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Apr 25, 2024
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2016-2017 Undergraduate Catalog [NOTE!!!! THIS IS AN ARCHIVED CATALOG. FOR THE CURRENT CATALOG, GO TO CATALOG.NIU.EDU]
Undergraduate Courses
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A complete list of undergraduate courses in alphabetical order.
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MATH 101 - Core Competency in Mathematics
Mastery of elementary skills and facts, understanding of logically correct arguments, abstract thinking, and problem solving ability. Not intended as preparation for MATH 110 or for courses numbered above MATH 110. Not available for credit to students who have previously received credit with a grade of C or better in a MATH course numbered above 110 except MATH 201. Not open for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: Intermediate algebra and geometry.
Credits: 3
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MATH 108 - Fundamentals of Mathematics I
Designed for and restricted to first-semester freshmen, specially admitted students. Does not count as credit for graduation.
Credits: 3
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MATH 109 - Fundamentals of Mathematics II
Designed for and restricted to first-year, specially admitted students. May be used to continue MATH 108. Does not count as credit for graduation. Used as preparation for MATH 101, MATH 110, or MATH 201.
Credits: 3
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MATH 110 - College Algebra
Algebraic and exponential functions, basic linear algebra. Requires skills and knowledge of intermediate algebra and plane geometry. Does not count for credit toward the major or minor in mathematical sciences. Not open for credit to students having credit in MATH 155 or MATH 211 or MATH 229. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: KCMA 098 with a grade of C or better, or MATH 109 with a grade of C or better, or previous credit in MATH 110, or satisfactory performance on the Mathematics Placement Examination.
Credits: 3
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MATH 155 - Trigonometry and Elementary Functions
Polynomials and rational functions, review of exponential and logarithmic functions, trigonometry, and complex numbers. Does not count for credit toward the major or minor in mathematical sciences. Not open for credit to students who have obtained a grade of C or better in MATH 229.
Prerequisites & Notes
PRQ: MATH 110 with a grade of C or better, or previous credit in MATH 155, or satisfactory performance on the Mathematics Placement Examination.
Credits: 3
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MATH 201 - Foundations of Elementary School Mathematics
Introduction to sets, geometry, measurement, logic, structure of mathematical systems, and the real number system. Open for credit only toward the majors in early childhood studies, elementary education, and special education. Does not count for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: One year of high school algebra and one year of high school geometry.
Credits: 3
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MATH 206 - Introductory Discrete Mathematics
Introduction to sets, algorithms, induction, recursion, relations, graphs, trees, and algebraic structure, with applications, many of which are in computer science. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 110 or satisfactory performance on the Mathematics Placement Examination.
Credits: 3
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MATH 210 - Finite Mathematics
Introduction to mathematical topics with applications to business, social science, and other fields. Includes such topics as functions and graphs, matrix algebra and solutions of systems of linear equations, inequalities and linear programming, elementary combinatorics, and probability. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 110 with a grade of C or better, or previous credit in MATH 210, or satisfactory performance on the Mathematics Placement Examination.
Credits: 3
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MATH 211 - Calculus for Business and Social Science
An elementary treatment of topics from differential and integral calculus, with applications in social science and business. Students may receive credit for both MATH 211 and MATH 229, but only one of them will count toward the minimum number of hours required for graduation. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 110 with a grade of C or better, or previous credit in MATH 211, or satisfactory performance on the Mathematics Placement Examination.
Credits: 3
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MATH 229 - Calculus I
A first course in calculus. Students may receive credit for both MATH 211 and MATH 229, but only one of them will count toward the minimum number of hours required for graduation.
Prerequisites & Notes
PRQ: MATH 155 with a grade of C or better or satisfactory performance on the Mathematics Placement Examination.
Credits: 4
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MATH 230 - Calculus II
Continuation of MATH 229. Techniques of integration and applications of integrals, transcendental functions, and applications of series.
