 1 credit. Prerequisite: Math 107, Math 146, or PTP. This course is designed for students intending to take Math 165, Calculus I, who have mastered most of, but not all, of the material covered in Math 107, Precalculus. Emphasis is therefore on topics such as inverse functions, partial fraction expansion, trigonometric identities, and applications of trigonometry, which are deemed most difficult for precalculus students. F

**115. Introduction to Mathematical Thought**. 3 credits. The course will focus on analysis and interpretation of common types of mathematical arguments as well as having students construct their own arguments. A combination of topics will be included, such as: elementary combinatorics, probability, statistics, set theory, number theory, geometry and topology, mathematical logic, the mathematics of voting, etc. S or On Demand.

**146. Applied Calculus I**. 3 credits. Prerequisite: PTP* or Math 103. A non-rigorous introduction to differential and integral calculus. Topics include limits, continuity, differentiation and integration techniques, and applications. F,S,SS

**165. Calculus I**. 4 credits. Prerequisites: PTP* or Math 112 or completion of Math 107 with a grade of C or better. Limits, continuity, differentiation, Mean Value Theorem, integration, Fundamental Theorem of Calculus. F,S,SS

**166. Calculus II**. 4 credits. Prerequisite: Completion of Math 165 with a grade of C or better or permission of the Mathematics Department. Techniques and applications of integration, exponential and logarithmic functions, parametric equations, infinite sequences and series. F,S,SS

**207. Introduction to Linear Algebra**. 2 credits. Prerequisite: Math 165. A computational treatment of systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, matrices, eigenvalues, eigenvectors, and diagonalizability. F,S

**208. Discrete Mathematics**. 3 credits. Prerequisite: PTP* or Math 103 or Math 107. Introduction to Set Theory, Functions and Relations, Permutations and Combinations, Logic, Boolean Algebra, Induction, Difference Equations. Other topics from Graphs, Finite Automata and Formal Languages. F,S,SS

**217. Introduction to Cultural Mathematics**. 3 credits. Prerequisite: C or better in Math 103 or equivalent. This course covers mathematical concepts within the context of cultures. Mathematical ideas are investigated in topics such as number systems, calendars, art, kinship relations, divination, and games. Examples are taken from cultures in many parts of the world. The main emphasis in the course is on learning how cultural activities can be considered mathematical and often include non-trivial mathematical ideas. One or more case studies of particular cultures will also be included. The case studies will consist of investigations into several cultural aspects that have mathematical connections. S/2

**265. Calculus III**. 4 credits. Prerequisite: Math 166. Multivariate and vector calculus including partial derivatives, multiple integration, line and surface integrals, Green's Theorem, Stokes' Theorem, the Divergence Theorem. F,S,SS

**266. Elementary Differential Equations**. 3 credits. Prerequisite: Math 265 and proficiency in a programming language. Solution of elementary differential equations by elementary techniques. Laplace transforms, introduction to matrix theory and systems of differential equations. F,S,SS

**277. Math for Elementary School Teachers**. 3 credits. Prerequisite: Admission to Teacher Education and PTP* or Math 103. For elementary education majors only. Development of the number systems used in elementary schools. Includes some methods and work with laboratory materials. F,S

**308. History of Mathematics**. 3 credits. Prerequisites: Math 166 or equivalent, or consent of instructor. This is a course on the conceptual and chronological history of mathematics. The course involves the interpretation and analysis of how and why mathematical ideas have developed over time, including political and cultural considerations. Topics include: numbers and continuing systems, non-Western developments, mathematics of Egypt, Babylonia and Greece, early European developments, the Renaissance, the Scientific Revolution and the development of calculus, women in mathematics, twentieth century mathematics. S

**315. Topics in Computational Mathematics**. 1-3 credits. Prerequisites: Math 266 and proficiency in a programming language, or consent of instructor. An introduction to mathematical methods useful in the computational analysis of problems in applied mathematics. Topics may include numerical methods, numerical simulation, symbolic computation, and theory of computation. May be repeated for credit with consent of instructor up to six credits. On Demand.

3**21. Applied Statistical Methods**. 3 credits. Prerequisite: Math 166. Introductory statistics for students with a background in single-variable calculus. Topics include descriptive statistics, continuous and discrete probability density functions, sampling distributions, point and interval estimation, and tests of hypotheses. F,S

**330. Set Theory and Logic**. 3 credits. Prerequisite: Math 166 or consent of instructor. Axioms and operations on sets, mathematical logic, relations and functions, development of the natural and real number systems, including field axioms and the completeness axiom for the real numbers. F,S

**352. Introduction to Partial Differential Equations**. 3 credits. Prerequisite: Math 266. Partial differential equations, Fourier series, special functions, series solutions to ordinary differential equations. S

**377. Geometry for Elementary Teachers**. 1-3 credits. For elementary education majors only. Experimental and inductive discovery in building geometric concepts at the elementary school level. On Demand.

**397. Cooperative Education**. Prerequisites: 15 completed credits in Math including Math 165, 166, 265, in addition to standard Co-op requirements. A practical work experience with an employer closely associated with the student's academic area. 1-8 credits repeatable to 18. Arranged by mutual agreement among student, department, and employer. A maximum of 6 cooperative education credits may be applied against requirements for a Math major. S/U grading only. F,S,SS

**400. Methods and Materials of Teaching Middle and Secondary School Mathematics**. 3 credits. Prerequisites: T&L 325. Co-requisites: T&L 345 and T&L 486. Various teaching methods, strategies and materials used in teaching middle and secondary school mathematics. National and State Standards for teaching and learning mathematics. Preparation/evaluation of tests, units, and materials of instruction. Recent developments in mathematics curriculum and in instructional alternatives. Issues in teaching and learning of school mathematics. Implementation of appropriate technology in the teaching and learning of mathematics. F

**403. Theory of Probability**. 3 credits. Prerequisite: Math 265. Sets, sample spaces, discrete probability, distribution functions, density functions, characteristic functions, study of normal, Poisson, binomial and other distributions with applications. S/2

**405. Selected Topics in Mathematics**. 1-3 credits. Prerequisite: permission of the Mathematics Department. May be repeated to maximum of six credits. On Demand.

