# Frank Swenton

## Professor of Mathematics

fswenton@middlebury.edu

work802.443.3421

**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]*

##### CSCI 1099 - GUI Applications in C++/Qt

GUI Applications in C++*Qt
In this coding-intensive course, students will gain an understanding of the C++ language through the development of Graphical User Interface (GUI) applications within the cross-platform Qt development environment. We will begin with small, simple applications, culminating in application development projects of the studentsâ€™ choosing, all the while building our understanding of fundamental C++ concepts such as classes, templates, pointers, constructors/destructors, and ownership. (Approval required)*

**WTR**

Winter 2014

##### CSCI 1100 - Graphical Bots

##### FYSE 1380 - Information & Structure

**Information & Structure**

In this seminar we will study the relationship between raw information and the structures that are used to organize, translate, transmit, and make sense of it. We will consider information broadly, ranging from physical to virtual and from analog to digital, as it is acted upon by structures including physical, chemical, biological, physiological, and neurological phenomena, as well as by the human constructs of language, art, mathematics, engineering, and computer science. Along the way we will encounter the concepts of entropy, approximation, noise, and ambiguity that are inherent in the information that surrounds us in both our academics and daily lives. 3 hrs. sem. **CW**

Fall 2012

##### INTD 0500 - Independent Study

##### MATH 0121 - Calculus I

**Calculus I**

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. **DED**

Spring 2013, Fall 2013

##### 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

##### 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 2011, Spring 2012, Fall 2014

##### 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 2013

##### MATH 0423 - Topics in Analysis

**Topics in Analysis**

In this course we will study advanced topics in real analysis, starting from the fundamentals established in MA401. Topics may include: basic measure theory; Lebesgue measure on Euclidean space; the Lebesgue integral; total variation and absolute continuity; basic functional analysis; fractal measures. (MATH 0323 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2012

##### MATH 0432 - Elementary Topology

**Elementary Topology**

An introduction to the concepts of topology. Theory of sets, general topological spaces, topology of the real line, continuous functions and homomorphisms, compactness, connectedness, metric spaces, selected topics from the topology of Euclidean spaces including the Jordan curve theorem. (MATH 0122 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2011

##### 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 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016

##### MATH 0704 - Senior Seminar

**Senior Seminar**

Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.

Fall 2012