Prerequisites & Notes
PRQ: MATH 229 with a grade of C or better.
Credits: 4
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MATH 232 - Calculus III
Continuation of MATH 230. Multivariable and vector calculus.
Prerequisites & Notes
PRQ: MATH 230 with a grade of C or better.
Credits: 4
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MATH 239 - Matrices, Vectors and Applications
Systems of linear equations, matrix algebra, determinants, n-dimensional real vector spaces, eigenvalues and eigenvectors. Least squares problems and the singular value decompositions. Except with departmental approval students may not receive credit for both MATH 239 and MATH 240. Not used in major GPA calculation for mathematical sciences majors.
Prerequisites & Notes
PRQ: MATH 232 or consent of department.
Credits: 3
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MATH 240 - Linear Algebra and Applications
Matrix algebra and solutions of systems of linear equations, matrix inversion, determinants. Vector spaces, linear dependence, basis and dimension, subspaces. Inner products, Gram-Schmidt process. Linear transformations, matrices of a linear transformation. Eigenvalues and eigenvectors. Applications. Constructing and writing mathematical proofs. A transition between beginning calculus courses and upper-level mathematics courses.
Prerequisites & Notes
PRQ: MATH 232.
Credits: 4
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MATH 280 - Introduction to Mathematical Reasoning
An introduction to the idea of mathematical proof. Emphasis on improving students’ ability to construct, explain, and justify mathematical arguments. Assists in the transition from the calculus sequence to more abstract, proof-oriented courses.
Prerequisites & Notes
PRQ: MATH 230.
Credits: 3
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MATH 297 - Directed Study
Selected readings to supplement lower-division mathematical sciences courses. May be repeated to a maximum of 6 semester hours.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 1-5
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MATH 302 - Introduction to Geometry
Basic concepts in plane and solid geometry, measurement, congruence and similarity, constructions, coordinate geometry, transformations and tessellations, topology, and selected topics. Not used in major or minor GPA calculations for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 229 or consent of department.
Credits: 3
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MATH 303 - Introduction to Number Theory
Problem solving, methods of proof, divisibility, primes, congruences, Diophantine equations, integer sequences, number-theoretic functions, and selected topics. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 229 or consent of department.
Credits: 3
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MATH 304 - History of Mathematics Through the 17th Century
Mathematical developments from the ancients through the 17th century. Emphasis on the development of an interrelationship among special topics from arithmetic, algebra, geometry and calculus, across different cultures and through time. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 229 or consent of department.
Credits: 3
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MATH 334 - Foundations of Applied Mathematics
Solution techniques for ordinary differential equations. Topics include hyperbolic functions, Laplace transforms, Fourier series, partial differential equations, and special functions. Not open for credit to students who have received credit for MATH 336.
Prerequisites & Notes
PRQ: MATH 232.
Credits: 4
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MATH 336 - Ordinary Differential Equations
Rudiments of the theory of ordinary differential equations and techniques of solution. Applications. Not available for credit to students who have received credit for MATH 334.
Prerequisites & Notes
PRQ: MATH 230.
Credits: 3
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MATH 353 - Axiomatic Geometry
The study and development of geometric axiomatic systems. Topics selected from Hilbert’s axioms for Euclidean geometry; projective, affine and Euclidean spaces over real vector spaces; convexity. Primarily intended for students preparing to teach mathematics.
Prerequisites & Notes
PRQ: MATH 240 or consent of department.
Credits: 3
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MATH 360 - Model Building in Applied Mathematics
An introduction to the formulation, analysis and interpretation of mathematical models in the study of selected problems in the natural sciences, the social sciences, and management science. Not open for credit to students having credit in MATH or STAT courses numbered 420 or above, except by consent of department.
Prerequisites & Notes
PRQ: MATH 230.
