Department of Mathematics

University of Denver


Warp to standard page links

Course Descriptions

Note: Not every course is offered every quarter, and special topics courses change too often to be listed here. See the courses page for other views of the department's courses.

Graduate credit cannot be earned in courses numbered below 3000. Courses numbered 4000 and above are open only to graduate students.

Some course numbers have changed beginning autumn quarter, 2002. Former course numbers are listed for your convenience.


MATH 1750 (Formerly MATH 0750) College Algebra & Trigonometry
Selected topics in algebra and analytic trigonometry intended to prepare students for calculus sequence ( MATH 1951, 1952, 1953). Cannot be used to satisfy the mathematics/computing core requirements. 4 qtr. hrs.

MATH 1951 (Formerly MATH 1950-1) Calculus I
Differentiation of functions of one variable. Use of a laptop computer and a computer algebra system is an integral component of the course. Students with high school trigonometry should enter sequence in fall quarter. Others should complete prerequisite MATH 1750 and enter sequence in winter quarter. Prerequisite: MATH 1750 or equivalent. 4 qtr. hrs.

MATH 1952 (Formerly MATH 1950-2) Calculus II
Differentiation and integration of functions of one variable. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1951. 4 qtr. hrs.

MATH 1953 (Formerly MATH 1950-3) Calculus III
Integration of functions of one variable, infinite sequences and series. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1952. 4 qtr. hrs.

MATH 1961 (Formerly MATH 1955-1) Honors Calculus I
Same topics as MATH 1951, enriched in one or more of the following ways: challenging group projects and presentations, use of Web-based course materials, greater emphasis on theory of calculus and applications. Use of a laptop computer and a computer algebra system is an integral component of the course. Can be used for partial fulfillment of academic requirements in Honors Program. Prerequisites: MATH 1750 or equivalent; a strong background, facility and interest in mathematics; or instructor's permission. 4 qtr. hrs.

MATH 1962 (Formerly MATH 1955-2) Honors Calculus II
Same topics as MATH 1952, enriched in the same ways as MATH 1961 enriches MATH 1951. Use of a laptop computer and a computer algebra system is an integral component of the course Prerequisites: MATH 1962. 4 qtr. hrs.

MATH 1963 (Formerly MATH 1955-3) Honors Calculus III
Same topics as MATH 1953, enriched in the same ways as MATH 1961 enriches MATH 1951. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisites: MATH 1962 4 qtr. hrs.

MATH 2050 Symbolic Logic
Modern propositional logic; symbolization and calculus of predicates, especially predicates of relation. Cross-listed as PHIL 2160. 4 qtr. hrs.

MATH 2060 Elements of Linear Algebra
Matrices, systems of linear equations, vectors, eigenvalues and eigenvectors; idea of a vector space; applications in the physical, social, engineering and life sciences. Prerequisite: MATH 1750 or equivalent. 4 qtr. hrs.

MATH 2070 Intro Differential Equations
Solution of linear differential equations; special techniques for nonlinear problems; mathematical modeling of problems from physical and biological sciences. Prerequisite: MATH 1953 or MATH 1963. 4 qtr. hrs.

MATH 2080 Calculus of Several Variables
Multivariable processes encountered in all sciences; multiple integration, partial differentiation and applications; algebra of vectors in Euclidean three-space; differentiation of scalar and vector functions. Prerequisite: MATH 1953 or MATH 1963. 4 qtr. hrs.

MATH 2200 Intro to Discrete Structures
Introduction to theory of sets; relations and functions; logic, truth tables and propositional calculus; proof techniques; introduction to combinatorial techniques. Prerequisite: high school algebra. 4 qtr. hrs.

MATH 3000 The Real World Seminar
Lectures by alumni and others on surviving culture shock when leaving the University and entering the job world. Open to all students regardless of major. Cross-listed as COMP 3000. 1 qtr. hr.

MATH 3070 Math Modeling and Comp Sim
Mathematical models in social, life, and management sciences; models include growth processes, epidemics, queues, land usage, etc.; Markov chains, optimization, game theory, graphy theory, etc. Prerequisites: completion of one 3000-level mathematics course and COMP 1672. 4 qtr. hrs.

