# Upper Level Course Descriptions

Courses marked with § have not been taught recently and are currently on hold. At some point, these courses may be removed from the catalog.

These descriptions and syllabi are provided for quick reference of the Spring 2015 catalog. Please refer to the Course Catalog for the most current course descriptions, or contact the Department of Mathematical Sciences directly for a specific syllabus.

###### 30011 Basic Probability and Statistics (3)

Analysis and representation of data. Controlled experiments and observations. Measurement errors. Correlation and regression. Sampling. Probability models and tests of models. Inference. Prerequisite: MATH 11010 or MATH 10774 or MATH 10775 with a minimum grade of C (2.0).

###### 30055 Mathematical Theory of Interest (3)

A calculus-based introduction to the mathematics of finance. Limited to deterministic analysis of interest rates annuities bonds and immunization. Emphasizes the mathematical theory of the subject matter. Prerequisite: MATH 12003 with a minimum grade of C (2.0).

###### 31011 Discrete Mathematics (3)

Discrete mathematical structures including sets, functions, relations, Boolean algebras, elementary combinatorics, discrete probability, and logic. Applications to algorithm complexity analysis and program correctness proof. Prerequisite: MATH 12002 with a minimum grade of C (2.0). Pre/corequisites: MATH 21001 or MATH 32051 with a minimum grade of C (2.0).

###### 32044 Introduction to Ordinary Differential Equations (3)

An introduction to ordinary differential equations and applications. Topics include solution methods, series solutions and singular points. Laplace transforms and linear systems. Applications include population dynamics, forced oscillations and resonance. Prerequisites: MATH 21001 and MATH 22005 with a minimum grade of C (2.0).

###### 32051 Mathematical Methods in the Physical Sciences I (4)

Mathematics background beyond Calculus I and II for upper-division courses in the physical sciences. Topics include complex numbers and arithmetic, linear algebra, partial differentiation and multiple integrals. Prerequisite: MATH 12003 with a minimum grade of C (2.0).

###### 32052 Mathematical Methods in the Physical Sciences II (4)

Additional mathematics background for upper-division courses in the physical sciences. Topics include vector analysis, Fourier series and transforms ordinary differential equations and partial differential equations. Prerequisites: MATH 22005 with a minimum grade of C (2.0); and MATH 21001 or MATH 32051 with a minimum grade of C (2.0).

###### 34001 Fundamental Concepts of Algebra (3)

Professionalized course in algebra for prospective secondary teachers. Postulational development of number system of algebra; other systems, related topics, applications. Prerequisite: MATH 12002 with a minimum grade of C (2.0).

###### 34002 Fundamental Concepts of Geometry (3)

Professionalized course in geometry for prospective secondary teachers. Origin and development of the geometry of Euclid with modern refinements, topics, approaches. Other geometries, applications. Prerequisite: MATH 12002 with a minimum grade of C (2.0).

###### 40011 Introduction to Probability Theory and Applications (3)

Permutations and combinations, discrete and continuous distributions, random variables, conditional probabilities, Baye's formula, mathematical expectation, law of large numbers, normal approximations, basic limit theorems. Prerequisite: MATH 12003 with a minimum grade of C (2.0).

###### 40012 Introduction to Statistical Concepts (3)

Sample spaces, continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, types of error, level and power of tests, sequential and nonparametric methods. Prerequisite: MATH 40011 with a minimum grade of C (2.0).

###### 40051 Topics in Probability Theory and Stochastic Processes (3)

Topics from conditional expectations, Markov chains, Markov processes, Brownian motion and Martingales and their applications to stochastic calculus. Prerequisite: MATH 40011 with a minimum grade of C (2.0).

###### 40055 Actuarial Mathematics I (4)

(Slashed with MATH 50055) Topics from survival models, stochastic analysis of annuities and life insurance and casualty models. Prerequisite: MATH 30055 and MATH 40011 with a minimum grade of C (2.0).

###### 40056 Actuarial Mathematics II (4)

Benefit premiums, benefit reserves and their analysis, decrement models, joint survivorship, risk models. Prerequisite: MATH 40055 with a minimum grade of C (2.0).

###### 40059 Stochastic Actuarial Models (3)

(Slashed with MATH 50059) Designed to prepare students for the Society of Actuaries examination on actuarial mathematics. Prerequisite: MATH 40011 with a grade of C (2.0) or higher.

###### 40093 Variable Title Workshop in Mathematics (1-6) §

(Repeatable for credit) Studies special topics in mathematics. Not acceptable for credit toward a major or minor in math without approval of student's adviser. S u/graded. Prerequisite: Permission.

###### 41001 Introduction to Modern Algebra I (3)

Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains, and homomorphisms. Prerequisite: MATH 21001 and MATH 22005 with a minimum grade of C (2.0); and MATH 31011 or MATH 41021 or MATH 47011 with a minimum grade of C (2.0).

###### 41002 Introduction to Modern Algebra II (3)

A continuation of MATH 41001, emphasizing properties of rings, their ideals, polynomial ring extensions, fields, finite degree extensions, roots of polynomials, constructability. Prerequisite: MATH 41001 with a minimum grade of C (2.0).

###### 41021 Theory of Matrices (3)

A rigorous study of the topics introduced in matrix algebra. Topics included are vector space preliminaries, canonical forms of matrices, diagonalizability criteria. Prerequisite: MATH 21001 and MATH 22005 with a grade of C (2.0) or better.

