Math 103a course syllabus

 

Text:  Contemporary Abstract Algebra, 7th Edition, by Joseph A. Gallian

Other Reference: Try using Google whenever you forget or donÕt understand a definition/theorem, or just want to see more.

 

Math 103a is the first quarter of a two-quarter sequence in abstract algebra. The main topic of this quarter is the theory of groups, emphasizing examples and applications.  No previous knowledge of abstract algebra will be assumed, but students will be expected to be able to understand and write basic proofs, as covered in Math 109.   Compared with Math 100a, this course emphasizes applications and goes less deeply into theory.  If you are planning to go to graduate school in math, you should take Math 100ab instead of Math 103ab.

 

Math 109 is the main prerequisite for this course. (A little linear algebra wouldnÕt hurt, either.) In particular, students are expected to understand basic definitions and techniques such as:

Proof by contradiction

Types of functions, e.g. one –to-one, onto

Equivalence relations (very important)

Proof by induction

Basic set notation

If you are shaky on any of these notions or had difficulty with Math 109, now is the time to review!

 

Topics:  The course will cover the first 10 chapters of the text by Gallian, including Chapter 0.  Examples of groups will be very important throughout the course.  Such examples include symmetries (with the operation of composition), matrices (operation of multiplication), permutations (operation of composition), integers mod n (operation of addition mod n or, if n is prime, multiplication mod n).  Basic notions (subgroup, coset, cyclic group, etc.) and basic theorems will be covered.

 

Course Organization:  As in any math course, ŌNo pain, no gain,Ķ so there will be weekly problems sets (linked below).  There will also be exams:

Midterm 1: Monday, January 30 in class.  You may bring one 8 ½ by 11 sheet of paper written on one side only.

Midterm 2: Monday, February 27 in class

Final: Monday, March 19, 11:00 am to 2:00 pm

Grading is based on the following. Homework: 20%, Midterms (2): 40%, Final: 40%

Here is a link to the weekly problem sets currently due.