University of Vermont

cems
College of
Engineering and Mathematical Sciences

Department of Mathematics & Statistics

Term: Spring 2013
Subject: Mathematics

Courses

MATH 001 - Elementary College Algebra

Review of fundamental operations and a more extensive study of fractions, exponents, radicals, linear and quadratic equations, ratio, proportion, variation, progressions, and the binomial theorem. Topics normally included in intermediate algebra in high school. Students who have satisfactorily completed two years of high school algebra, or the equivalent, receive no credit for this course. Offered only in Evening Division and Summer Session. Prerequisite: One year of high school algebra.

MATH 009 - College Algebra

Sets, relations, functions with particular attention to properties of algebraic, exponential, logarithmic functions, their graphs and applications in preparation for MATH 019. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 019 or above. Pre/co-requisites: Two years of secondary school algebra; one year of secondary school geometry.

MATH 010 - Pre-Calculus Mathematics

Skills in working with numerical, algebraic, and trigonometric expressions are developed in preparation for MATH 021. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 019 or above. Prerequisite: Two years of secondary school algebra; one year of secondary school geometry.

MATH 016 - Fund Concepts Elem School Math

Topics include geometry, measurement, probability, statistics, algebra, number theory, and problem solving to provide background for future instruction in elementary and middle school mathematics. Prerequisite: Three years of secondary school math.

MATH 017 - Applications of Finite Math

Introduction to mathematics of finite systems with applications, such as probability, statistics, graph theory, fair division and apportionment problems, voting systems. Prerequisites: Two years of secondary school algebra or MATH 009 or MATH 010.

MATH 019 - Fundamentals of Calculus I

Introduction to limits and differential calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 021. Credit not given for more than one of the courses MATH 019, MATH 021 unless followed by MATH 022. See MATH 023. Prerequisite: MATH 009 or MATH 010, or sufficiently strong background in secondary school algebra and geometry.

MATH 020 - Fundamentals of Calculus II

Introduction to integral calculus with a wide variety of applications. A student who completes MATH 020 may be admitted to MATH 022; however, MATH 019, MATH 023 is preferable to MATH 019, MATH 021, MATH 022 or MATH 019, MATH 020, MATH 022. Prerequisite: MATH 019.

MATH 021 - Calculus I

Introduction to calculus of functions of one variable including: limits, continuity, techniques and applications of differentiation and integration. Prerequisites: MATH 010, or strong background in secondary school algebra and trigonometry. Credit not given for more than one course in the pair MATH 019, MATH 021 unless followed by MATH 022.

MATH 022 - Calculus II

Techniques and applications of integration. Polar coordinates, Taylor polynomials, sequences and series, power series. Prerequisite: MATH 021. Credit will not be given for both MATH 022 and MATH 023.

MATH 023 - Transitional Calculus

Intended to make the transition from a B or better in MATH 019 to MATH 121. Topics are similar to MATH 022 but recognizing different backgrounds of students in MATH 019 versus MATH 021. Prerequisite: B or better in MATH 019. Credit will not be given for both MATH 022 and MATH 023.

MATH 052 - Fundamentals of Mathematics

Emphasizing proofs, fundamental mathematical concepts and techniques are investigated within the context of number theory and other topics. Co-requisite: MATH 021. Credit not given for both MATH 052 and MATH 054.

MATH 095 - Concepts in Alg & Trig

Introductory courses or seminars on topics beyond the scope of existing departmental offerings. See Schedule of Courses for specific titles. Prerequisite: Instructor permission.

MATH 121 - Calculus III

Vectors, vector-valued functions. Calculus of functions of several variables: partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes' and Green's theorems. Prerequisite: MATH 022.

MATH 124 - Linear Algebra

Matrices, linear dependence, vector spaces, linear transformations, characteristic equations and applications. Prerequisite: MATH 022 or Instructor permission. Co-requisite: MATH 121 recommended but not required. .