###### 41038 Intermediate Logic (3)

(Cross-listed with CS 41038 and MATH 51038 and PHIL 41038 and PHIL 51038) Study of first order predicate calculus with identity and function symbols. Prerequisite: none.

###### 41045 Metalogic (3)

(Cross-listed with CS 41045 and CS 51045 and MATH 51045 and PHIL 41045 and PHIL 51045) May be counted toward B.A. or B.S. mathematics major. Consideration of various metatheorems, including soundness and completeness of propositional and predicate calculus, undecidability of predicate calculus and incompleteness of the theory of arithmetic. Prerequisite: PHIL 41038.

###### 42001 Introduction to Analysis I (3)

Topics include basic structure of the real numbers, Cauchy sequences, convergence, completeness of the real numbers, continuity, differentiation and Riemann integration. Prerequisite: MATH 21001 and MATH 22005 with a minimum grade of C (2.0).

###### 42002 Introduction to Analysis II (3)

Topics include further development of integration theory, infinite series, uniform convergence, several variable calculus and metric spaces. Prerequisite: MATH 42001 with a minimum grade of C (2.0).

###### 42011 Mathematical Optimization (3)

Analytic and numerical techniques for location of extreme points of functions and calculus of variations. Both constrained and unconstrained problems are considered. Prerequisite: MATH 21001 and MATH 22005 with a minimum grade of C (2.0).

###### 42021 Graph Theory and Combinatorics (3)

Fundamentals and applications of combinatorial mathematics. Topics include traversability, colorability, networks, inclusion and exclusion, matching and designs. Prerequisite: MATH 21001 and MATH 12003 with a minimum grade of C (2.0).

###### 42024 Numbers and Games (3)

The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory. Prerequisite: MATH 21001 with a minimum grade of C (2.0).

###### 42031 Mathematical Models and Dynamical Systems (3)

Formulation and analysis of mathematical models for a variety of phenomena. Mathematical methods from optimization dynamical systems and probability are developed and applied. Modern software tools are utilized. Prerequisite: MATH 32044 or 32052 with a minimum grade of C (2.0).

###### 42039 Modeling Projects (3)

(Slashed with MATH 52039) Individual and small-group projects concerned with the formulation and analysis of mathematical models in a variety of areas. Written and oral reports are required. Prerequisite: MATH 42031 with a minimum grade of C (2.0).

###### 42041 Advanced Calculus (3)

The calculus and applications of scalar and vector functions of several variables. Vector differential and integral calculus. Applications to field theories, electricity and magnetism, and fluid flow. Prerequisite: MATH 21001 and MATH 22005 with a minimum grade of C (2.0).

###### 42045 Introduction to Partial Differential Equations (3)

An introduction to Fourier series, Fourier transforms and partial differential equations. Wave, heat and potential equations of mathematical physics. Additional topics include Green's functions and the Method of Characteristics for wave equations. Prerequisite: MATH 32044 with a minimum grade of C (2.0).

###### 42048 Introduction to Complex Variables (3)

Algebra of complex numbers, analytic functions, mappings, Cauchy integral theory, residue theory and applications. Prerequisite: MATH 22005 with a minimum grade of C (2.0).

###### 42201 Introduction to Numerical Computing I (3)

(Slashed with MATH 52201; Cross-listed with CS 42201 and CS 52201) An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-squares data fitting, nonlinear equations and systems, and optimization problems. Prerequisite: MATH 12003 with a minimum grade of C (2.0); MATH 21001 or MATH 32051 with a minimum grade of C (2.0); and CS 10061 or CS 13001 or both CS 13011 and CS 13012 with a minimum grade of C (2.0).

###### 42202 Introduction to Numerical Computing II (3)

(Cross-listed with CS 42202 and CS 52202 and MATH 52202) A continuation of MATH 42201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Prerequisite: MATH 42201 with a minimum grade of C (2.0); and MATH 32044 or 32052 with a minimum grade of C (2.0).

###### 45011 Differential Geometry (3)

Analytic and metric differential geometry of curves and surfaces. Prerequisite: MATH 22005 with a minimum grade of C (2.0).

###### 45021 Euclidean Geometry (3)

Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles: cross-ratio, groups, constructions, geometric generalizations; inversion. Prerequisite: MATH 21001 with a minimum grade of C (2.0); or special approval of instructor.

###### 45022 Linear Geometry (3)

Using transformations as a tool to study geometry and to differentiate between different kinds of geometry. Linear algebra methods applied to geometry. Prerequisite: MATH 21001 with a minimum grade of C (2.0).

###### 46001 Elementary Topology (3)

Metric spaces, introduction to topological spaces, separation axioms. Prerequisite: MATH 22005 with a minimum grade of C (2.0).

###### 47011 Theory of Numbers (3)

Divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations. Prerequisite: MATH 12003 with a minimum grade of C (2.0).

###### 47021 History of Mathematics (3)

Survey from Babylonian and Egyptian mathematics to 20th century mathematics with emphasis on the development of algebra, geometry, calculus, number theory. Prerequisite: 3 hours of mathematics beyond MATH 22005 with a minimum grade of C (2.0).

###### 49995 Selected Topics in Mathematics and its Applications (1-4)

(repeated registration permitted) various special courses will be announced in the schedule of classes under this course number with different section numbers. Prerequisite: Permission.

###### 49996 Individual Study (1-4)

(repeatable for credit) Prerequisite: special approval.

###### 49998 Research (1-15)

(repeatable for credit) Prerequisite: special approval.