*Interim Head of Department:* Professor Jeffrey Tollefson

*Department Office:* Room 123, Mathematical Sciences Building

### 1011Q. Introductory College Algebra and Mathematical Modeling

Three credits. Four class periods. Not open for credit to students who have passed any Q course. Strongly recommended as preparation for Q courses for students whose high school algebra needs reinforcement.

Emphasizes two components necessary for success in 1000-level courses which employ mathematics. The first component consists of basic algebraic notions and their manipulations. The second component consists of the practice of solving multi-step problems from other disciplines, called mathematical modeling. The topics include: lines, systems of equations, polynomials, rational expressions, exponential and logarithmic functions. Students will engage in group projects in mathematical modeling.

### 1020Q. Problem Solving

Three credits. Recommended preparation: MATH 1011Q or the equivalent. Not eligible for course credit by examination. Not open for credit to students who have passed any mathematics course other than MATH 1010, 1011Q, 1030Q, 1040Q, 1050Q, 1060Q or 1070Q. *Vinsonhaler*

An introduction to the techniques used by mathematicians to solve problems. Skills such as Externalization (pictures and charts), Visualization (associated mental images), Simplification, Trial and Error, and Lateral Thinking learned through the study of mathematical problems. Problems drawn from combinatorics, probability, optimization, cryptology, graph theory, and fractals. Students will be encouraged to work cooperatively and to think independently.

### 1030Q. Elementary Discrete Mathematics

Three credits. Recommended preparation: MATH 1011Q or the equivalent. Not open for credit to students who have passed any mathematics course other than MATH 1010, 1011Q, 1020Q, 1040Q, 1050Q, 1060Q or 1070Q.

Topics chosen from discrete mathematics. May include counting and probability, sequences, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems, voting methods, apportionment methods, mathematics of finance, number theory.

### 1040Q. Elementary Mathematical Modeling

Three credits. Recommended preparation: MATH 1011Q or the equivalent. Not open to students who have passed any mathematics course other than MATH 1010, 1011Q, 1020Q, 1030Q, 1050Q, or 1070Q. This course and MATH 1060Q cannot both be taken for credit. This course should not be considered as adequate preparation for MATH 1071Q, 1131Q, or 1151Q.

Use of algebraic and trigonometric functions with technology to analyze quantitative relationships and illustrate the role of mathematics in modern life; graphical numerical and symbolic methods. Most sections require a graphing calculator; some require work with a computer spreadsheet.

### 1050Q. Mathematical Modeling in the Environment

Three credits. Recommended preparation: MATH 1011Q or the equivalent. A solid background and good performance in high school algebra are highly recommended.

An interdisciplinary approach to environmental issues, such as: ground water contamination, air pollution, and hazardous materials handling. Emphasis on mathematical models, social and ethical implications, and physical and chemical principles. Includes a spread sheet program for water and air pollution data; a computer modeling package to analyze hazardous materials emergencies; creative use of the internet and field research. CA 3.

### 1060Q. Precalculus

Three credits. Prerequisite: A qualifying score on the mathematics placement assessment. Not open for credit to students who have passed MATH 1120, 1125Q, or 1131Q. Students may not receive credit for this course and MATH 1040Q.

Preparation for calculus. Review of algebra. Functions and their applications; in particular, polynomials, rational functions, exponentials, logarithms, and trigonometric functions.

### 1070Q. Mathematics for Business and Economics

Three credits. Recommended preparation: MATH 1011Q or the equivalent.

Linear equations and inequalities, exponents and logarithms, matrices and determinants, linear programming. Applications.

### 1071Q. Calculus for Business and Economics

Three credits. (One credit for students who have passed MATH 1121, 1131Q or 1151Q. ) Recommended preparation: MATH 1011Q or the equivalent, and MATH 1070Q, and a qualifying score on the mathematics placement assessment. Not open for credit to students who have passed MATH 1110Q.

Derivatives and integrals of algebraic, exponential and logarithmic functions. Functions of several variables. Applications.

### 1110Q. A Survey of Calculus with Applications I

Three credits. Recommended preparation: MATH 1011Q or the equivalent. Not open for credit to students who have passed MATH 1071Q, 1121, 1131Q, or 1151Q.

Derivatives and integrals of elementary functions including the exponential and logarithm functions; applications include optimization, marginal functions, exponential growth and decay, compound interest.

