Back to Math Department Home Page Math 461, Abstract Algebra -- Spring 2005
Erol Barbut, Professor of Mathematics
Office: 420, Brink Hall (WSU: Neill 301)
email: ebarbut@uidaho.edu
Phone: (509) 335-4122 or 1-800-824-2889, press 0, and
then 335-4122
FAX: (208) 885-6165 or (208) 885-5843 (Math Department)
Address:
Department of
Mathematics
PO Box 441103
Moscow, ID 83844-1103
Office Hours: ThTh 10:30-11:30,3:00-4:00 (Pacific time).
Textbook: A First Course in Abstract Algebra, Sixth Ed.
John B. Fraleigh
Addison Wesley Longman, 1998
ISBN 0-201-33596-4
Prerequisites: Recommended prereq for Math 461: at least one of
the following: Math 215, 286, 330, 390. For description of these courses, please follow
the link to The University of Idaho Catalog.
Goals of the course: To learn about the power of mathematical abstraction, as applied to the study of finite groups and their applications. We will also gain experience in construction of proofs to theorems and making accurate definitions of mathematical concepts.
Software: Although not required for class, you are encouraged to play with the group theory features of Maple, which is available on the student machines.
For an interesting account of the history of Group Theory, click here. This link is to a page of a popular Web site on the history of mathematics.
Another interesting site is http://mathworld.wolfram.com/topics/FiniteGroups.html In this site you will find the definitions of many of the concepts we have seen plus a rich set of additional information well worth exploring.
Homework: There will be 10 problem sets. Each problem set will be worth 10 points. They are due at the lecture indicated by HW#N.
Tests: There will be three 50 minute exams. Each of these will be worth 100 points. In addition, there will be a two hour final exam. The final exam will be worth 200 points.
Grading: Your grade will be based on a total of 600 points. The letter grade you receive will be determined relative to the class average, with the class average counting as a B-.
Lecture Chapter Section Chapter
HW#1: 0.2: 12 a,c,e, 16,17; 0.4: 4, 10, 12, 30, 36, 38.
| 1 | Sets and Relations | 0.2 |
| 2 | Equivalence Relations | 0.2 |
| 3 | Complex and Matrix Algebra | 0.4 |
| 4 | HW#1 Binary Operations | 1.1 |
HW#2: 1.1: 2, 4, 18, 20, 24; 1.2: 23, 24, 27, 32 ; 1.3: 2, 4, 10, 28, 30, 34, 40.
| 5 | Isomorphic Binary Structures | 1.2 |
| 6 | Groups | 1.3 |
| 7 | HW#2 Subgroups | 1.4 |
HW#3: 1.4: 2, 4, 21, 27, 43, 47, 51, 54, 55; 1.5: 4, 6, 10, 27, 43, 44, 45, 46, 47, 53, 60.
| 8 | Cyclic Groups | 1.5 |
| 9 | Cyclic Groups | 1.5 |
| 10 | HW#3 Permutation Groups | 2.1 |
HW#4: 2.1: 4, 5, 12, 18, 20, 36. 42; 2.2: 2, 8, 16, 30.
| 11 | Cayley's Theorem | 2.1 |
| 12 | Review | |
| 13 | --------- Exam 1 -------- | |
| 14 | Orbits, Cycles, Alternating Groups | 2.2 |
| 15 | Cosets | 2.3 |
| 16 | HW#4 Lagrange's Theorem | 2.3 |
HW#5: 2.3: 5, 6, 7, 8. 12, 25, 36, 43.
| 17 | Direct Products | 2.4 |
| 18 | Finitely Generated Abelian Groups | 2.4 |
| 19 | HW#5 Finitely Gen. Abelian Groups | 2.4 |
HW#6: 2.4: 1. 3, 4, 6, 8, 17, 22, 24, 43, 49.
| 20 | Binary Linear Codes | 2.5 |
| 21 | Parity Check Matrix Decoding | 2.5 |
| 22 | HW#6 Coset Decoding | 2.5 |
| 23 | Homomorphisms | 3.1 |
| 24 | " " | 3.1 |
| 25 | Factor Groups | 3.2 |
| 26 | HW#7 Fundamental Homomorphism Th. | 3.2 |
HW#8: 3.1: 2, 3, 6, 8, 12, 16, 22, 24, 28, 45; 3.2: 2, 5, 6, 12, 24, 30, 31, 35, 38.
| 27 | Review | |
| 28 | --------- Exam 2 -------- | |
| 29 | Group Action on a Set | 3.5 |
| 30 | Orbits | 3.5 |
| 31 | Applications of G-Sets to Counting | 3.6 |
| 32 | HW#8 " " " | 3.6 |
HW#9: 3.5: 1, 2, 3, 13; 3.6: 1, 3, 4, 5, 7.
| 33 | Isomorphism Theorems | 4.1 |
| 34 | " " " | 4.1 |
| 35 | " " " | 4.1 |
| 36 | p-Groups | 4.2 |
| 37 | HW#9 " " | 4.2 |
HW#10: 4.2: 2, 3, 11, 13, 17.
| 38 | Sylow Theorems | 4.2 | |
| 39 | Review | ||
| 40 | ---------- Exam 3 -------- | ||
| 41 | HW#10 Sylow Theorems | 4.3 | |
| 42 | " " | 4.3 | |
| 43 | Applications of the Sylow Theory | 4.3 | |
| 44 | R e v i e w | ||
Back to Math Department Home Page