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Morris Courses

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MATHEMATICS (MATH)
Division of Science and Mathematics
Division of Science & Mathematics - Adm
 
MATH 901 - Basic Algebra
(0.0 cr [max 4.0 cr]; 0 cr toward graduation, 4 cr toward financial aid; fall, every year)
Sets, absolute values, linear equations and inequalities, functions and graphs, arithmetic of complex numbers, quadratics, radicals, exponents and logarithms, and linear systems of equations.



MATH 1001 - Survey of Math (M/SR)
(4.0 cr; Prereq-2 yrs high school math; spring, every year)
Introductory topics in mathematics, such as number system, geometry, algebra, discrete mathematics, statistics, logic, and the history of mathematics, including applications in today's world.



MATH 1012 - PreCalculus I: Functions
(4.0 cr; Prereq-placement; no credit for students who have received credit for Math 1014; fall, spring, every year)
Linear and quadratic functions, power functions with modeling; polynomial functions of higher degree with modeling; real zeros of polynomial functions; rational functions; solving equations in one variable; solving systems of equations; exponential and logarithmic functions, and the graphs of these functions.



MATH 1013 - PreCalculus II: Trigonometry (M/SR)
(2.0 cr; Prereq-placement; no credit for students who have received credit for Math 1014; fall, spring, every year)
Angles and their measures; trigonometric functions; the circular functions of trigonometry; graphs of sine, cosine, tangent, cosecant, secant, and cotangent functions; algebra of trigonometric functions; inverse trigonometric functions; solving problems with trigonometry; analytic trigonometry; fundamental trig identities; proving trigonometric identities; sum and difference identities; multiple-angle identities; the Law of Sines; the Law of Cosines.



MATH 1014 - Intensive Pre-Calculus (M/SR)
(4.0 cr; Prereq-second year of high school algebra, @; offered periodically)
Offered online only. Linear and quadratic functions, power functions with modeling; polynomial functions of higher degree with modeling; real zeros of polynomial functions; rational functions; solving equations in one variable; solving systems of equations; exponential and logarithmic functions, and the graphs of these functions. Angles and their measures; trigonometric functions; the circular functions of trigonometry; graphs of sine, cosine, tangent, cosecant, secant, and cotangent functions; algebra of trigonometric functions; inverse trigonometric functions; solving problems with trigonometry; analytic trigonometry; fundamental trig identities; proving trigonometric identities; sum and difference identities; multiple-angle identities; the Law of Sines; the Law of Cosines.



MATH 1021 - Survey of Calculus (M/SR)
(4.0 cr; Prereq-1012 or placement; spring, every year)
Short course for students in social sciences, biological sciences, and other areas requiring a minimal amount of calculus. Topics include basic concepts of functions, derivatives and integrals, exponential and logarithmic functions, maxima and minima, partial derivatives; applications.



MATH 1101 - Calculus I (M/SR)
(5.0 cr; Prereq-1012, 1013 or placement; fall, spring, every year)
Limits and continuity; the concepts, properties, and some techniques of differentiation, antidifferentiation, and definite integration and their connection by the Fundamental Theorem. Partial differentiation. Some applications. Students learn the basics of a computer algebra system.



MATH 1102 - Calculus II (M/SR)
(5.0 cr; Prereq-1101; fall, spring, every year)
Techniques of integration. Further applications involving mathematical modeling and solution of simple differential equations. Taylor's Theorem. Limits of sequences. Use and theory of convergence of power series. Students use a computer algebra system.



MATH 1993 - Directed Study
(1.0 - 5.0 cr [max 10.0 cr]; Prereq-approved directed study form; fall, spring, every year)
An on- or off-campus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum. In particular, students are encouraged to take at least one credit of a directed study in problem solving in mathematics. Such courses, at different levels, are available each term.