### 1125Q. Calculus Ia

Three credits. Recommended preparation: some exposure to the content of MATH 1060Q (Precalculus) or the equivalent. Students cannot receive credit for MATH 1125Q and MATH 1120, 1131Q or 1151Q. Students who have not passed the Calculus Placement Survey take this course rather than MATH 1131Q or 1151Q.

Limits, derivatives, and extreme values of algebraic, trigonometric, exponential and logarithmic functions, with supporting algebraic topics. MATH 1125Q covers the content of approximately the first half of MATH 1131Q.

### 1126Q. Calculus Ib

Three credits. Prerequisite: MATH 1125Q. Recommended preparation: A grade of C- or better in MATH 1125Q. Students cannot receive credit for MATH 1126Q and MATH 1121, 1131Q or 1151Q. Substitutes for MATH 1131Q or 1151Q as a requirement.

A continuation of the differential calculus of algebraic, trigonometric, exponential and logarithmic functions of MATH 1125Q ending with antidifferentiation, the definite integral, some techniques and applications. MATH 1126Q covers the content of approximately the second half of MATH 1131Q.

### 1131Q. Calculus I

(115Q ) Four credits. Prerequisite: A qualifying score on the mathematics placement assessment. Students cannot receive credit for MATH 1131Q and either MATH 1120, 1121, 1126Q, or 1151Q. (Two credits for students who have passed MATH 1125Q.) Suitable for students with some prior calculus experience. Substitutes for MATH 1126Q, or 1151Q as a requirement.

Limits, continuity, differentiation, antidifferentiation, definite integral, with applications to the physical and engineering sciences.

### 1132Q. Calculus II

(116Q ) Four credits. Prerequisite: A qualifying score on the mathematics placement assessment, and one of MATH 1126Q, 1131Q, or 1151Q, or advanced placement credit for calculus (a score of 4 or 5 on the Calculus AB exam or a score of 3 or better on the Calculus BC exam). Recommended preparation: A grade of C- or better in MATH 1126Q or 1131Q. Not open to students who have passed MATH 1122 or 1152Q.

Transcendental functions, formal integration, polar coordinates, infinite sequences and series, vector algebra and geometry, with applications to the physical sciences and engineering.

### 1151Q. Honors Calculus I

Four credits. Prerequisite: A qualifying score on the mathematics placement assessment. Students cannot receive credit for MATH 1151Q and either MATH 1121 or 1131Q. May be used in place of MATH 1131Q to fulfill any requirement satisfied by MATH 1131Q.

The subject matter of MATH 1131Q in greater depth, with emphasis on the underlying mathematical concepts.

### 1152Q. Honors Calculus II

Four credits. Prerequisite: A qualifying score on the mathematics placement assessment, and MATH 1151Q or advanced placement credit for calculus (a score of 4 or 5 on the calculus AB examination or a score of 3 on the Calculus BC examination) or consent of instructor. Students cannot receive credit for MATH 1152Q and either MATH 1122 or 1132Q. May be used in place of MATH 1132Q to fulfill any requirement satisfied by MATH 1132Q.

The subject matter of MATH 1132Q in greater depth, with emphasis on the underlying mathematical concepts.

### 1793. Foreign Study

Credits and hours by arrangement. Prerequisite: Consent of the Department Head or Undergraduate Coordinator required, normally before the student’s departure. May be repeated for credit (to a maximum of 15 for MATH 1793 and 3793 together).

### 1795Q. Special Topics Lecture

Credits, prerequisites, and hours as determined by the Senate Curricula and Courses Committee. May be repeated for credit with a change in topic.

### 2010Q-2011Q. Fundamentals of Algebra and Geometry

Three credits each semester. Prerequisite: PSYC 1100 and three credits of Mathematics; open only to students enrolled in the Elementary Education program in the Neag School of Education or by consent of instructor. May not be counted in any of the major groups described in the Mathematics Departmental listing.

Development of the number system with applications to elementary number theory and analytic geometry.

### 2110Q. Multivariable Calculus

Four credits. Four class periods. Prerequisite: MATH 1132Q or 1152Q or a score of 4 or 5 on the Advanced Placement Calculus BC exam. Recommended preparation: A grade of C- or better in MATH 1132Q. Not open for credit to students who have passed MATH 2130Q, or 2143Q.