Credits: 3
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MATH 380 - Elementary Combinatorics
Permutations, combinations, generating functions, Dirichlet principle, Ramsey’s theorem, principle of inclusion-exclusion. Graphs, trees, circuits, Latin squares.
Prerequisites & Notes
PRQ: MATH 230.
Credits: 3
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MATH 401 - Clinical Secondary School Experience in Mathematics
A discipline-based clinical experience for students seeking initial secondary licensure in mathematics. Includes observations, evaluation, methods, and problems practicum as a part of a minimum of 40 clock hours of supervised and formally evaluated experiences in the particular setting likely for the student teaching experience. S/U grading.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 1-2
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MATH 402 - Methods of Instruction in the Mathematics Curriculum for Elementary School
Crosslisted as TLEE 402X. Methods, techniques, materials, curricular issues, learning theories, and research utilized in the teaching of elementary school mathematics. Attention given to the teaching of exceptional students and to planning for multicultural learning situations. Intended for students in education. Accepted for credit as an elementary mathematics methods course, but not as an upper-division mathematical content course. Not open for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors.
Prerequisites & Notes
PRQ: MATH 201 with a grade of C or better and junior standing or consent of department.
Credits: 3
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MATH 404 - Methods of Instruction in the Mathematics Curriculum for Middle School I
Methods, materials, curricular issues, learning theories, and research utilized in the teaching of middle school mathematics, particularly relating to instruction in grades 5 and 6. Intended for students in the middle level teacher licensure program. Accepted for credit as a middle school mathematics methods course, but not as an upper-division mathematics content course. Not open for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences major or minors.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 3
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MATH 410 - Methods of Instruction in the Mathematics Curriculum for the Middle School II
Objectives, problems, strategies, and trends in teaching middle school mathematics. Applications of learning theory and research focusing on remediation, presentation of new concepts, and the use of manipulatives. Accepted for credit as a middle school mathematics methods course, but not as an upper-division mathematical content course. Accepted as mathematical sciences credit only for those preparing to teach middle grades. Not used in major or minor GPA calculations for mathematical sciences majors or minors. For those seeking or holding middle grades education licensure.
Prerequisites & Notes
PRQ: MATH 229 and consent of the department.
Credits: 3
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MATH 411 - Methods of Instruction in the Mathematics Curriculum for Secondary School I
Methods and trends of instruction in the pre-secondary school mathematics with particular focus on mathematical practices and processes. Covers the teaching and learning of rational numbers, algebraic reasoning, patterns, functions, measurement, geometric concepts, and statistics and probability. Accepted for credit toward the major or minor only for those preparing to teach. Accepted for credit as a methods course for secondary school, but not as an upper-division mathematical content course. Not used in major or minor GPA calculation except for mathematics education majors and minors.
Prerequisites & Notes
PRQ: MATH 229 and consent of department.
Credits: 3
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MATH 412 - Methods of Instruction in the Mathematics Curriculum for Secondary School II
Objectives and organization of the curriculum and instructional materials for mathematics programs for secondary school with attention to methods of instruction, use of various representations and technology, and engaging students in mathematical practices. Accepted for credit toward the major or minor only for those preparing to teach. Accepted for credit as a methods course for secondary school, but not as an upper-division mathematical content course. Not used in major or minor GPA calculation except for mathematics education majors and minors.
Prerequisites & Notes
CRQ: MATH 401 and consent of department.
Credits: 3
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MATH 413 - Student Teaching (Secondary) in Mathematics
Student teaching for 10 weeks or for one semester. Assignments to be arranged with the Office of Educator Licensure in the College of Liberal Arts and Sciences after approval by the Department of Mathematical Sciences. Not available for credit in the major. See “Educator Licensure Requirements.” S/U grading.
Prerequisites & Notes
PRQ: MATH 412 and consent of department.