MATH 2101 - Calculus III (M/SR)
(4.0 cr; Prereq-1102 or #; fall, spring, every year)
Multivariable and vector calculus. Three-dimensional analytic geometry; partial differentiation; multiple integration; gradient, divergence, and curl; line and surface integrals; divergence theorem; Green and Stokes theorems; applications.



MATH 2111 - Linear Algebra (M/SR)
(4.0 cr; Prereq-1101 or #; fall, spring, every year)
Matrix algebra, systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, inner-product spaces, characteristic values and polynomials, eigenspaces, minimal polynomials, diagonalization of matrices, related topics; applications.



MATH 2202 - Mathematical Perspectives (M/SR)
(4.0 cr; Prereq-1101; spring, every year)
Introduction to the methodology and subject matter of modern mathematics. Logic, sets, functions, relations, cardinality, and induction. Introductory number theory. Roots of complex polynomials. Other selected topics.



MATH 2211 - History of Mathematics
(4.0 cr; Prereq-Math course above 1100 or #; fall, even academic years)
Historical development of various areas in mathematics and important figures in mathematics from ancient to modern times.



MATH 2401 - Differential Equations (M/SR)
(4.0 cr; Prereq-1102 or #; fall, every year)
First-order and second-order differential equations with methods of solution and applications, Laplace transforms, systems of equations, series solutions, existence and uniqueness theorems, the qualitative theory of differential equations.



MATH 2501 - Probability and Stochastic Processes (M/SR)
(4.0 cr; =[STAT 2501]; Prereq-1101 or #; fall, every year)
Same as Stat 2501. Probability theory; set theory, axiomatic foundations, conditional probability and independence, Bayes' rule, random variables. Transformations and expectations; expected values, moments, and moment generating functions. Common families of distributions; discrete and continuous distributions. Multiple random variables; joint and marginal distributions, conditional distributions and independence, covariance and correlation, multivariate distributions. Properties of random sample and central limit theorem. Markov chains, Poisson processes, birth and death processes, and queuing theory.



MATH 2993 - Directed Study
(1.0 - 5.0 cr [max 25.0 cr]; Prereq-approved directed study form; fall, spring, every year)
An on- or off-campus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum. In particular, students are encouraged to take at least one credit of a directed study in problem solving in mathematics. Such courses, at different levels, are available each term.



MATH 3211 - Geometry (M/SR)
(4.0 cr; Prereq-Math course above 1100; fall, odd academic years)
Synthetic approach to Euclidean and non-Euclidean geometries. Selected topics from affine, hyperbolic, spherical, projective geometries. Possible comparisons of analytic and synthetic approaches. May include other related topics or use of computer software for geometry.



MATH 3221 - Analysis (M/SR)
(4.0 cr; Prereq-1102, 2202 or #; fall, every year)
Introduction to real and complex analysis. The main topics of calculus-convergence, continuity, differentiation, integration, and series-applied and extended in advanced settings with emphasis on precise statements and rigorous proofs. Concept of metric space. Other topics and applications.



MATH 3231 - Abstract Algebra I (M/SR)
(4.0 cr; Prereq-2111, 2202 or #; spring, every year)
Systematic study of groups and rings, making use of linear algebra. Groups as codifying symmetry throughout mathematics and its applications. The Euclidean algorithm and its consequences, both for integers and polynomials. Other selected topics and applications.



MATH 3401 - Operations Research (M/SR)
(4.0 cr; Prereq-1100 or higher or #; spring, every year)
Topics include, but not limited to, linear and integer linear programming formulations, sensitivity analysis and duality, network models and applications.



MATH 3411 - Discrete and Combinatorial Mathematics (M/SR)
(4.0 cr; Prereq-1100 or higher or #; fall, every year)
Propositional logic; equivalence relations; recurrence equations; structures and properties of undirected and directed graphs; applications of the aforementioned topics.