Two- and three-dimensional vector algebra, calculus of functions of several variables, vector differential calculus, line and surface integrals.

### 2130Q. Honors Multivariable Calculus

Four credits. Prerequisite: MATH 1152Q or advanced placement credit for one year of calculus (a score of 4 or 5 on the Calculus BC examination) or consent of instructor. Not open to students who have passed MATH 2110Q or 2143Q. May be used in place of MATH 2110Q to fulfill any requirement satisfied by MATH 2110Q.

The subject matter of MATH 2110Q in greater depth, with emphasis on the underlying mathematical concepts.

### 2141Q-2142Q. Advanced Calculus I, II

Both semesters. 4 credits each semester. May be taken for honors credit but open to any qualified student. Prerequisite: A year of calculus (that may include high school) and instructor consent. MATH 2141Q may be used in place of MATH 1131Q or 1151Q to fulfill any requirement satisfied by MATH 1131Q or 1151Q. MATH 2142Q may be used in place of MATH 1132Q or 1152Q to fulfill any requirement satisfied by MATH 1132Q or 1152Q to fulfill any requirement satisfied by MATH 1132Q or 1152Q or 2710.

A rigorous treatment of the mathematics underlying the main results of one-variable calculus. Intended for students with strong interest and ability in mathematics who are already familiar with the computational aspects of basic calculus.

### 2143Q-2144Q. Advanced Calculus III, IV

Both semesters. 4 credits each semester. May be taken for honors credit but open to any qualified student. Prerequisite: MATH 2142Q or consent of instructor. MATH 2143Q may be used in place of MATH 2110Q to fulfill any requirement satisfied by MATH 2110Q. MATH 2144Q may be used in place of MATH 2410Q, MATH 2420Q, or MATH 2210 to fulfill any requirement satisfied by MATH 2410Q, MATH 2420Q, or MATH 2210.

A rigorous treatment of more advanced topics, including vector spaces and their application to multivariable calculus and first-order, second-order and systems of differential equations.

### 2210Q. Applied Linear Algebra

Three credits. Prerequisite: MATH 1132Q, 1152Q or 2142Q. Recommended preparation: A grade of C- or better in MATH 1132Q. Not open for credit to students who have passed MATH 2144Q or 3210.

Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications.

### 2360Q. Geometry

Three credits. Prerequisite: MATH 1126Q, 1131Q, 1151Q, or 2142Q. MATH 1126Q may be taken concurrently.

Deductive reasoning and the axiomatic method, Euclidean geometry, parallelism, hyperbolic and other non-Euclidean geometries, geometric transformations.

### 2410Q. Elementary Differential Equations

Three credits. Prerequisite: MATH 1132Q, 1152Q or 2142Q. Recommended preparation: A grade of C- or better in MATH 1132Q; and MATH 2110Q or 2130Q. Not open for credit to students who have passed MATH 2144Q or 2420Q.

Introduction to ordinary differential equations and their applications, linear differential equations, systems of first order linear equations, numerical methods.

### 2420Q. Honors Differential Equations

Three credits. Prerequisite: MATH 1152Q or instructor consent. Not open to students who have passed MATH 2410Q or 2144Q. MATH 2420Q satisfies any requirement met by MATH 2410Q, and provides superior preparation for prospective mathematics, science, and engineering majors.

The subject matter of MATH 2410Q in greater depth, with emphasis on the underlying mathematical concepts.

### 2610. Introduction to Actuarial Science

Three credits. Prerequisite: Consent of instructor.

An introduction to actuarial science, covering many of the topics in the first Foundations of Actuarial Practice module, Role of the Actuary, of the Society of Actuaries. Topics include: what an actuary is and does; external forces that influence actuarial work; and the framework and processes actuaries use to perform actuarial work using Microsoft Excel.

### 2620. Financial Mathematics I

(Also offered as MATH 5620.) Three credits. Prerequisite: MATH 1132Q, 1152Q or 2141Q.

Fundamental concepts of financial mathematics, with applications in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, duration calculation, asset/liability management, investment income, capital budgeting and valuing contingent cash flows.

### 2710. Transition to Advanced Mathematics

Three credits. Prerequisite: MATH 1132Q or 1152Q. Not open for credit to students who have passed MATH 2143Q. Students intending to major in mathematics should ordinarily take MATH 2710W or this course during the third or fourth semester.

