# Frank Swenton

## Professor of Mathematics

fswenton@middlebury.edu

work(802) 443-3421

Fall 2019: Monday, Wednesday, Thursday 2:00 - 4:15 PM, and by appointment

Warner Hall 504

**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]*

##### FYSE 1223 - Communication:Analog & Digital ▹

**Communication: From Analog to Digital and Back Again**

In this seminar we will undertake an interdisciplinary study of the nearly ubiquitous process of communicationâ€”that is, the transmission and receipt of information. This will run the gamut from oral to written to digital language; from humans to cells to subatomic particles; from hearing to sight to touch; and from its first origins into the modern day. Throughout, we will observe the interplay between the analog world in which we physically live and the increasingly digital world that humanity has created through modern technology, and we will attempt to gain a larger perspective on the transformation that has taken place, along with its effects. 3 hrs sem. **CW**

Fall 2020

##### INTD 0500 - Independent Study

**Independent Study**

Approval Required

Winter 2017, Winter 2018, Winter 2019, Winter 2020

##### 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 2017, Spring 2019, Fall 2019

##### 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 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 2019, Spring 2020

##### 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**

Spring 2020

##### 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, Spring 2019

##### 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.

Fall 2016, Winter 2017, Spring 2017, Winter 2018, Winter 2019, Spring 2019, Winter 2020, Spring 2020, Spring 2021

##### MATH 0732 - Topology Seminar ▹

**Topology Seminar**

Topology is the rigorous mathematical study of shape at the most fundamental levelâ€”for example, the shapes of the letters I and U are topologically equivalent, but neither is equivalent to that of the letter O. In this senior seminar students will encounter topological objects such as manifolds, braids, and knots, studying them using tools ranging from combinatorial to geometric to algebraic. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs sem.

Fall 2020