MATH 3080 Introduction to Probability
Basic probablity models, combinatorial methods, random variables, independence, conditional probablility, probability laws, applications to classical problems. Prerequisite: MATH 1952. 4 qtr. hrs.

MATH 3090 Mathematical Probability
Limit theorems for independent random variables, multivariate distributions, generating functions, random walks and statistical techniques. Prerequisites: MATH 1953 or MATH 1963 and MATH 3080. 4 qtr. hrs.

MATH 3120 Introduction to Topology
Point set topology including topological spaces, connectedness, compactness and separation axioms; preparation for advanced courses in analysis. Prerequisite: junior standing. 4 qtr. hrs.

MATH 3151 (Formerly MATH 3150-1) Linear Algebra I
Vector spaces, linear mappings, matrices, inner product spaces, eigenvalues and eigenvectors. Prerequisite: MATH 2060. 4 qtr. hrs.

MATH 3152 (Formerly 3150-2) Linear Algebra II
Linear operators on finite dimensional vector spaces, eigenvalues, eigenvectors, Jordan forms; special properties of self-adjoint and normal operators; special topics. Prerequisite: MATH 3151. 4 qtr. hrs.

MATH 3161 (Formerly MATH 3160-1) Intro to Real Analysis I
A theoretical introduction to limits and continuity; sequences and series of numbers and functions; a theoretical introduction to the foundations of calculus. Prerequisite: MATH 2080. 4 qtr. hrs.

MATH 3162 (Formerly 3160-2) Intro to Real Analysis II
A theoretical introduction to limits and continuity; sequences and serices of numbers and functions; a theoretical introduction to the foundations of calculus. Prerequisite: MATH 2080.

MATH 3170 Intro Algebraic Structures
Semigroups, groups, rings, fields and their morphisms. Prerequisites: junior standing and one year of university-level mathematics. 4 qtr. hrs.

MATH 3180 Mathematical Statistics
Mathematical foundations of statistical theory, random sampling, theoretical distributions, estimation, test of hypotheses, limit theorems, correlation and regression, nonparametric statistics, decision theory. Students may not receive credit for both MATH 3180 and 3190. Prerequisites: MATH 1953 or MATH 1963 and MATH 3080. 4 qtr. hrs.

MATH 3190 Stats for Soc & Behav Science
Basic statistical techniques commonly used in quantitative analysis in the fields of economics, political science and sociology; probability, sampling theory, hypothesis testing, analysis of variance and correlation, regression analysis. Students may not receive credit for both MATH 3190 and MATH 3180. 4 qtr. hrs.

MATH 3200 Discrete Structures
Discrete mathematical structures and non-numerical algorithims; graphy theory, monoids, propositional calculus, lattices, Boolean algebras; emphasis on applications to computer science. Cross-listed as COMP 3200. Prerequisites: MATH 2200 or COMP 2300 and COMP 1672. 4 qtr. hrs.

MATH 3221 Automata & Formal Languages I
Introduction to computability, effective procedures, format languages, undecidability; finite automata and regular languages. Prerequisites: MATH 3200 or COMP 3200. 4 qtr. hrs.

MATH 3222 Automata & Formal Languages II
Pushdown automata and context-free languages; Turing machines; decidability, recursive and recursively enumerable sets. Prerequisite: MATH 3221. MATH 3221. 4 qtr. hrs.

MATH 3311 (Formerly MATH 3310-1) Intro to Operations Research I
Linear optimization models, simplex algorithm, sensitivity analysis and duality, network models, dynamic programming, applications to physical, social and management sciences. Prerequisite: MATH 2060. 4 qtr. hrs.

MATH 3312 (Formerly MATH 3310-2) Intro to Operations Research II
Nonlinear and stochastic models, elementary queuing theory, integer programming, introduction to simulation; applications to physical, social and management sciences. Prerequisites: MATH 1953 or MATH 1963 and MATH 3311. 4 qtr. hrs.

