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| Mathematics (Math) |
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Bevelacqua, Collings, Dearden, Dunnigan, Gilsdorf, Halcrow, J. Iiams, M. Iiams, Khavanin, Metzger, Millspaugh (Chair), Peterson, Richards, Takahashi and Zerr
The functions of the Mathematics Department within the total framework of the University are varied. Besides the training of undergraduate and graduate majors in the field of Mathematics, the Department offers courses designed to meet the needs of students in business; engineering; physical, social, and biological sciences; and elementary and secondary education.
The student considering mathematics as a career should realize that emphasis in mathematics courses will change as he/she progresses through college and graduate school. The early emphasis on solving problems is later subordinated to the more important tasks of formulating problems in mathematical language and of dealing effectively with mathematical structures and abstract ideas.
It should be stressed that an effective mathematician in any type of employment should be a well-educated person. He/she should have not only the technical background of calculus and differential equations taken by most scientists and engineers, and the more advanced mathematical training required for a major in mathematics, but should also have taken a selection of courses from other disciplines. A student who plans to continue beyond the bachelor’s degree in mathematics should also acquire a reading knowledge of at least one and preferably two of the foreign languages in which much of the current literature in mathematics is written, namely, German, Russian, and French. All students should, of course, acquire fluency in the written and oral expression of ideas in English.
The main fields of opportunity in mathematics today are teaching, mathematical statistics, mathematics in industry, mathematics in government and actuarial mathematics. The Mathematics Department provides a test center for Actuarial Examinations and offers several courses which enable the student to prepare for them.
Students may pursue the B.S. degree with a major in mathematics through the College of Arts and Sciences. Teacher certification is possible provided appropriate requirements are met.
Elective courses to be taken toward the bachelor’s degree are decided in consultation with an adviser from the Mathematics Department, and vary according to the needs of the student, consistent with the particular objective of the general education and mathematical education of the student.
Placement in Mathematics. Appropriate initial enrollment in mathematics courses at UND is determined by a combination of entrance and placement tests or the acceptance of credits for transfer, Advanced Placement (AP) and College Level Examination Program (CLEP). Students enrolling without such previous credit are directed to entry level mathematics courses, courses numbered 102 through 165 and 277 depending on their scores on the ACT Mathematics test and/or a combination of scores on tests from the Placement Testing Program (PTP) sponsored by the Mathematical Association of America.
Anyone without the required prerequisites enrolling in a mathematics course may be dropped from the class by the instructor.
College of Arts and Sciences
B.S. WITH MAJOR IN MATHEMATICS
All students are urged to take courses in disciplines which make use of mathematics such as Physics, Chemistry, Engineering, Computer Science and Biology. Students considering graduate school are urged to take a full year of Advanced Calculus, Math 431 and 432.
Required 125 credits (36 of which must be numbered 300 or above, and 60 of which must be from a 4-year institution) including: |
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I. |
General Education Requirements (see University
GER listing). |
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II. |
Non-Mathematics Requirements:
Three hours of Computer Science and 8-9 hours of writing courses as approved by the Mathematics Department
(see http://www.und.edu/dept/math/majinfo.html). |
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III. |
The Following Curriculum of 39 Major Hours: |
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Math 165, 166, 265 |
Calculus I, II, III |
(12) |
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Math 327 |
Applied Linear Algebra |
(3) |
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or |
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Math 442 |
Linear Algebra |
(3) |
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Math 266 |
Elementary Differential Equations |
(3) |
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Mathematics Sequences
Two full two-semester sequences from the
list below. |
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At least one sequence must include two
400 level courses. |
(12) |
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Math
208 & 408 |
Discrete
Mathematics & Combinatorics |
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Math
352 & 412 |
Introduction to Partial Differential Equations
and Differential Equations |
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Math 409, 435, 471 |
Any two of these three (for at most one
sequence):
Geometry, Number Theory, Complex Variables |
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Math
421 & 422. |
Statistical
Theory I & II |
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Math
431 & 432 |
Advanced
Calculus I & II |
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Math
441 & 442 |
Abstract
Algebra & Linear Algebra |
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Math
461 & 462 |
Numerical
Analysis I & II |
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Electives
Math courses numbered 208 and above, excluding 277, 377, 400, 477
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(9) |
TEACHER LICENSURE |
Through a partnership with the College of Education and Human Development and the Department of Teaching and Learning, students may seek secondary licensure in Mathematics. The following program of study must be completed:
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I. |
Mathematics program of study |
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a. The General Education, Non-Mathematics, and Mathematics Core require- ments as described above. |
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b. Complete Math 208, 308, 321, and 330.
