# Priscilla Bremser

## Nathan Beman Professor of Mathematics

bremser@middlebury.edu

work(802) 443-5555

Mon. 3:00 - 4:30, Tues. 2:30 - 4:00, Fri. 2:00 - 3:00, 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 0101 - Mathematical Problem-Solving ▹

**Mathematical Problem-Solving**

This course is designed primarily for students concurrently enrolled in MATH 121 or MATH 122 who would benefit from structured support to reinforce their mathematical backgrounds, and these students will be given priority at registration. We will emphasize problem-solving rather than a collection of procedures, using problems selected to strengthen students’ conceptual understanding of the material and their strategic competence. In an inquiry-based setting, students will practice and improve their algebra and trigonometry skills, with an emphasis on effective exposition of mathematical arguments.(This is a half credit course.)(Approval required.) 1.5 hrs. disc.

Fall 2022

##### MATH 0109 / EDST 0109 - Mathematics for Teachers

**Mathematics for Teachers**

What mathematical knowledge should elementary and secondary teachers have in the 21st century? Participants in this course will strengthen and deepen their own mathematical understanding in a student-centered workshop setting. We will investigate the number system, operations, algebraic thinking, measurement, data, and functions, and consider the attributes of quantitative literacy. We will also study recent research that describes specialized mathematical content knowledge for teaching. (Students looking for a course in elementary school teaching methods should consider EDST 0315 instead.) 3 hrs. lect. **DED**

Fall 2021

##### 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 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**

Spring 2018, Fall 2019, Fall 2020, Spring 2022

##### 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.

Spring 2018, Winter 2019, Winter 2020, Spring 2020, Winter 2021, Spring 2021, Winter 2022, Spring 2022, Winter 2023, Spring 2023

##### 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

Spring 2020, Fall 2022