Math 117: General Course Outline
Catalog Description
    117. Algebra for Applications. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 110A. Integers, congruences; fields, applications of finite fields; polynomials; permutations, introduction to groups.
Textbook
    L. Childs, A Concrete Introduction to Higher Algebra, 3rd Ed., Springer-Verlag.
Reviews & Exams
    The following schedule is based on 26 lectures. The remaining three classroom meetings are for midterm exams and a review.
Schedule of Lectures

Lecture
Section
Topics
1-2
Ch 2 A--D
Induction and binomial theorem
3
Ch 3 A
Division theorem, bases
4-5
Ch 3 B--D; Ch 4 A, B
Euclidean algorithm, Bezout's identity, unique factorization
6-9
Ch 5; Ch 6
Congruences, congruence classes, and error-correcting codes
10-11
Ch 7
Rings and fields
12-13
Ch 9 A--D
Theorems of Euler and Fermat
14
Ch 10 B
RSA codes
15-16
Ch 12 A, B
Chinese remainder theorem
17
Ch 12 C
Application of Chinese remainder theorem to RSA cryptography
18-20
Ch 13, ch 14
Polynomials, unique factorization
21
Ch 15 D, F, C
Complex numbers, fundamental theorem of algebra
22-23
Ch 17 A, B
Congruences modulo a polynomial and Chinese remainder theorem
24-26
Ch 18
Fast polynomial multiplication, fast Fourier transform
Comments

Note: The book contains a wealth of interesting topics (e.g. Sturm's theorem, group theory), which can be substituted for material in the last five lectures at the instructor's discretion.

Outline update: D. Gieseker, 1/97
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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