

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]; 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. [Note: 0 cr toward graduation, 4 cr toward financial aid]
MATH
1001
 Excursions in Mathematics
(M/SR)
(4.0 cr; Prereq2 yrs high school math; fall, spring, every year) Introduction to the breadth and nature of mathematics and the power of abstract reasoning, with applications to topics that are relevant to the modern world, such as management science, statistics, voting, fair division of assets, symmetry and patterns of growth.
MATH
1012
 PreCalculus I: Functions
(4.0 cr; =[02223]; PrereqMath 0901 or placement; 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. [Note: no credit for students who have received credit for Math 1014]
MATH
1013
 PreCalculus II: Trigonometry
(M/SR)
(2.0 cr; PrereqMath 0901 or placement; 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; multipleangle identities; the Law of Sines; the Law of Cosines. [Note: no credit for students who have received credit for Math 1014]
MATH
1014
 Intensive PreCalculus
(M/SR)
(4.0 cr; fall, spring, 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; multipleangle identities; the Law of Sines; the Law of Cosines.
PrereqSecond year of high school algebra, college consent.
MATH
1021
 Survey of Calculus
(M/SR)
(4.0 cr; Prereq1012 or placement; credit will not be granted for Math 1021 if a grade of C or higher has previously been received for Math 1101; 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; Prereq1012, 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; Prereq1101; 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]; fall, spring, every year) An on or offcampus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum.
MATH
2101
 Calculus III
(M/SR)
(4.0 cr; Prereq1102 or #; fall, spring, every year) Multivariable and vector calculus. Threedimensional 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; Prereq1102 or #; fall, spring, every year) Matrix algebra, systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, innerproduct spaces, characteristic values and polynomials, eigenspaces, minimal polynomials, diagonalization of matrices, related topics; applications.
MATH
2202
 Mathematical Perspectives
(M/SR)
(4.0 cr; Prereq1101; 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; Prereq1101 or higher or #; fall, even academic years) Historical development of various areas in mathematics and important figures in mathematics from ancient to modern times.
MATH
2212
 Introduction to Knot Theory
(M/SR)
(4.0 cr; Prereq1101 or higher or #; fall, offered periodically) Introduction to the mathematical study of knots. Presentation, tabulation, and invariants of knots. Additional selected topics from lowdimensional topology.
MATH
2401
 Differential Equations
(M/SR)
(4.0 cr; Prereq1102 or #; fall, every year) Firstorder and secondorder 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]; Prereq1101 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 10.0 cr]; fall, spring, every year) An on or offcampus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum.
MATH
3211
 Geometry
(M/SR)
(4.0 cr; Prereq1102 or higher or #; fall, odd academic years) Synthetic approach to Euclidean and nonEuclidean 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
 Real Analysis I
(4.0 cr; Prereq1102, 2202 or #; fall, every year) Introduction to real analysis. The main topics of singlevariable calculusconvergence, continuity, differentiation, and series as they are applied and extended in advanced settings with emphasis on precise statements and rigorous proofs. Structure of the real numbers, open and closed sets. Integration, metric spaces, and other topics and applications as time allows.
MATH
3231
 Abstract Algebra I
(4.0 cr; Prereq2111, 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
(4.0 cr; Prereq1101 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
(4.0 cr; Prereq1102 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
(2.0 cr; =[MGMT 3501]; Prereq1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or #; spring, every year) Same as Mgmt 3501. Formulations of realworld 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 (CPMPERT); transportation problem.
MATH
3502
 Applied Probabilistic Modeling for Management Science
(2.0 cr; =[MGMT 3502]; Prereq1101 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, birthanddeath 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 10.0 cr]; fall, spring, every year) An on or offcampus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum.
MATH
4201
 Complex Analysis
(2.0 cr; Prereq3221 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 II
(2.0 cr; Prereq3221 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; Prereq2202 or #; fall, spring, offered periodically) Selected topics from point set topology and/or algebraic topology.
MATH
4231
 Abstract Algebra II
(2.0 cr; Prereq3231 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; Prereq2202 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; Prereq2111, 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, predatorprey 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; Prereqsr math major or #; full year course begins fall sem; AF only, fall, every year) This is a fullyear 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 10.0 cr]; fall, spring, every year) An on or offcampus learning experience individually arranged between a student and a faculty member for academic credit in areas not covered in the regular curriculum.