**408. Combinatorics**. 3 credits. Prerequisites: Math 208 and 166. Introduction to the techniques and reasoning needed in combinatorial problem-solving. The course may include topics related to combinatorics, such as graph theory. S

**409. Geometry**. 3 credits. Prerequisite: Math 208 or 330. Metric and synthetic approach to Euclidean geometry. The usual topics in elementary geometry treated in a mathematically logical way. Topics include congruence, inequalities, parallelism, similarity, area, solid geometry and the circle. F

**412. Differential Equations**. 3 credits. Prerequisite: Math 266. Basic types of ordinary differential equations. Existence and uniqueness of solutions. F/2

**415. Topics in Applied Mathematics**. 1-3 credits. Prerequisites: Math 265 and consent of instructor. An introduction to selected areas in applied mathematics chosen from a variety of topics including: Applied algebra, difference equations, linear programming, modeling and simulation, operations research, optimization, partial differential equations and computers in mathematics. Topics to be considered will be illustrated with examples and practical applications. May be repeated for credit with consent of instructor up to a maximum of six credits. On Demand.

**416. Topics in Statistics**. 1-3 credits. Prerequisites: An elementary statistics course and either Math 265 and 321, or consent of instructor. An introduction to a variety of topics in statistics including: Linear models in categorical analysis, Bayesian methods, decision theory, ridge regression, Non parametric techniques, stochastic games and models. The number of topics to be considered during a semester will be limited to permit greater depth of coverage and sufficient practical illustrations. May be repeated for credit with consent of instructor up to six credits. On Demand.

**421, 422. Statistical Theory I and II**. 3 credits each. Prerequisite: For 421, Math 265; for 422, Math 421. Discrete and continuous random variables, expectation, moments, moment generating functions, properties of special distributions, introduction to hypothesis testing, sampling distributions, Central Limit Theorem, curve of regression, correlation, empirical regression by least squares, maximum likelihood estimation, Neyman-Pearson lemma, likelihood ratio test, power function, chi-square tests, change of variable, "t" and "F" tests, one and two-way ANOVA, nonparametric methods. F,S

**425. Cryptological Mathematics**. 3 credits. Prerequisite: Math 208. This course develops the math behind elementary symmetric-key cryptoschemes and a variety of public-key schemes. Modern block ciphers may be discussed. F/2

**431. Introduction to Analysis I**. 3 credits. Prerequisite: Math 330 or consent of instructor. Development of the real number system, functions, sequences, limits, continuity, and differentiation. F

**432. Introduction to Analysis II**. 3 credits. Prerequisite: Math 431. A continuation of Math 431, topics in the second semester include integration, partial differentiation, infnite series, power series and vector analysis. S

**435. Theory of Numbers**. 3 credits. Prerequisite: Math 208 or 330. Basic properties of numbers, including divisibility, primes, congruences, Diophantine equations and residue theory. S

**441. Abstract Algebra**. 3 credits. Prerequisite: Math 330 or consent of instructor. Rings, integral domains, fields, elements of group theory. F

**442. Linear Algebra**. 3 credits. Prerequisites: Math 265 and 330 or consent of instructor. A theoretical treatment of systems of linear equations, matrices, vector spaces, linear transformations and elementary canonical forms. S

**460. Mathematical Modeling**. 3 credits. Prerequisites: Math 266 or consent of instructor. The primary goal of the course is to present the mathematical analysis provided in scientific modeling. Topics may include population modeling, mechanical vibrations, traffic flow, epidemic modeling, queues and decay processes. F/2

**461. Numerical Analysis I**. 3 credits. Prerequisites: Math 266. Numerical techniques for: the solution of equations in one or several unknowns, approximate integration, differential equations, approximation theory, optimization theory and matrix analysis. Corresponding error analysis will be investigated. F/2, S/2

**471. Introduction to Complex Variables**. 3 credits. Prerequisites: Math 265 or consent of instructor. The complex plane, analytic functions, complex integration, power series, the theory of residues and contour integration, conformal mapping, Fourier and Laplace transformations, and applications. F/2

**477. Topics in Elementary School Mathematics**. 1-3 credits. May be repeated for credit up to six credits. For elementary education majors only. Selected topics from Mathematical concepts appropriate to the elementary school curriculum. On Demand.

**479. Topics in Mathematics Education**. 1-3 credits. Prerequisite: Consent of instructor. May be repeated for up to six credits. Selected topics from mathematical concepts appropriate for K-12 educators. On Demand.

**488. Senior Capstone**. 3 credits. Prerequisite: Senior standing with a major in mathematics. This course is designed to help students transition into working mathematicians. Thus the course will address 1) written and oral expression of mathematical material and concepts, 2) research and problem solving in mathematics, and 3) technology in mathematics, and its appropriate use. Material will build on the core areas of calculus, linear algebra, and differential equations. F

**494, 495. Reading Course in Mathematics**. 1-3 credits, repeatable to six credits. Consent of instructor required. Directed individual reading on selected topics not developed in other courses. F,S,SS