Basic concepts, principles, and techniques of mathematical proof common to higher mathematics. Logic, set theory, counting principles, mathematical induction, relations, functions. Concepts from abstract algebra and analysis.

### 2710W. Transition to Advanced Mathematics

Three credits. Prerequisite: MATH 1132Q or 1152Q; and ENGL 1010 or 1011 or 2011. Not open for credit to students who have passed MATH 2143Q. Only open to Mathematics majors. Students intending to major in mathematics should ordinarily take MATH 2710 or this course during the third or fourth semester.

### 2720W. History of Mathematics

Three credits. Prerequisite: Either (i) MATH 2110Q or 2130Q, and either 2210 or 2410Q, or (ii) 2144Q or 2420Q; and ENGL 1010 or 1011 or 2011. This course may not be counted in any of the major groups described in the Mathematics Departmental listing.

A historical study of the growth of the various fields of mathematics.

### 2794W. Mathematics Writing Seminar

Two credits. Prerequisite: MATH 2144Q or one of MATH 2110Q, 2130Q, 2143Q and one of MATH 2210Q, 2410Q, 2420Q; ENGL 1010 or 1011 or 2011.

Contemporary topics in mathematics.

### 3094. Undergraduate Seminar

Three credits. Prerequisite: Open only with consent of instructor. This course, with a change of topic, may be repeated for credit.

### 3146. Introduction to Complex Variables

(Also offered as MATH 5046.) Three credits. Prerequisite: MATH 2110Q and 2410Q, or 2144Q or 2420Q. Not open for credit to students who have passed MATH 5046.

Functions of a complex variable, integration in the complex plane, conformal mappings.

### 3150. Analysis I

Three credits. Prerequisite: MATH 2144Q or 2410Q or 2420Q; MATH 2110Q or 2130Q or 2143Q; and a grade of C or better in either MATH 2142Q or 2710.

Introduction to the theory of functions of one real variable.

### 3151. Analysis II

Three credits. Prerequisite: MATH 3150.

Introduction to the theory of functions of several real variables.

### 3160. Probability

Three credits. Prerequisite: MATH 2110Q, 2130Q or 2143Q.

Introduction to the theory of probability. Sets and counting, probability axioms, conditional probabilities, random variables, limit theorems.

### 3165. Honors Probability

Three credits. Prerequisite: MATH 2130Q or 2143Q. Not open to students who have passed MATH 3160. May be used in place of MATH 3160 to satisfy any requirement satisfied by MATH 3160.

The subject matter of MATH 3160 in greater depth, with emphasis on the underlying mathematical concepts.

### 3170. Elementary Stochastic Processes

(Also offered as STAT 3965.) Three credits. Prerequisite: STAT 3025Q or 3345Q or 3375Q or MATH 3160.

Conditional distributions, discrete and continuous time Markov chains, limit theorems for Markov chains, random walks, Poisson processes, compound and marked Poisson processes, and Brownian motion. Selected applications from actuarial science, biology, engineering, or finance.

### 3210. Abstract Linear Algebra

Three credits. Prerequisite: MATH 2144Q or 2210Q; and a grade of C or better in either MATH 2142Q or 2710.

Vector spaces and linear transformations over fields.

### 3230. Abstract Algebra I

Three credits. Prerequisite: A grade of C or better in either MATH 2142Q or 2710. Recommended preparation: MATH 2144Q or 2210.

The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields.

### 3231. Abstract Algebra II

Three credits. Prerequisite: MATH 3230. Recommended preparation: MATH 3210.

Topics from ring theory, Galois theory, linear and multilinear algebra, or algebraic geometry.

### 3240. Introduction to Number Theory

Three credits. Prerequisite: A grade of C or better in either MATH 2142Q or 2710.

Euclid’s algorithm, modular arithmetic, Diophantine equations, analogies between integers and polynomials, and quadratic reciprocity, with emphasis on developing both conjectures and their proofs.

### 3250. Combinatorics

Three credits. Prerequisite: A grade of C or better in either MATH 2142Q or 2710.

Analysis of combinatorial problems and solution methods. Topics include: Enumeration, generating functions, bijective proofs, sieve methods, recurrence relations, graphs, partially ordered sets, and extremal combinatorics.

