Spring 2015 MATH H113 001 LEC

Honors Introduction to Abstract Algebra
Units/CreditFinal Exam GroupEnrollment
46: TUESDAY, MAY 12, 2015 1130-230PLimit:36 Enrolled:22 Waitlist:0 Avail Seats:14 [on 03/22/15]
Additional Information: 

Prerequisites: 54 or a course with equivalent linear algebra content.

Syllabus: Algebra and “algebraic thinking” permeates all of the modern Mathematics and now is also deeply affecting Mathematical Physics. The course is designed to be a broad and intensive introduction into “algebraic thinking”. The first weeks will be spent on introducing the student to the language of structures, explaining what constitutes a “structure”, and illustrating the corresponding concepts with a number of key examples. From the very beginning we will be building material to illustrate the concepts of a category and a functor. To make the student familiar with the language of categories is one of the aims of this course.

In the second part of the course I will consider a few case studies, demonstrating some fascinating applications of Algebra (for example the proof of a famous result in Logic to the effect that “every tautology has a proof’) and the techniques used in the classification of finite groups (we shall prove, for example, that a nonabelian simple group of order ≤ 60 is canonically isomorphic to the alternating group on a set of 5 elements naturally associated with the group).

Along the way I will be constantly “opening windows” and leading students into various “wings” of the edifice of modern Mathematics. After successfully completing the course, the student will have ample opportunities to develop in various directions.

This course is aimed at an enthusiastic, ambitious and a diligent student. It is expected that the students enrolled in the class will be actively following the lectures. There is no text that could replace them.

Office: 995 Evans Hall

Office Hours: TBA

Required Text: no required text; lectures are a primary source, various sets of notes distributed by the instructor — the secondary source for the material covered in class

Recommended Reading: Mac Lane, Birkhoff, “Algebra” (an excellent text for self study written by two great masters)

Grading: TBA

Homework: assigned and collected regularly throughout the semester; your course grad will directly reflect the quality of your homework.

Course Webpage: TBA