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

## MATH 050-066, First Year Seminars

Current, upcoming, and recent FYS course descriptions can be found here.

## 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 non-science majors.

## MATH 117, Aspects of Finite Mathematics

• Topics include basic counting problems and finite probability problems.
• For non-science majors.

## MATH 118, Aspects of Modern Mathematics

• Nontechnical introduction.
• Topics covered will vary, according to the instructor.
• For non-science majors.

## MATH 119, Introduction to Mathematical Modeling

• Introduction to use of mathematics for modeling real-world phenomena in nontechnical setting.
• Uses algebraic, graphical, and numerical properties of elementary functions to interpret data.
• For non-science majors.

## MATH 130, Precalculus Mathematics

• Prerequisite: MATH 110.
• Introduction to 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 232.

## 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 231, 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 or 283.
• Vector algebra, curves and surfaces in space, partial derivatives, multiple integrals.

## MATH 233H, Calculus of Functions of Several Variables (Honors)

• Prerequisite: Consent of the instructor.
• The honors section of MATH 233

## MATH 241, BioCalculus I

• Prerequisite: C- or better in MATH 130, or placement by the department.
• Limits, derviatives, and integrals of functions of one variable motivated by/applied to discrete-time dynamical systems.

## MATH 283, BioCalculus II

• Prerequisite: C- or better in MATH 231 or 241, or placement by the department.
• Students receive no credit for this course if received credit for MATH 383.
• Techniques of integration, indeterminate forms, Taylor's series.
• Introduction to linear algebra motivated by/applied to ordinary differential equations
• Systems of ordinary differential equations used to model biological processes.

## MATH 290, Directed Exploration in Mathematics

• Prerequisite: permission of Director of Undergraduate Studies and direct supervision of faculty member; no more than seven semester hours credit awarded.
• Deeper investigation of topics in mathematics which may or may not be connected with existing courses.

## MATH 295, Undergraduate Seminar in Mathematics

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

• 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 or MATH 283.
• Transition from computational to theoretical mathematics.
• Topics from foundations of mathematics: logic, set theory, relations and functions, induction, premutations and combinations, recurrence.

## MATH 383, First Course in Differential Equations

• Prerequisite: MATH 233.
• Systems of linear equations, vectors and matrices, basis and independence.
• Introductory ordinary differential equations, first and second order differential equations with applications, higher order equations, and systems of linear differential equations.
• Linear algebra introduced as needed.

## MATH 383H, First Course in Differential Equations (Honors)

• 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 410, Teaching and Learning Mathematics

• Prepares majors to become high school mathematics teachers.
• Involves field work in high school and college levels.

## 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 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 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 formulae.
• 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 PHYS 104-105, or PHYS 116-117.
• 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: PHYS 104-105, of PHYS 116-117 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 or 283.
• 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
• 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
• 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 381.
• Notions and models of Euclidean and non-Euclidean geometries.
• Topics include order, congruence, and distance.

## MATH 555, Introduction to Dynamics

• Prerequisites: MATH 383.
• Topics may include: interation of maps, orbits, periodic points, attractors, symbolic dynamics, bifurcations, fractals, chaotic systems, others.

## MATH 564, Mathematical Modeling

• Prerequisites: MATH 283 or 383 and some programming ability.
• 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 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 547 or 577.
• 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 547 or 577 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. More detailed course descriptions can be found in the Undergraduate Bulletin.

## MATH 641, Enumerative Combinatorics

Prerequisite: MATH 578

## MATH 643, Combinatorial Structures

Prerequisite: MATH 578

## MATH 656, Complex Analysis

Prerequisite: MATH 653.

## MATH 657, Qualitative Theory of Differential Equations

Prerequisites: MATH 653 and knowledge of linear algebra

## MATH 661 (ENVR 661), Scientific Computation I

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

## MATH 662 (COMP 662, ENVR 662), Scientific Computation II

Prerequisite: MATH 661.

## MATH 668 (ENVR 668), Methods of Applied Mathematics I

Prerequisite: Undergraduate course in differential equations

## MATH 669 (ENVR 669), Methods of Applied Mathematics II

Prerequisite: MATH 669