Algebra I, spring 2013
Algebra I, spring 2013
Lecturer
Scope
10 cu.
Type
Intermediate studies.
Prerequisites
High school mathematics knowledge, in particular, students are assumed to be familiar with mathematical induction, high school level combinatorics, algebraic thinking and symbolic reasoning.
Contents
The following topics will be covered by the lectures:
-Sets
-Relations and operations
-Elementary number theory
-Groups
-Rings
-Integral domains, division rings, fields
-Polynomials
Lectures
Weeks 3-8 and 11-18, Thursday 14-16 in room DK118 and Friday 10-12 in room CK108. Two hours of exercise classes per week.
Easter holiday 28.3.-3.4.
| contents |
|---|---|
week 3 (Jan 17-18) | sets |
week 4 (Jan 24-25) | relations, ordering |
week 5 (Jan 31-Feb 1) | functions, operations, divisibility |
week 6 (Feb 7-8) | greatest common divisor, congruences |
week 7 (Feb 14-15) | groups, subgroups |
week 8 (Feb 21-22) | cyclic groups, permutation groups |
week 11 (Mar 14-15) | cosets, normal subgroups |
week 12 (Mar 21-22) | quotient groups, group homomorphisms |
week 14 (Apr 4-5) | group homomorphisms, group isomorphisms |
week 15 (Apr 11-12) | rings, subrings, ideals |
week 16 (Apr 18-19) | quotient rings, ring homomorphisms and isomorphisms |
week 17 (Apr 25-26) | integral domains, division rings, fields |
week 18 (May 2-3) | polynomials |
Exams
There will be a midterm exam and a final exam.
| Date | Time | Room |
|---|---|---|---|
Midterm exam | February 28 (Thursday) | 14-16 | DK118 |
Final exam | May 10 (Friday) | 12-15 | C123 |
Notice: You may check the results of your exams and the exercise points on the noticeboard in the corridor of the 3rd floor.
Bibliography
This course is based on the textbook "Schaum's Outline of Abstract Algebra (2nd edition)", by Lloyd Jaisingh and Frank Ayres. A copy of the chapters of the book that are most relevant to the lectures can be found in a white folder in room C326.
Exercise groups
Group | Day | Time | Place | Instructor |
|---|---|---|---|---|
1. | Tuesday | 12-14 | CK108 | Kaisa Kangas |
Exercises
| Date of exercise class |
|---|---|
1. | Jan 22 |
2. | Jan 29 |
3. | Feb 5 |
4. | Feb 12 |
5. | Feb 19 |
6. | Mar 12 |
7. | Mar 19 |
8. | Mar 26 |
9. | Apr 9 |
10. | Apr 16 |
11. | Apr 23 |
12. | Apr 30 |
13. | No exercise class. |
Registration
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