Frank Swenton
Professor of Mathematics

- Office
- 75 Shannon 214
- Tel
- (802) 443-3421
- fswenton@middlebury.edu
- Office Hours
- CSCI Fall 2021: Tuesday, Thursday 9:30 - 12:15 PM, and by appointment
- Additional Programs
- Computer Science Mathematics
Courses Taught
CSCI 0200
Math Foundations of Computing
Course Description
Mathematical Foundations of Computing
In this course we will provide an introduction to the mathematical foundations of computer science, with an emphasis on formal reasoning. Topics will include propositional and predicate logic, sets, functions, and relations; basic number theory; mathematical induction and other proof methods; combinatorics, probability, and recurrence relations; graph theory; and models of computation. (CSCI 0145 or CSCI 0150) (Juniors and Seniors by waiver) 3 hrs. lect./lab
Terms Taught
Requirements
CSCI 0301
Current
Theory of Computation
Course Description
Theory of Computation
This course explores the nature of computation and what it means to compute. We study important models of computation (finite automata, push-down automata, and Turing machines) and investigate their fundamental computational power. We examine various problems and try to determine the computational power needed to solve them. Topics include deterministic versus non-deterministic computation, and a theoretical basis for the study of NP-completeness. (CSCI 0200 and CSCI 0201) 3 hrs. lect./disc.
Terms Taught
Requirements
CSCI 0318
OOP & GUI Application Dev
Course Description
Object-Oriented Programming and GUI Application Development
In this coding-intensive course students will deepen their understanding of data structures, algorithms, and object-oriented programming concepts through development of GUI (Graphical User Interface) applications. After a brief introduction to C++ and our development environment, Qt, we will immerse ourselves in them through work on an array of application development projects. Along the way, we will be introduced to a number of software development principles and build an understanding of fundamental object-oriented concepts in C++, including classes and inheritance, templates, pointers, constructors/destructors, and ownership. (CSCI 0202 or by waiver) 3 hrs lect./disc.
Terms Taught
Requirements
FYSE 1223
Communication:Analog & Digital
Course Description
Communication: From Analog to Digital and Back Again
In this seminar we will undertake an interdisciplinary study of the nearly ubiquitous process of communication—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.
Terms Taught
Requirements
INTD 0500
Independent Study
Course Description
Independent Study
Approval Required
Terms Taught
MATH 0122
Calculus II
Course Description
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. 4 hrs. lect.
Terms Taught
Requirements
MATH 0200
Linear Algebra
Course Description
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.
Terms Taught
Requirements
MATH 0223
Multivariable Calculus
Course Description
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.
Terms Taught
Requirements
MATH 0323
Real Analysis
Course Description
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.
Terms Taught
Requirements
MATH 0325
Complex Analysis
Course Description
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.
Terms Taught
Requirements
MATH 0500
Current
Upcoming
Advanced Study
Course Description
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.
Terms Taught
MATH 0732
Topology Seminar
Course Description
Topology Seminar
Topology is the rigorous mathematical study of shape at the most fundamental level—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.
Terms Taught