MATH 173 - Basic Combinatorial Theory

Introduction to basic combinatorial principles emphasizing problem-solving techniques. Enumeration, generating functions, Fibonacci numbers, pigeonhole principle, inclusion-exclusion, and graph theory. Prerequisites: MATH 052 or MATH 054 or CS 064.

MATH 195 - Math Ed Lesson Prep

See Schedule of Courses for specific titles.

MATH 230 - Ordinary Differential Equation

Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: MATH 121. Corequisite: MATH 124 or Instructor permission. Credit not granted for more than one of the courses MATH 230 or MATH 271.

MATH 235 - Mathematical Models & Analysis

Techniques of Undergraduate calculus and linear algebra are applied for mathematical analysis of models of natural and human-created phenomena. Students are coached to give presentations. Prerequisites: MATH 121 and any of MATH 124, MATH 230, or MATH 271.

MATH 241 - Anyl in Several Real Vars I

Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 052, MATH 121, MATH 124 or Instructor permission.

MATH 242 - Anyl Several Real Variables II

Differentiation and integration in n-space, uniform convergence of functions, fundamental theorem of calculus, inverse and implicit function theorems. Prerequisite: MATH 241.

MATH 252 - Abstract Algebra II

Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations. Prerequisite: MATH 251.

MATH 255 - Elementary Number Theory

Divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences. Prerequisite: MATH 052 or MATH 054.

MATH 266 - Chaos,Fractals&Dynamical Syst

Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Co-requisite: MATH 271 or MATH 230 or Instructor permission. Cross-listed with: CSYS 266.

MATH 271 - Adv Engineering Mathematics

Differential equations and linear algebra, including linear ordinary differential equations, Laplace transforms, matrix theory, and systems of differential equations. Examples from engineering and physical sciences. Prerequisite: MATH 121. Credit not granted for both MATH 230 and MATH 271. No credit for Mathematics majors.

MATH 273 - Combinatorial Graph Theory

Paths and trees, connectivity, Eulerian and Hamiltonian cycles, matchings, edge and vertex colorings, planar graphs, Euler's formula and the Four Color Theorem, networks. Prerequisite: MATH 052 or MATH 054, or Instructor permission.

MATH 293 - Undergraduate Honors Thesis

Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.

MATH 294 - Undergraduate Honors Thesis

Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.

MATH 295 - Topics in Math History

For advanced students in the indicated fields. Lectures, reports, and directed readings on advanced topics. Prerequisite: Instructor permission. Credit as arranged. Offered as occasion warrants.

MATH 300 - Principles of Complex Systems

Introduction to fundamental concepts of complex systems. Topics include: emergence, scaling phenomena, and mechanisms, multi-scale systems, failure, robustness, collective social phenomena, complex networks. Students from all disciplines welcomed. Pre/co-requisites: Calculus and statistics required; Linear Algebra, Differential Equations, and Computer programming recommended but not required. Cross-listed with: CSYS 300.

MATH 331 - Theory of Func of Complex Var

Differentiation, integration, Cauchy-Riemann equations, infinite series, properties of analytic continuation, Laurent series, calculus of residues, contour integration, meromorphic functions, conformal mappings, Riemann surfaces. Prerequisite: MATH 242.

MATH 339 - Partial Differential Equations

Classification of equations, linear equations, first order equations, second order elliptic, parabolic, and hyperbolic equations, uniqueness and existence of solutions. Prerequisite: MATH 230; MATH 242.

MATH 351 - Topics in Algebra

Topics will vary each semester and may include algebraic number theory, algebraic geometry, and the arithmetic of elliptic curves. Repeatable for credit with Instructor permission. Prerequisite: MATH 252.

MATH 373 - Combinatorics

Topics will vary each semester and may include combinatorial designs, coding theory, topological graph theory, cryptography. Prerequisite: MATH 251 or MATH 273; or Instructor permission.

MATH 382 - Seminar

Topical discussions with assigned reading. Required of M.S. degree candidates.