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Math
441 & 442
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Math
409 & 435
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c. Math 208, 308, 321 and 330 |
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II. |
Admission to the Secondary Program, normally while taking T&L 325. (See Col-
lege of Education and Human Development for admission and licensing require-
ments.) |
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III.
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The program in Secondary Education, to include:
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T&L 325 |
Exploring Teaching in Secondary Schools |
(3) |
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T&L 345 |
Curriculum Development and Instruction |
(3) |
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T&L 350 |
Development and Education of Adolescents |
(3) |
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T&L 386 |
Field Experience (Optional) |
(1) |
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T&L 390 |
Special Topic |
(1-3) |
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Math 400 |
Methods and Materials of Teaching Middle
and Secondary School Mathematics |
(3) |
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T&L 433 |
Multicultural Education |
(3) |
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T&L 460 |
Microteaching |
(2) |
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T&L 486 |
Field Experience |
(1) |
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T&L 487 |
A full semester of student teaching, normally
taken during the semester of graduation |
(16) |
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T&L 488 |
Senior Seminar |
1 |
Mathematics majors seeking secondary licensure must have an advisor in both the Mathematics Department and the Department of Teaching and Learning. |
MINOR IN MATHEMATICS |
Required 20 credits as follows: |
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Math 165, 166, 265 |
Calculus I, II, III |
(12) |
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t least three additional courses numbered 208 and above, not including 277, 377, 397 or 477. Math 405, 415, 416, 494, and 495 may be used only with prior approval from the Mathematics Department. |
MINOR IN MATHEMATICS FOR ELEMENTARY EDUCATION |
Required 20 credits of Mathematics, including: |
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Math 115 |
Introduction to Mathematical Thought |
(3) |
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Math 277 |
Math for Elementary School Teachers |
(3) |
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Math 377 |
Geometry for Elementary Teachers |
(3) |
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Math 477 |
Topics in Elementary School Mathematics |
(3) |
| And, at least one of the following: |
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Math 146 |
Applied Calculus I |
(3) |
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Math 165 |
Calculus I |
(4) |
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Math 166 |
Calculus II |
(4) |
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Math 208 |
Discrete Mathematics |
(3) |
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All electives may be selected from Mathematics
courses above Math 102. |
MINOR IN STATISTICS (Plan A) |
Requires 3 semesters of calculus (Math
165, 166, 265) as prerequisite. |
Required: 9 credits, including: |
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*Math 421, 422 |
Statistical Theory I, II |
(6) |
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3 hours from: |
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Biol 470 |
Biometry |
(3) |
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EFR
513 |
Basic
Computer Applications in Education |
(2) |
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EFR 514 |
Small System Computer |
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Applications in Education |
(3) |
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EFR 516 |
Statistics II |
(3) |
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ChE 515 |
Design of Engineering Experiments |
(3) |
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Econ 410 |
Empirical Methods in Economics I |
(3) |
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EE 411 |
Communications Engineering |
(3) |
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Math 321 |
Applied Statistics |
(3) |
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Math 403 |
Theory of Probability |
(3) |
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Math 415 |
Topics in Applied Math (when appropriate) |
(3) |
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Math 416 |
Topics in Statistics |
(1-3) |
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Psyc 541 |
Advanced Univariate Statistics |
(3) |
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Psyc 542 |
Test Construction and Multivariate Analysis |
(3) |
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Psyc 543 |
Experimental Design |
(3) |
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Soc 521 |
Advanced Analytical Methods |
(3) |
MINOR IN STATISTICS (Plan B) |
Requires Math 146, Applied Calculus, as prerequisite. |
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Required: 12 credits from: |
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Biol 470 |
Biometry |
(3) |
