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.