Instructor: T. Y. Lam
Textbook: Fraleigh, Abstract Algebra
In the first two years in college, a student of mathematics will have been exposed to concepts such as numbers, sets, mappings, permutations, symmetries, polynomials, vectors, matrices, and linear transformations. What are the common features of, and basic principles behind, all of these diverse concepts? The answer to this question lies in a course in Modern Abstract Algebra.
Math 113 is a junior-level introduction to the ideas and methods of abstract algebra. Starting with a review of the integers, mathematical induction and equivalence relations, the course guides the students through an axiomatic study of the "three pillars of algebra": Groups, Rings, and Fields. For many students, this will likely be the first course in which they are exposed to abstract thinking and serious proof-writing. To ease this transition, we'll back up our discussions with a copious use of concrete examples. Mid-way through the course, however, the students will hopefully begin to develop an appreciation for the power and beauty of the abstract approach, and feel comfortable in constructing algebraic proofs on their own. From there on, the whole field of modern algebra opens up for their enjoyment and pursuit.
The basic language of abstract algebra is now not only at the very foundations of mathematics, but is also widely and effectively used in physics, statistics, engineering, computer science and other technology fields. In view of this, Math 113 is as well-suited for students in these areas as for students in mathematics.