MATH 3501 - Applied Deterministic Modeling for Management Science (M/SR)
(2.0 cr; =[MGMT 3501]; Prereq-1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or #; spring, every year)
Same as Mgmt 3501. Formulations of real-world problems as Linear Programming or Integer Linear Programming models; graphical solutions of some LP models. Linear Programming: the Simplex method, intuitive ideas behind the Simplex method. Using software to solve LP problems; interpreting optimal solutions; sensitivity analysis; duality. Network diagram representation; critical path method (CPM-PERT); transportation problem.



MATH 3502 - Applied Probabilistic Modeling for Management Science (M/SR)
(2.0 cr; =[MGMT 3502]; Prereq-1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or #; spring, every year)
Same as Mgmt 3502. Short review of probability and statistics; mean and variance of a data set; discrete and continuous random variables (especially the exponential distribution and the Poisson distribution). Decision and game theory. Decision trees, types of decision criteria. Queueing models, birth-and-death processes; Markovian or Poisson arrivals and exponential service times; M/M/k and M/M/8 queues; Statistical Quality Control; inventory control system.



MATH 3993 - Directed Study
(1.0 - 5.0 cr [max 25.0 cr]; Prereq-approved directed study form; fall, spring, every year)
An on- or off-campus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum. In particular, students are encouraged to take at least one credit of a directed study in problem solving in mathematics. Such courses, at different levels, are available each term.



MATH 4201 - Complex Analysis
(2.0 cr; Prereq-3221 or #; fall, spring, offered periodically)
Differentiable and analytic functions of a complex variable. Contour integral theorems. Laurent expansions. Other topics optional.



MATH 4211 - Real Analysis
(2.0 cr; Prereq-3221 or #; fall, spring, offered periodically)
Differentiation of functions of several variables. The extension of integration to other forms of integrals. Introduction to measure theory. Other optional topics.



MATH 4221 - Topology
(2.0 cr; Prereq-2202 or #; fall, spring, offered periodically)
Selected topics from point set topology and/or algebraic topology.



MATH 4231 - Abstract Algebra II
(2.0 cr; Prereq-3231 or #; fall, spring, offered periodically)
Selected topics from the theory of finite groups, Galois theory of fields, and/or the theory of rings.



MATH 4241 - Number Theory
(2.0 cr; Prereq-2202 or #; fall, spring, offered periodically)
Selected topics from modular congruences, theory of primes, classical Diophantine equations, and the connections with algebraic curves.



MATH 4252 - Differential Geometry
(2.0 cr; Prereq-#; fall, spring, offered periodically)
Geometry of curves and surfaces. Frames, curvature, torsion, orientation, differential forms, topological properties of surfaces. The notion of differentiable manifold. Selected applications.



MATH 4253 - Combinatorics
(2.0 cr; Prereq-#; fall, spring, offered periodically)
Selected topics from graph theory, the theory of ordered sets, and/or enumerative combinatorics.



MATH 4401 - Numerical Methods with Applications in Mathematical Modeling
(4.0 cr; Prereq-2111, 2401 or #; fall, spring, offered periodically)
Finite differences; interpolation; numerical integration; numerical solutions of differential, algebraic, and transcendental equations; continuous mathematical models.



MATH 4452 - Mathematical Modeling
(4.0 cr; Prereq-#; fall, spring, offered periodically)
Mathematical topics include, but are not limited to, differential and difference equations, discrete and continuous dynamical systems, predator-prey models, discrete and continuous optimization models, probabilistic models, stochastic and Poisson processes, and queuing models. Applications are drawn from different areas in the sciences and social sciences.



MATH 4901 - Senior Seminar
(2.0 cr; Prereq-sr; full year course begins fall sem; fall, every year)
This is a full-year course, required for all mathematics majors in their senior year. Students must attend year round and present one of the seminars.



MATH 4993 - Directed Study
(1.0 - 5.0 cr [max 25.0 cr]; Prereq-approved directed study form; fall, spring, every year)
An on- or off-campus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum. In particular, students are encouraged to take at least one credit of a directed study in problem solving in mathematics. Such courses, at different levels, are available each term.



 
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