# Priscilla Bremser

## Nathan Beman Professor of Mathematics

bremser@middlebury.edu

work(802) 443-5555

Spring 2020: Monday 2:00 - 4:00, Thursday 3:00 - 4:00, Friday 1:30 - 2:30, and by appointment.

Axinn 301

**Degrees, Specializations & Interests:**

A.B., Smith College; M.A., Ph.D., Johns Hopkins University. Research in Number Theory, Finite Fields, and Mathematics Education.

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

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

##### FYSE 1212 - Mathematics For All

**Mathematics for All**

What kinds of mathematical knowledge are necessary for full participation in contemporary democratic society? How well, and how fairly, do our schools educate students in quantitative skills and reasoning? By what measures might we judge success? We will learn about different approaches to mathematics education in light of these questions. Readings will include selections from *Mathematics for Democracy*: *The Case for Quantitative Literacy* (L.A. Steen, Editor), as well as recent articles by education researchers. To connect theory and actual practice, students in this class will conduct a service-learning project in a local school. All are welcome, regardless of mathematical background. 3 hrs. sem. **CW**

Fall 2019

##### 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 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**

Fall 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 2017, Spring 2018, Fall 2019, Fall 2020

##### MATH 0241 - Elementary Number Theory

**Elementary Number Theory**

Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver) **DED**

Fall 2016

##### 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**

Fall 2020

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

##### MATH 0703 - Finite Fields Seminar

**Finite Fields Seminar**

This course is a tutorial in the theory and applications of finite fields, which lie in the intersection of algebra and number theory. Working in small groups, students will study the fundamental structure and properties of finite fields (also known as Galois fields). They will then work independently, exploring applications in cryptography, coding theory, or other areas. 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 0241 or MATH 0302; Approval required) 3 hrs. Sem

Fall 2017, Spring 2020

##### 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.

Spring 2017