# Frank Swenton

## Professor of Mathematics

fswenton@middlebury.edu

work(802) 443-3421

On leave academic year (2017-18)

on leave academic year

**Degrees, Specializations & Interests:**

B.S., The Ohio State University; Ph.D., Princeton University;

(Combinatorial Low-dimensional Topology)

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### INTD 0500 - Independent Study

**Independent Study**

Approval Required

Winter 2015, Winter 2016, Winter 2017, Winter 2018

##### MATH 0122 - Calculus II

**Calculus II**

A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. **DED**

Spring 2015, Spring 2016, Spring 2017

##### MATH 0200 - Linear Algebra ▹

**Linear Algebra**

Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2014, Fall 2016, Fall 2018

##### MATH 0223 - Multivariable Calculus

**Multivariable Calculus**

The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2015

##### MATH 0302 - Abstract Algebra I

**Abstract Algebra**

Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2015

##### MATH 0323 - Real Analysis

**Real Analysis**

An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc. **DED**

Fall 2015

##### MATH 0325 - Complex Analysis

**Complex Analysis**

An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2017

##### MATH 0500 - Advanced Study

**Advanced Study**

Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017, Spring 2017, Winter 2018