Priscilla Bremser

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

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.

Fall 2021

DED

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 equivalent) 3 hrs. lect./disc.

Spring 2022

DED

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.

Spring 2023

DED

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 2021, Winter 2022, Spring 2022, Winter 2023, Spring 2023, Fall 2023, Winter 2024, Winter 2025

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 2022