College of Natural and Health Sciences

School of Mathematical Sciences

- Contact (970) 351.2820
- www.unco.edu/NHS/mathsci

## MATH 508 Workshop

A variety of workshops on special topics within the discipline. Goals and objectives will emphasize the acquisition of general knowledge and skills in the discipline. Repeatable, under different subtitles.

## MATH 510 Seminar in Mathematics

Study discussion and student presentation of topics in mathematics. S/U graded. Repeatable, under different subtitles.

## MATH 513 Professional Renewal

Update skills and knowledge of professionals in the discipline. Goals and objectives will be specifically directed at individual professional enhancement rather than the acquisition of general discipline knowledge or methodologies. S/U or letter graded. Repeatable, under different subtitles.

## MATH 520 Functions and Equations

Graduates only. Polynomial equations including DeMoivre's Theorem, the Fundamental Theorem of Algebra, methods of root extraction (e.g. Newton, Graffe) multiplicities, symmetric functions, matrices and determinants. Elementary computer applications.

## MATH 522 Directed Studies

Individualized investigation under the direct supervision of faculty member. (Minimum of 37.5 clock hours required per credit hour.) Repeatable, maximum concurrent enrollment is two times.

## MATH 523 Modern Algebra

A study of groups, rings and fields with a special emphasis on groups and fields.

## MATH 525 Linear Algebra I

Prerequisite: MATH 321. Vector spaces, linear transformations, matrices, eigenvalues, canonical forms, quadratic forms and other selected topics.

## MATH 528 Discrete Mathematics

Graduates only. A broad, deep survey of topics in enumerative combinatorics, with a focus on mathematical reasoning and problem solving.

## MATH 529 Mathematical Problem Solving

Graduates only. Techniques in problem solving applied to algebra, number theory, geometry, probability, discrete mathematics, logic and calculus. A study of Polya's heuristic rules of mathematical discovery.

## MATH 531 Basic Analysis I

Prerequisite: MATH 233 with a grade of C or better (C- is not acceptable), and permission of instructor. Sequence of two courses to extend studies of calculus and analysis into the mathematical rigor and logic of analysis. Includes: real numbers, sequences, topology, limits, continuity, differentiation, series and integration.

## MATH 532 Basic Analysis II

## MATH 534 Continuous Mathematics

Graduates only. An exploration of select topics in real analysis providing a deeper understanding of real numbers, continuous functions, and the theoretical underpinnings of calculus.

## MATH 537 Mathematical Modeling

Graduates only. Introduction to the process of mathematical modeling using a wide selection of mathematical tools, with an emphasis on development, verification and interpretation of models and communication of results.

## MATH 540 Introduction to Topology

Point-set topology and the foundations of real analysis.

## MATH 543 Modern Geometry

A survey of both traditional Euclidean geometry and contemporary geometries, in which applications of geometry are integrated into the study of the mathematical structure of geometrical systems.

## MATH 545 Introductory Analysis

Prerequisite: MATH 540. Sequences, series, differentiation, Riemann-Stieltjes Integral, series of functions, special functions and functions of several variables.

## MATH 550 Applied Probability and Statistics

Graduates only. Methods related to descriptive and inferential statistics and the concept of probability are investigated in depth.

## MATH 560 Introductory Complex Variables

Prerequisite: MATH 432 or equivalent. First course in complex variables, especially for potential calculus teachers. After preliminaries, proceed directly to power series, Laurent's series, contour integration, residue theory, polynomials and rational functions.

## MATH 564 History of Mathematics

Graduates only. Survey of mathematical conceptual development and the people involved from antiquity to the present, including content connections and use of primary and secondary sources.

## MATH 591 Abstract Algebra and Number Theory

Graduates only. A problem solving approach to a survey of core abstract algebra topics including groups, rings, integral domains, fields and number theory related results.

## MATH 595 Topics in Mathematics

Topics from various fields of mathematics which reflect specific interests of instructors and students. Repeatable, under different subtitles.

## MATH 599 Mathematics Action Research Project Seminar

Graduates only. Students research a mathematical problem relevant to their own teaching and write an expository paper on that topic. Repeatable, no limitations.

## MATH 609 Abstract Algebra I

Prerequisite MATH 523 or equivalent. Groups and rings and their structure. Sylow theorems. Modules. History and applications.

## MATH 622 Directed Studies

Individualized investigation under the direct supervision of a faculty member. (Minimum of 37.5 clock hours required per credit hour.) Repeatable, maximum concurrent enrollment is two times.

## MATH 651 Statistical Science

Graduates only. The course focuses on statistical inference problems, applied linear models including multiple regression, ANOVA, linear mixed models and categorical data analysis including generalized linear models.

## MATH 695 Special Topics

Topics from various fields of mathematics, for example, algebraic topology, functional analysis, Lie groups and algebras or nonlinear analysis. Repeatable, under different subtitles.

## MATH 709 Abstract Algebra I

Prerequisite MATH 523 or equivalent. Groups and rings and their structure. Sylow theorems. Modules. History and applications.

## MATH 723 Abstract Algebra II

Prerequisite MATH 709. Polynomial Noetherian rings and ideals. Fields and Galois theory. Structure of fields. History and applications.

## MATH 727 Representation Theory

Introduction to Representation Theory of various mathematical structures. Emphasis is on group representations.

## MATH 728 Topics in Discrete Mathematics

Prerequisite: MATH 678. A broad yet deep survey of current topics in combinatorics and graph theory essential for teachers K-16, including applications to probability, coding theory, sorting and matching algorithms and optimization.

## MATH 732 Complex Variables

Prerequisite: A course in complex analysis. Analytic and meromorphic functions in the complex plane. Integration, conformal mapping and advanced topics.

## MATH 733 Geometric Analysis

Prerequisites: MATH 525; MATH 540 recommended. Analysis of functions of several variables, unifying and extending ideas from calculus and linear algebra. Includes the implicit function theorem and Stokes' Theorem.

## MATH 735 Real Analysis

Abstract spaces, Lebasque measure, continuity, integration and differentiation theorems, Baire category.

## MATH 736 Real Analysis II

Prerequisite: MATH 735. Topics from real and functional analysis such as: measure theory, distributions, metric spaces and other topics of the instructor's choice.

## MATH 744 Differential Geometry

Prerequisite: A course in Analysis. A course in the differential geometry of curves and surfaces. Both modern and classical aspects will be covered.

## MATH 764 Difference Equations and Chaos

Applications of difference equations in problem solving and modeling, especially in the area of chaos.

## MATH 778 Mathematical Logic

The notion of proof, first order logic, set theory, ordinals, cardinals and an overview of the most important recent results in the field.

## MATH 791 Number Theory

Prerequisite: MATH 732. A survey of topics in arithmetic and analytic number theory, such as Eulers' function, quadratic reciprocity, continued fractions and the distribution of prime numbers.

## MATH 795 Special Topics

Topics from various fields of mathematics, for example, algebraic topology, functional analysis, Lie groups and algebras or nonlinear analysis. Repeatable, under different subtitles.

## MATH 797 Doctoral Proposal Research

Required of all doctoral students. Four hours of credit for doctoral dissertation proposal research must be earned in partial fulfillment of requirements before admission to candidacy. Repeatable, maximum of four credits.

## MATH 799 Doctoral Dissertation

Required of all doctoral candidates. S/U graded. Repeatable, no limitations.