MATH 3400 Introduction to Geometry
Specific geometrical systems including finite, Euclidean, non-Euclidean and projective geometries. Prerequisites: junior standing and one year of university-level mathematics. 4 qtr. hrs.

MATH 3451 Chaos, Dynamics & Fractals I
Introduction to one-dimensional dynamical systems, fractals; fixed and periodic points; sources and sinks; period doubling and tangent node bifurcations; chaotic dynamical systems; Sarkovskii's Theorem. Prerequisites: MATH 2080 and instructor's permission. 4 qtr. hrs.

MATH 3452 Chaos, Dynamics & Fractals II
Dynamical systems in two (or more) real variables or one complex variable; stable manifold theorem; Henon attractor; Julia sets; Mandelbrodt set. Prerequisite: MATH 3451 or instructor's permission. 4 qtr. hrs.

MATH 3550 Intro to Theory of Numbers
Concepts of nonanalytical number theory and its history; prime numbers, divisibility, continued fractions, modular arithmetic, Diophantine equations and unsolved conjectures. Prerequisites: junior standing and one year of university-level mathematics. 4 qtr. hrs.

MATH 3571 (Formerly MATH 3570-1) Intro to Numerical Methods I
Algorithmic approach to numerical problems, solution of systems of linear equations, interpolation and approximation, numerical integration, and the numerical solution of ordinary and partial differential equations. Cross-listed as COMP 3571. Prerequisites: MATH 1952 or MATH 1962, and MATH 2060 and COMP 1672. 4 qtr. hrs.

MATH 3572 (Formerly MATH 3570-2) Intro to Numerical Methods II
Algorithmic approach to numerical problems, solution of systems of linear equations, interpolation and approximation, numerical integration, and the numerical solution of ordinary and partial differential equations. Cross-listed as COMP 3572. Prerequisites: MATH 3571 or COMP 3571. 4 qtr. hrs.

MATH 3651 Diff Eqns and Applied Math I
Modeling of phenomena by ordinary differential equations; techniques of analysis and solution of such equations; oscillation theory and boundary value problems, power series methods, special functions, Laplace transforms and difference equations. Prerequisites: MATH 2060 and MATH 2070. 4 qtr. hrs.

MATH 3652 Diff Eqns and Applied Math II
Modeling of phenomena by ordinary and partial differential equations; classification of second order partial differential equations; separation of variables, transform methods, special functions, method of characteristics. Prerequisite: MATH 3651. 4 qtr. hrs.

MATH 3705 Topics in Mathematics
4 qtr. hrs.

MATH 3706 Intro to Computer Algebra
Introduction to computer algebra, the algorithmic solution of mathematical problems; use of computer algebra software (MAPLE or MATHEMATICA); algorithms for analysis and manipulation of polynomial, algebraic, and trigonometric expressions; algorithms for differentiation and integration; applications to calculus and differential equations. Cross- listed as COMP 3706. Prerequisites: MATH 2070 and either COMP 1672 or COMP 1680. 4 qtr. hrs.

MATH 3707 Math Methods Computer Algebra
Mathematical theory and algorithms used to design modern computer algebra systems. Includes selected topics from integer algorithms, greatest common divisor algorithms for polynomials, polynomial factorization algorithm, resultant computation and applications, polynomial decomposition, and the Risch integration algorithm. Cross-listed as COMP 3707. Prerequisite: MATH 3706, COMP 3706 or 1680. 4 qtr. hrs.

MATH 3730 Vector Analysis
Differential vector calculus, gradient, divergence, curl; introduction to differential geometry, integration, Stokes' theorem in several variables. Prerequisite: MATH 2080. 4 qtr. hrs.

MATH 3851 (Formerly MATH 3850-1) Functions Complex Variable I
Complex numbers, analytic functions, complex integration, series expansions, residue theory, conformal maps, advanced topics and applications. Prerequisite: MATH 2080. 4 qtr. hrs.

MATH 3852 (Formerly MATH 3850-2) Functions Complex Variable II
Advanced topics in complex analysis with applications. Prerequisite: MATH 3851. MATH 3851. 4 qtr. hrs.

