Undergraduate Course Descriptions

More detailed course descriptions can be found in the Undergraduate Bulletin.

MATH 050-089. First Year Seminars

MATH 100, Review of Basic Algebra

Prerequisite: placement by Achievement Test.
For students unprepared for Math 110.
Hours credit for this course do not count for any Mathematics requirement, nor for hours required for graduation.

MATH 110, Algebra

Prerequisite: placement by Achievement Test.
Basic algebraic expressions, functions, exponents, logarithms.
Emphasis on problem solving.

MATH 116, Intuitive Calculus

Nontechnical approach to basic concepts of calculus.
For nonscience majors.

MATH 117, Finite Mathematics

Topics include basic counting problems and finite probability problems.
For nonscience majors.

MATH 118, Selected Topics in Mathematics

Nontechnical introduction.
Topics covered will vary, according to the instructor.
For nonscience majors.

MATH 119, Introduction to Mathematical Modeling

Topics emphasize elementary mathematical applications in other disciplines including compound interest and loan repayment, amount of medication in the blood stream, world oil consumption and reserves, spread of diseases, radioactive decay, pollution buildup and water filtering, and fish populations with and without harvesting.
An entry level course appropriate for any student not planning to take calculus.

MATH 130, Trigonometry and Analytic Geometry

Prerequisite: Math 110.
Trigonometric functions and their applications.
Graphs of functions, conics, translations, rotations.

MATH 152, Calculus for Business and Social Sciences

Prerequisite: Math 110.
Introductory survey of differential and integral calculus.
Emphasis on techniques and applications of interest for business and social sciences.
This is a terminal course, not adequate preparation for Math 32.

MATH 231, Calculus of Functions of One Variable I

Prerequisite: grade of C- or better in Math 130, or placement by the department.
Limits, derivatives, and integrals of functions of one variable.

MATH 232, Calculus of Functions of One Variable II

Prerequisite: grade of C- or better in Math 31, or placement by the department.
Calculus and the elementary transcendental functions.
Techniques of integration, indeterminate forms, Taylor's formula, infinite series.

MATH 233, Calculus of Functions of Several Variables

Prerequisite: Math 232.
Vector algebra, curves and surfaces in space, partial derivatives, multiple integrals.

MATH 233H, Calculus of Functions of Several Variables

Prerequisite: Consent of the instructor.
The honors course on vectors and multivariable calculus

MATH 295, Undergraduate Seminar in Mathematics

Prerequisite: permission of the instructor.
Seminar on a chosen topic.

MATH 296, Undergraduate Reading and Research in Mathematics

Prerequisite: permission of Director of Undergraduate Studies.
For students working on honors projects.

MATH 307 (EDUC 307), Revisiting Real Numbers and Algebra

Preparation for teaching pre-college mathematics.
Explores real numbers and algebra with emphasis on problem solving and mathematical reasoning.

MATH 381, Discrete Mathematics

Prerequisite: Math 232.
Topics from logic and set theory.
Relations and functions, induction, premutations and combinations, recurrence.

MATH 383, Linear Algebra and Differential Equations

Prerequisite: Math 233.
Systems of linear equations, vectors and matrices, basis and independence.
Introductory ordinary differential equations, systems of linear differential equations.
Linear algebra will be introduced as needed.

MATH 383H

The honors section of Math 383

MATH 401, Mathematical Concepts in Art

Mathematical theories of proportion, perspective, symmetry, and aesthetics.
Illustrated by examples from painting, architecture, and sculpture.

MATH 406 (BIOS 506), Mathematical Methods in Biostatistics

Prerequisite, Math 232 or equivalent.
Mathematical techniques in biostatistics.
Use in the life sciences and public health.
Includes review of calculus, topics from intermediate calculus, and introductory matrix theory.

MATH 411, Developing Mathematical Concepts

Prerequisite: consent of the instructor.
Studies how mathematical concepts are developed.
Service course for teachers.

MATH 418, Basic Concepts of Analysis for High-School Teachers

Prerequisites: Math 233 and 381 and consent of instructor.
Examination of high-school mathematics from an advanced perspective.
Number systems and the behavior of functions and equations.
Designed primarily for prospective or practicing high-school teachers.

MATH 515, History of Mathematics

Prerequisite: Math 381.
General survey of the history of mathematics.

MATH 521, Advanced Calculus I

Prerequisites: Math 233 and Math 381.
Real number system.
Continuity, uniform continuity, and differentiability of functions of one variable.
The Riemann integral in one variable.
Uniform convergence, infinite series, power series.

MATH 522, Advanced Calculus II

Prerequisite: Math 383 and Math 521.
Functions of several variables.
The derivative as a linear transformation, inverse and implicit function theorems.
Riemann theory of multiple integration.

MATH 523, Functions of a Complex Variable with Applications

Prerequisite: Math 383.
Complex numbers, elementary functions and their mapping properties.
Power series, analytic functions.
Contour integrals, Cauchy's theorem, Cauchy's formula.
Laurent series, elementary conformal mapping, harmonic functions.

MATH 524, Elementary Differential Equations

Prerequisite: Math 383.
Linear differential systems.
Power series solutions.
Laplace transforms.
Numerical methods.

MATH 528, Mathematical Methods for the Physical Sciences I

Prerequisites: Math 383 and Physics 104-105, or equivalent.
Theory and application of Laplace transform, Fourier series and Fourier transform.
Sturm-Liouville problems.
Students will be expected to do some numerical calculations with a programmable calculator or a computer.