Credits: 7-12
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MATH 415 - Uses of Technology in the Mathematics Curriculum for Grades K-12
Hands-on experiences working with current technology (scientific calculators, graphics calculators, computers, and computer software) for elementary, middle school, and secondary school mathematics. Presentation and evaluation of methods and strategies for employing technology as a regular part of instruction and assessment, including discussion of educational foundations. Accepted as mathematical sciences credit only for those preparing to teach. Not accepted for credit as an upper-division mathematical content course for licensure purposes. Not used in major or minor GPA calculations.
Prerequisites & Notes
CRQ: MATH 402, MATH 410, or MATH 412.
Credits: 3
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MATH 416 - Topics in Mathematics for Teachers
Selected topics in mathematical sciences. Intended primarily for students preparing to teach mathematics. Not used in major or minor GPA calculation except for mathematics education majors and minors.
Prerequisites & Notes
PRQ: MATH 229 or consent of department.
Credits: 3
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MATH 419 - Secondary School Mathematics Clinical Experience
Fifteen clock hours of pre-student teaching clinical experience.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 0
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MATH 420 - Abstract Algebra I
Introduction to group theory. Properties of the integers, functions, and equivalence relations. A concrete approach to cyclic groups and permutation groups; isomorphisms and the theorems of Lagrange and Cayley.
Prerequisites & Notes
PRQ: MATH 240.
Credits: 3
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MATH 421 - Abstract Algebra II
Continuation of MATH 420. Homomorphisms and factor groups; introduction to commutative rings, with emphasis on polynomial rings; and fields, and algebraic extensions. Applications to classical geometric problems.
Prerequisites & Notes
PRQ: MATH 420.
Credits: 3
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MATH 423 - Linear and Multilinear Algebra
General theory of vector spaces, linear transformations, and matrices. Topics selected from determinants, tensor products, canonical forms, and bilinear and quadratic forms.
Prerequisites & Notes
PRQ: MATH 240 and MATH 420, or consent of department.
Credits: 3
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MATH 430 - Advanced Calculus I
Re-examination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral.
Prerequisites & Notes
PRQ: MATH 232 and MATH 240, or MATH 334.
Credits: 3
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MATH 431 - Advanced Calculus II
Further study of sequences and series of functions; functions of several variables.
Prerequisites & Notes
PRQ: MATH 430.
Credits: 3
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MATH 432 - Advanced Calculus III
Line and surface integrals, the Riemann-Stieltjes integral, gamma and beta functions, and Fourier series and integrals. Applications to probability theory and mathematical physics.
Prerequisites & Notes
PRQ: MATH 431 or both MATH 334 and PHYS 385.
Credits: 3
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MATH 434 - Numerical Linear Algebra
Roundoff errors and computer arithmetic. Direct and iterative methods for solving linear systems; norms and condition numbers, iterative refinement. Linear least squares problems: the normal equations and QR approach for overdetermined systems. Numerical methods for eigenvalues: an introduction to the QR iteration. Extensive use of computers.
Prerequisites & Notes
PRQ: MATH 232; either MATH 239 or MATH 240; and either CSCI 230 or CSCI 240 or approved equivalent.
Credits: 3
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MATH 435 - Numerical Analysis
Polynomial interpolation, numerical solutions of nonlinear equations, least squares approximation by polynomials, orthogonal polynomials, economization of power series. Numerical integration including quadrature formulae, adaptive quadrature, composite quadrature formulae, and Romberg integration. Numerical methods for initial value problems including Taylor series methods, Runge-Kutta methods, and multistep methods. Extensive use of computers.
Prerequisites & Notes
PRQ: MATH 232, either MATH 239 or MATH 240, and either CSCI 230 or CSCI 240 or approved equivalent.
Credits: 3
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MATH 438 - Theory of Differential Equations
Topics include linear systems, existence and uniqueness of solutions, nonlinear equations, and stability.
Prerequisites & Notes
PRQ: MATH 232, MATH 240, and either MATH 334 or MATH 336, or consent of department.