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EFR 513 |
Basic Computer Applications in Education |
(2) |
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EFR 514 |
Small System Computer Applications in Education |
(3) |
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EFR 516 |
Statistics II |
(3) |
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ChE 515 |
Design of Engineering Experiments |
(3) |
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No more than 1 class from: |
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Econ
210 |
Elementary Business and Economics Statistics |
(3) |
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Psyc 241 |
Introduction to Statistics |
(4) |
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Soc 326 |
Sociological Statistics |
(3) |
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Econ 410 |
Empirical Methods in Economics I |
(3) |
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EE 411 |
Communications Engineering |
(3) |
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Math 321 |
Applied Statistics |
(3 |
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Math 403 |
Theory of Probability |
(3) |
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Math 415 |
Topics in Applied Math (when appropriate) |
(3) |
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Math 416 |
Topics in Statistics |
(1-3) |
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Math 421 |
Statistical Theory I |
(3) |
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Math 422 |
Statistical Theory II |
(3) |
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Psyc 541 |
Advanced Univariate Statistics |
(3) |
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Psyc 542 |
Test Construction and Multivariate Analysis |
(3) |
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Psyc 543 |
Experimental Design |
(3) |
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Soc 521 |
Advanced Analytical Methods |
(3) |
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. S
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. Prerequisites: 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, the material covered in Math 107, Pre-Calculus. Emphasis is therefore on topics such as inverse functions, partial fraction expansion, trigonometric identities, and applications of trigonometry, which are deemed most difficult for pre-calculus students. F, S
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. F 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
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
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 either 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 counting 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.
321. 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
327. Applied Linear Algebra. 3 credits. Prerequisite: Math 166. A practical treatment of systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, matrices, eigenvalues, and eigenvectors. 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. 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. Prerequisite: T&L 325. Corequisites: T&L 345, 486. Various teaching methods, strategies and materials used in teaching middle and secondary school mathematics. National and State Standards for teaching and learning mathematics. Curriculum development. Preparation/evaluation of tests, units, and materials of instruciton. Recent developments in mathematics curriculum and in instructional alternatives. Issues in teaching and learning of school 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. Prerequisite: 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: 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, 432. Advanced Calculus I and II. 3 credits each. Prerequisite: for 431, Math 330 or consent of instructor; For 432, Math 431. Real number system, functions, sequences, limits, continuity, differentiation, integration, partial differentiation, infinite series, power series and vector analysis. F,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/2
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. Prerequisite: 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
450. Elements of Topology. 3 credits. Prerequisite: Math 330 or consent of instructor. Set operations, mappings, functions, continuity, compactness, connectedness and topological spaces with special emphasis on topologies of the real line. On demand.
460. Mathematical Modeling. 3 credits. Prerequisite: Math 266 and either 327 or 442, 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, 462. Numerical Analysis I and II. 3 credits each. Prerequisite: Math 266 and a scientific programming language. Prerequisite for 462 is Math 461 or consent of instructor. 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
465. Topics in Operations Research. 3 credits. Prerequisites: Math 265 and either 327 or 442, or consent of instructor. The primary goal of this course is to present mathematical methods useful in the analysis of problems that involve making decisions. Topics may include optimization, mathematical programming, network analysis, decision theory, game theory, queueing theory, and dynamic programming. S/2
471. Introduction to Complex Variables. 3 credits. Prerequisite: Math 265. 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.
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 |
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