MATH 529, Mathematical Methods for Physical Sciences II

Prerequisites: Physics 104-105 and one of Math 521, 524, 528, or equivalent.
Introduction to boundary value problems for the diffusion, Laplace, and wave PDEs.
Introduction to complex variables including the calculus of residues.
Bessel functions and Legendre functions.

MATH 533, Elementary Theory of Numbers

Prerequisite: Math 381.
Divisibility, Euclidean algorithm, congruences, residue classes.
Euler's function, primitive roots, Chinese remainder theorem.
Quadratic residues, continued fractions, Gaussian integers.

MATH 534, Elements of Modern Algebra

Prerequisite: Math 381.
Binary operations, groups, subgroups, quotient groups, rings, polynomials.

MATH 535 (STOR 435), Introduction to Probability

Prerequisite: Math 233.
Random variables, moments, binomial, Poisson, normal and related distributions.
Generating functions, sums and sequences of random variables, statistical applications.

MATH 547, Linear Algebra for Applications

Prerequisite: Math 233.
Algebra of matrices with applications.
Solution of linear systems by Gaussian elimination.
The Gram-Schmidt procedure.
Eigenvalues and eigenvectors.

MATH 548, Combinatorial Mathematics

Prerequisite: Math 381 or equivalent, or permission of instructor.
Topics chosen from:
Generating functions, theory of counting, partial ordering,
principle of inclusion-exclusion, Moebius inversion, others.

MATH 550, Topology

Prerequisite: Math 233. Corequisite: Math 383 or permission of instructor.
Surface topology, classification of compact surfaces.
Euler characteristic, orientability, vector fields on surfaces.
Tessellations, fundamental group.

MATH 551, Euclidean and Non-Euclidean Geometries

Prerequisite: Math 232 or permission of instructor.
Notions and models of Euclidean and non-Euclidean geometries.
Topics include order, congruence, and distance.

MATH 555, Introduction to Dynamics

Prerequisites: Math 383 and consent of instructor.
Topics may include: interation of maps, orbits, periodic points, attractors, symbolic dynamics, bifurcations, fractals, chaotic systems, others.

MATH 564, Mathematical Modeling

Prerequisites: Math 383 and some programming ability, or consent of instructor.
Models and numerical simulations, using differential equations, iterated maps, and probability.
Applications may include geophysical flows and climate change, epidemics, ecological models, conservation laws, cell biology.

MATH 565, Computer Assisted Mathematical Problem Solving

Prerequisite: Math 383.
Computer as a tool in solving a variety of mathematical problems.
Possible topics: roots of equations, solutions to differential equations, others.
Introduction to appropriate programming language. Emphasis on graphics.

MATH 566, Introduction to Numerical Analysis

Prerequisites: Math 383 and some knowledge of computer programming.
Iterative methods, interpolation, polynomial and spline approximations.
Numerical differentiation and integration, solution of ODEs and PDEs.

MATH 577, Linear Algebra

Prerequisites: Math 381 and Math 383.
Vector spaces, linear transformations, duality, diagonalization, Jordan canonical form.
Inner product spaces, spectral theorem.
Bilinear forms, multi-linear forms.

MATH 578, Algebraic Structures

Prerequisite: Math 577 or 547.
Permutation groups, matrix groups, symmetry groups, finite abelian groups.
Residue class rings, algebras of matrices and polynomials.
Real and complex numbers, rational functions, quadratic fields.

MATH 579, Topics in Matrix Theory

Prerequisites: Math 577 or 547, or equivalent, and some knowledge of computer programming.
Quadratic and Hermitian forms, Sylvester's theorem, applications to systems of linear ODE.
Approximation of eigenvalues and eigenvectors.
Perron-Frobenius theorem, integer matrices, applications to combinatorics.

MATH 590, Topics in Analysis

Prerequisite: Math 522 or consent of the instructor.
Topics to be chosen by the instructor.
Topics have included linear spaces, Fourier analysis, optimization.

MATH 591, Topics in Algebra

Prerequisite: consent of the instructor.
Topics to be chosen by instructor.
Topics have included number theory, field theory, algebraic geometry.

MATH 592, Topics in Geometry

Prerequisite: consent of the instructor.
Topics to be chosen by the instructor.
Topics have included non-Euclidean geometries, finite geometries, polytopes, topology.

Note: the following courses are taken by both undergraduate and graduate students.

MATH 641, Enumerative Combinatorics

Prerequisite: Permission of instructor.

MATH 643, Combinatorial Structures

Corequisite: Math 676 or permission of instructor.

MATH 653, Introductory Analysis

Prerequisite: advanced calculus.

MATH 656, Complex Analysis

Prerequisite: Math 653.

MATH 657, Qualitative Theory of Differential Equations

Prerequisites: linear algebra and Math 653, or consent of instructor.

MATH 676, Linear Algebra

Prerequisite: Math 578 or permission of instructor.

MATH 661, Scientific Computation I

Prerequisites: linear algebra, advanced calculus, and knowledge of a computer language.

MATH 662, Scientific Computation II

Prerequisite: Math 661.

MATH 668, Methods of Applied Mathematics I

Prerequisite: consent of instructor.

MATH 669, Methods of Applied Mathematics II