### 3260. Introduction to Mathematical Logic

Three credits. Prerequisite: A grade of C or better in either MATH 2142Q or 2710. Recommended preparation: PHIL 2211.

Formalization of mathematical theories, elementary model theory with applications to algebra, number theory, and non-standard analysis. Additional topics: Elementary recursion theory and axiomatic set theory. Emphasis on the applications of logic to mathematics rather than the philosophical foundations of logic.

### 3265. Applied Mathematical Logic

Three credits. Prerequisite: MATH 2142; or a grade of C or better in MATH 2710; or CSE 2500; or PHIL 2211Q.

Applied logic selected from set theory, computability theory, nonclassical logic, and type theory. Topics may include ordinal and cardinal numbers, transfinite recursion, the ZFC axioms, models of computation, undecidable problems, modal logic, intuitionistic logic.

### 3330. Elements of Topology

Three credits. Prerequisite: MATH 2110Q or 2130Q or 2143Q; and a grade of C or better in either MATH 2142Q or 2710.

Metric spaces, topological spaces and functions, topological properties, surfaces, elementary topics in geometric topology.

### 3370. Differential Geometry

Three credits. Prerequisite: A grade of C or better in either MATH 2142Q or 2710 and either (i) MATH 2110Q or 2130Q, and 2410Q or 2420Q, or (ii) MATH 2144Q.

The in-depth study of curves and surfaces in space.

### 3410. Differential Equations for Applications

Three credits. Prerequisite: MATH 2110Q and 2144Q or 2410Q or 2420Q. Not open for credit to students who have passed MATH 3412.

Series solutions of differential equations, Bessel functions, Fourier series, partial differential equations and boundary value problems, nonlinear differential equations.

### 3435. Partial Differential Equations

Three credits. Prerequisite: MATH 2110Q and one of MATH 2410Q or 2420Q or 2144Q.

Solution of first and second order partial differential equations with applications to engineering and the sciences.

### 3510. Numerical Analysis I

Three credits. Prerequisite: Either (i) MATH 2110Q or 2130Q, 2410Q, and either 2210 or 3210 or (ii) MATH 2144Q; and knowledge of at least one programming language.

Analysis of numerical methods associated with linear systems, eigenvalues, inverses of matrices, zeros of non-linear functions and polynomials. Roundoff error and computational speed.

### 3511. Numerical Analysis II

Three credits. Prerequisite: MATH 3510.

Approximate integration, difference equations, solution of ordinary and partial differential equations.

### 3545. Actuarial Case Studies using SAS™

One credit. Prerequisites: MATH 2620, MATH 3160, STAT 3375Q, and consent of instructor.

Design, development, testing, and implementation of solutions to problems in actuarial science using SAS™.

### 3550. Programming for Actuaries

Three credits. Prerequisite: Consent of instructor.

Design, development, testing and implementation of programs to solve actuarial problems using software such as Microsoft Office Excel with Visual Basic.

### 3610. Probability Problems

One credit. Two class periods. Prerequisite: MATH 2110Q, 2130Q or 2143Q; and MATH 3160.

Preparation through problem solving for the probability actuarial examination, which tests a student’s knowledge of the fundamental probability tools for quantitatively assessing risk. Recommended prior knowledge: a thorough command of probability, as well as basic concepts in insurance and risk management.

### 3615. Financial Mathematics Problems

One credit. Two class periods. Prerequisite: MATH 2620.

Preparation for the financial mathematics actuarial examination, which tests a student’s knowledge of the theory of interest and financial economics at an introductory level.

### 3621. Actuarial Statistics

Three credits. Prerequisite: MATH 3160 and STAT 3375Q.

Regression and time series applied to actuarial science. Covers the learning objectives established by the Society of Actuaries for Validation by Educational Experience in Applied Statistics.

### 3630. Actuarial Mathematics I

(Also offered as MATH 5630.) Three credits. Prerequisite: MATH 3160 or STAT 3375Q; and MATH 2620. MATH 3630 is not open to students who have passed MATH 5630.

Provides the mathematical foundations of life contingencies and their applications to quantifying risks in other actuarial contexts. Topics include survival and life table models, actuarial present value calculations in annuities and insurances, and premium and reserve calculations based on a single life.

