# University of Vermont

## UVM Course Directory

Term: Fall 2019

Subject: Mathematics

##### MATH 009 - QR: 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 - QR: 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 021 or above. Prerequisite: Two years of secondary school algebra; one year of secondary school geometry.

##### MATH 015 - QR: Elementary School Math

Operations with real numbers: decimals, fractions, percents, integers. Set operations, Venn diagrams, algebra, and problem solving provide background for future instruction in elementary/middle school mathematics. Prerequisite: Three years of secondary school math.

##### MATH 017 - QR: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 018 - QR: Basic Mathematics

Data, statistics, modeling, algebra, word problems, calculus. Students who do well in the algebra section may continue with MATH 019 or MATH 021. Prerequisite: three years of high school math. No credit for CEMS students.

##### MATH 019 - QR: 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 - QR:Fundamentals of Calculus II

Introduction to integral calculus with a wide variety of applications. Students completing MATH 020 may be admitted to MATH 022; however, MATH 019 and MATH 023 is preferable to MATH 019 and (MATH 020 or MATH 021) and MATH 022. Prerequisite: MATH 019 or MATH 021.

##### MATH 021 - QR: 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 or MATH 023.

##### MATH 022 - QR: Calculus II

Vectors and vector operations. 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 - QR: 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 040 - Geometry for Educators

An examination of geometric relationships using reasoning and proof. Topics include Euclidean, non-Euclidean and finite geometries, affine transformations, constructions, and spatial geometry. Provides background for future instruction in middle and high school geometry. Prerequisites: Three credits of Mathematics at MATH 015 or above, minimum Sophomore standing.

##### MATH 052 - QR:Fundamentals of Mathematics

Emphasizing proofs, fundamental mathematical concepts and techniques are investigated within the context of number theory and other topics. Prerequisite: MATH 021 or MATH 023. Credit not given for more than one of MATH 052, MATH 054 and CS 064.

##### MATH 121 - QR: Calculus III

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 or MATH 023.

##### MATH 122 - QR: Applied Linear Algebra

Vectors, matrices, linear independence, vector spaces (with focus on real n-space), determinants, linear transformations, eigenvalues and eigenvectors. Applications from engineering and the sciences incorporated through required computer assignments. Credit not given for both MATH 122 and MATH 124. Prerequisite: MATH 022 or MATH 023.

##### MATH 124 - QR: Linear Algebra

Vector spaces, linear independence, bases, linear transformations, matrices, determinants, change of basis characteristic equations, eigenvalues and eigenvectors, with applications. Emphasis on understanding and gaining facility with these concepts including proofs. Credit not given for both MATH 122 and MATH 124. Prerequisite: MATH 022 or MATH 023. Co-requisite: MATH 121 or MATH 052.

##### MATH 141 - QR:Real Anlys in One Variable

Principles of analysis in one variable. Heine-Borel and Bolzano-Weierstrass theorems; rigorous development of differential and integral calculus; infinite sequences and series of functions. May not be taken concurrently with or after MATH 241. Prerequisite: MATH 052 (preferred) or CS 064.

##### MATH 173 - QR: 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 (preferred) or CS 064.

##### MATH 183 - QR: Fndmntls of Financial Math

Students will be introduced to the basic ideas and algebraic structures of interest theory, time-value of money, annuities, loans, bonds, cash-flows and portfolios. Prerequisites: MATH 020, MATH 022 or MATH 023.

##### MATH 230 - QR:Ordinary Diffrntl Equation

Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: MATH 121. Corequisite: MATH 122 or MATH 124. Credit not granted for more than one of the courses MATH 230 or MATH 271.

##### MATH 237 - QR:Intro to Numerical Analysis

Error analysis, root-finding, interpolation, least squares, quadrature, linear equations, numerical solution of ordinary differential equations. Prerequisites: MATH 121; MATH 122 or MATH 124 or MATH 271; CS 020 or CS 021. Cross-listed with: CS 237.

##### MATH 241 - QR:Anyl in Several Real Vars I

Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 052 or Math 141 or MATH 151; MATH 121; MATH 122 or MATH 124.

##### MATH 251 - QR: Abstract Algebra I

Basic theory of groups, rings, fields, homomorphisms, and isomorphisms. Prerequisites: MATH 052 or MATH 141 or MATH 151; MATH 122 or MATH 124.

##### MATH 271 - QR:Adv Engineering Mathematics

Differential equations, Laplace transforms, matrix theory, and systems of differential equations; brief introduction to Fourier series. Examples from engineering and physical sciences. Credit not granted for both MATH 230 and MATH 271. No credit for Mathematics majors. Prerequisite: MATH 121.

##### MATH 273 - QR: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.

##### MATH 292 - Independent Study

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional classroom/laboratory setting under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

##### 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 295 - Special Topics

For advanced students in the indicated fields. Lectures, reports, and directed readings on advanced topics. 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 330 - Adv Ordinary Diff Equations

Linear and nonlinear systems, approximate solutions, existence, uniqueness, dependence on initial conditions, stability, asymptotic behavior, singularities, self-adjoint problems. Prerequisite: MATH 230.

##### MATH 333 - Thry Functions Real Variables

Lebesgue measure and integration theory, Monotone and Dominated Convergence Theorems and applications, product measures, basic theory of LP-spaces. Prerequisite: MATH 242.

##### MATH 354 - Algebraic Topology

Homotopy, Seifert-van Kampen Theorem; simplicial, singular, and Cech homology. Prerequisite: MATH 241 or MATH 353.

##### MATH 392 - Independent Study

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional classroom/laboratory setting under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

##### MATH 395 - Advanced Special Topics

Subject will vary from year to year. May be repeated for credit.