Alexander Diesl
Professor of Mathematics
Noncommutative ring theorist, sees mathematics as a central part of a well-rounded liberal arts education.
My research concerns a type of abstract algebraic structure known as a ring. A ring is a set of elements (familiar examples include such things as numbers, polynomials, matrices, or functions) endowed with both an addition operation and a multiplication operation. My current research interests involve classification questions and the visualization of algebraic structures.
At Wellesley, I have taught courses at the introductory, intermediate, and advanced levels. I view mathematics very much as a liberal art, and I strive to adhere to this philosophy in every class that I teach. During the summer of 2010, I advised three Wellesley students in a research project concerning zero-divisor graphs of rings.
I am also interested in the future of mathematics education at the secondary level in the United States.
In my spare time, I am often found playing with my kids.
Education
- B.A., Johns Hopkins University
- M.A., Johns Hopkins University
- Ph.D., University of California-Berkeley
Current and upcoming courses
Abstract Algebra
MATH305
In this course, students examine the structural similarities between familiar mathematical objects such as number systems, matrix sets, function spaces, general vector spaces, and mod n arithmetic. Topics include groups, rings, fields, homomorphisms, normal subgroups, quotient spaces, isomorphism theorems, divisibility, and factorization. Many concepts generalize number theoretic notions such as Fermat's little theorem and the Euclidean algorithm. Optional subjects include group actions and applications to combinatorics.
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Number Theory
MATH223
Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.