### 3631. Actuarial Mathematics II

(Also offered as MATH 5631.) Three credits. Prerequisite: MATH 3630. MATH 3631 is not open to students who have passed MATH 5631.

A continuation of Actuarial Mathematics I. Topics include calculations of premiums and reserves based on multiple lives, multiple decrement and multiple state models. This course, along with MATH 3630, helps students prepare for the actuarial examination on models for quantifying risk.

### 3632. Loss Models

Three credits. Prerequisite or corequisite: MATH 3630.

Topics from the fourth actuarial examination relating to survival, severity, frequency and aggregate models, and the use of statistical methods to estimate parameters of such models given sample data.

### 3634. Actuarial Models

Three credits. Prerequisite: MATH 3160 or STAT 3025Q or 3375Q; and MATH 2620.

Introduction to the design of computerized simulations for analyzing and interpreting actuarial and financial problems. This course, together with MATH 5637, 5640, and 5641, helps the student prepare for the actuarial examination on the construction and evaluation of risk models.

### 3650. Financial Mathematics II

Three credits. Prerequisite: MATH 2620 and ACCT 2001, which may be taken concurrently. Not open for credit to students who have passed MATH 5621.

The continuation of MATH 2620. Measurement of financial risk, the mathematics of capital budgeting, mathematical analysis of financial decisions and capital structure, and option pricing theory.

### 3660. Advanced Financial Mathematics

Three credits. Prerequisite: MATH 2620 and 3160.

Advanced topics in financial mathematics such as single period, multi-period and continuous time financial models; Black-Scholes formula; interest rate models; and immunization theory.

### 3670W. Technical Writing for Actuaries

Three credits. Prerequisite: ENGL 1010 or 1011 or 2011; consent of Director of Actuarial Science required.

Students will write a technical report on an advanced topic in actuarial science.

### 3710. Introduction to Mathematical Modeling

Three credits. Prerequisite: MATH 2144Q or 2420Q; or MATH 2210 and 2410Q. Not open for credit to students who have passed MATH 5530 or 5540, CHEM 305, or PHYS 5350.

Construction of mathematical models in the social, physical, life and management sciences. Linear programming, simplex algorithm, duality. Graphical and probabilistic modeling. Stochastic processes, Markov chains and matrices. Basic differential equations and modeling.

### 3790. Field Study Internship

One to three credits. May be repeated for credit (to a maximum of 6 credits). Prerequisite: Consent of the Department Head, Director of the Actuarial Program, or the Undergraduate Coordinator required; completion of freshman-sophomore level requisite courses in the major. Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory).

### 3793. Foreign Study

Credit and hours by arrangement. Prerequisite: Consent of the Department Head or Undergraduate Coordinator required, normally before the student’s departure. May count toward the major with consent of the Advisor and either the Department Head or Undergraduate Coordinator. May be repeated for credit (to a maximum of 15 for MATH 1793 and 3793 together).

### 3794. Problem Seminar

One credit. One class period. Prerequisite: MATH 1132 or 1152Q. This course, with a change of topic, may be repeated for credit.

Problem sequences selected from algebra, geometry, calculus, combinatorics, and other branches of mathematics, designed to introduce mathematical concepts and to give experience in problem solving.

### 3795. Special Topics

Credits and hours by arrangement. With a change in content, may be repeated for credit. Prerequisites and recommended preparation vary.

### 3796W. Senior Thesis in Mathematics

Three credits. Prerequisite: ENGL 1010 or 1011 or 2011; open only by consent of Department Head or Departmental Honors Committee.

The student should define a general subject area for the thesis before choosing a thesis advisor and seeking consent at the time of registration. The student should submit a written proposal for the senior thesis to the advisor by the end of the semester preceding enrollment for thesis credit.

### 3798. Variable Topics

Three credits. With a change in topic, may be repeated for credit. Prerequisites and recommended preparation vary.

### 3799. Independent Study

Credits and hours by arrangement. Prerequisite: Open only with consent of instructor. This course, with a change of topic, may be repeated for credit.

### 4110. Introduction to Modern Analysis

(Also offered as MATH 5110.) Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5510.

Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, functions of several variables.

### 4210. Advanced Abstract Algebra

(Also offered as MATH 5210.) Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5210.

Group theory, ring theory and modules, and universal mapping properties.

### 4310. Introduction to Geometry and Topology

(Also offered as MATH 5310.) Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5310.

Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.