Credits: 3
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MATH 439 - Applied Mathematics for Sciences and Engineering
Designed mainly for science and engineering majors. Topics include the formulation of the basic partial differential equations from engineering and classical physics, separation of variables for the wave, heat, and Laplace equations, Fourier series and Sturm-Liouville theory, applications of Laplace and Fourier transform techniques to partial differential equation problems, eigenfunction expansions, method of characteristics, perturbation methods, Green’s functions, orthogonal expansions, and numerical methods.
Prerequisites & Notes
PRQ: MATH 232 and MATH 336.
Credits: 3
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MATH 440 - Elements of Complex Analysis
Beginning course in complex analysis emphasizing the applications of complex function theory.
Prerequisites & Notes
PRQ: MATH 232 and MATH 240, or MATH 334, or equivalent.
Credits: 3
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MATH 442 - Elements of Partial Differential Equations
Theory of partial differential equations emphasizing the basic nature of solutions of hyperbolic, parabolic, and elliptic equations as represented, respectively, by the wave, heat, and Laplace equations. Solution techniques covered include the method of characteristics, separation of variables, generalized eigenfunction expansions, and the Fourier integral and transform. Theoretical approaches are presented for the following topics: convergence and uniform convergence of Fourier series, Bessel’s inequality, Green’s identities, Sturm-Liouville theory, uniqueness of solutions, existence of fundamental solutions, and the maximum principle.
Prerequisites & Notes
PRQ: MATH 232, MATH 240, and MATH 336.
Credits: 3
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MATH 444 - Linear Programming and Network Flows
Introduction to linear programming, network flows, and applications.
Prerequisites & Notes
PRQ: MATH 239 or MATH 240, or consent of department.
Credits: 3
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MATH 450 - Introduction to Topology
Basic notions of metric and topological spaces; additional topics from combinatorial and algebraic topology may be included.
Prerequisites & Notes
PRQ: MATH 430.
Credits: 3
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MATH 456 - Linear Geometry
Treatment of affine and related geometries using the techniques of linear algebra.
Prerequisites & Notes
PRQ: MATH 420.
Credits: 3
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MATH 460 - Modeling Dynamical Systems
Involves students in the process of translating some questions about the observed world into mathematical form, combining formal reasoning with intuitive insights. Phenomena susceptible to formulation in terms of difference equations and various kinds of differential equations are investigated. Concepts of equilibrium, stability, bifurcation, limit cycles, and chaos illustrated.
Prerequisites & Notes
PRQ: MATH 232, MATH 239 or MATH 240, MATH 336, PHYS 253, and PHYS 273, or consent of department.
Credits: 3
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MATH 480 - Number Theory
Divisibility, primes, congruences, quadratic reciprocity, Diophantine equations, continued fractions, and selected topics.
Prerequisites & Notes
PRQ: MATH 420 or consent of department.
Credits: 3
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MATH 490X - Topics in Computer Science
Crosslisted as CSCI 490. A. Algorithms C. Automata, Computability, and Formal Languages Selected topics from major areas in computer science. May be repeated when subject varies.
Prerequisites & Notes
PRQ: Senior standing and consent of department.
Credits: 3
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MATH 494 - Directed Research/Internship in Mathematical Sciences
May be either academic, consisting of a project guided by a faculty member; or industrial, consisting of an approved project in industry. May be repeated to a maximum of 3 semester hours. S/U grading.
Prerequisites & Notes
PRQ: Mathematical sciences majors, junior/senior standing, and consent of department.
Credits: 1-3
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MATH 496 - Seminar in Computational Mathematics
Builds on the required courses in the computational mathematics emphasis to give the student in-depth experience doing projects.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 3
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MATH 497 - Undergraduate Readings in Mathematics
Selected readings from mathematical literature. May be repeated to a maximum of 6 semester hours.
Prerequisites & Notes
PRQ: Consent of department.
Credits: 1-3
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