MATH 3950 Undergraduate Research Seminar
Opportunity to conduct mathematics research; bridges the gap between homework exercises and research problems with directed readings and challenging projects. Prerequisite: instructor's permission. 0 to 4 qtr. hrs.

MATH 3991 Independent Study
Cannot be arranged for any course that appears in regular course schedule for that particular year. 0 to 4 qtr. hrs.


Note: enrollment in courses listed at the 4000-level and above is limited to graduate students.
DU Mathematics Course Descriptions

MATH 4091 Mathematical Probability
Limit theorems for independent random variable, multivariate distributions, generating functions, random walks, statistical techniques. Prerequisite(s): MATH 1953 or equivalent, MATH 3080. 3 qtr. hrs.

MATH 4092 Stochastic Processes
Stochastic models in biology, physics, economics; Markov, Poisson, renewal branching, birth-death, queuing processes. Prerequisite: MATH 4091. 3 qtr. hrs.

MATH 4161, 4162, 4163 Mathematical Structures
Algebraic, logical, geometrical structures; sets, categories, groups, rings, fields, multilinear algebra, partially ordered sets, projective geometries, algebraic topology. Prerequisite(s): MATH 3170. 3 qtr. hrs.

MATH 4221 Automata and Formal Languages I
Computability, effective procedures, formal languages, undecidability; finite automata, regular languages. Prerequisite(s): MATH 3200. 3 qtr. hrs.

MATH 4222 Automata and Formal Languages II
Pushdown automata, context-free languages; Turing machines; computational complexity. Prerequisite(s): MATH 4221. 3 qtr. hrs.

MATH 4251,4252, 4253 (Formerly MATH 4250-1,2,3) Modern Analysis
Metric spaces, point set topology, Hilbert and Banach spaces, symmetric compact operators; Lebesgue integral, LP spaces, measure theory. Prerequisite(s): MATH 3152, MATH 3161. 3 qtr. hrs.

MATH 4501, 4502, 4503 (Formerly MATH 4500-1,2,3) Functional Analysis
Advanced topics in structure of linear spaces, generalized functions; spectral theory of operators in Hilbert spaces; applications to partial differential equations, semigroups, stochastic processes. Prerequisite(s): MATH 4253. 3 qtr. hrs.

MATH 4701 Combinatorial Algorithms
Basic enumeration techniques; representations of combinatorial objects; algorithms for searching, sorting, generating combinatorial objects; graph algorithms. 3 qtr. hrs.

MATH 4705 Special Topics in Mathematics
Varying selected advanced topics in mathematics, depending on student demand. Possible alternatives include calculus of variations, partial differential equations, algebraic topology, differential manifolds, special functions. 3 qtr. hrs.

MATH 4707 Mathematical Methods of Computer Algebra
Mathematical theory and algorithms used to design modern computer algebra systems; includes selected topics from: integer algorithms, greatest common divisor algorithms for polynomials, polynomial factorization algorithm, resultant computation and applications, polynomial decomposition, and the Risch integration algorithm. Cross-listed as MATH 3707 and COMP 4707. Prerequisite(s): MATH 3706. or COMP 3706. 3 qtr. hrs.

MATH 4851, 4852 (Formerly MATH 4850-1,2) Introduction to Functions of a Complex Variable
Concepts of complex numbers, functions of a complex variable, continuity and differentiability in complex plane; advanced topics, applications. Prerequisite(s): MATH 2080. 3 qtr. hrs.

MATH 4991 Independent Study (MA/MS)
Cannot be arranged for any course that appears in regular course schedule for that particular year. arr.

MATH 4995 Independent Research (MA/MS)
Research projects undertaken in conjunction with a faculty member. arr.

MATH 5000 Doctoral Seminar
Techniques, methods used in mathematical, computing research. Includes proofs, bibliographic searching, writing styles, what constitutes an acceptable dissertation. arr.

MATH 5991 Doctoral Independent Study
Cannot be arranged for any course that appears in the regular course schedule for that particular year. arr.

MATH 5995 Independent Research
Research leading to a dissertation. arr.



DU Department of Mathematics

Standard page links