MATH 116 Basic Algebraic Structures (Spring 2006)

2005 - 06 Spring

MATH 116: Basic Algebraic Structures




People:


Section 01: Sergey Finashin (M-137)
Section 02: Turgut �nder (M-140)
Section 03: Ay�e Berkman (M-242)
All Sections: �zcan Kasal (M-232), P�nar U�urlu (M-232)

Exams:


Exam 1: 21 March 2006, Tuesday 17:40
Contents: 1.4, 1.5, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3 (Theorem 3.22 and the rest of section 3.3 are not included).
Exam 2: 2 May 2006, Tuesday 17:40
Contents: 3.4, 4.1, 4.4, 4.5, 5.1, 5.2, 6.2, 7.1, 7.2. (See above or below for the excluded parts.)
Final: 22 May 2006, Monday (Contents: Everything)


Grading:


Exam 1 - 30 points
Exam 2 - 30 points
Final - 40 points


Outline of the course:

Weeks Topics Sections
1 Binary operations 1.4, 1.5
2 Integers, divisibility, prime factors, greatest common divisor 2.1-2.4
3 Congruence of integers, congruence classes 2.5, 2.6
4 Groups, subgroups 3.1, 3.2
5 Subgroups, cyclic groups 3.2, 3.3
6 Cyclic groups, isomorphisms 3.3, 3.4
7 Permutation groups + Exam 1 4.1.
8 Normal subgroups, quotient groups 4.4*, 4.5**
9 Rings 5.1.
10 Ring isomorphisms, integral domains 5.2, 6.2***
11 Fields, the fields of real and complex numbers 5.2, 7.1, 7.2
12 Polynomials, divisibility 8.1, 8.2
13 GCD, factorization + Exam 2 8.2, 8.3
14 Zeros of a polynomial 8.4****

(*) 4.8, 4.9, 4.17, 4.19 and 4.20 will be skipped.
(**) Only 4.21 and 4.22.
(***) We will cover 6.7 and 6.8 (only in the context of isomorphisms).
(****) 8.30 - 8.33 will not be covered.

Exercises:

Solving exercises (NOT reading the solutions but really solving them) is an essential part of every math course and MATH 116 is no exception. Therefore to start studying for the exam the day before is not a good idea, because there is simply no time to work on all the exercises. We recommend you to solve the exercises of a section within the same week that the section is covered in the class. Good luck and have fun!

Suggested Problems:

Section 1.4: 1, 2a, 2f, 3, 4, 5, 6, 8, 9, 10e, 10k, 13

Section 1.5: 2a, 2b, 3d, 3e, 3i, 20, 22, 23, 24, 26

Section 2.1: 1-27

Section 2.3: 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 29

Section 2.4: 2a, 3c, 3j, 4a, 5, 7, 9, 10, 11, 13, 14, 15, 16, 19, 27

Section 2.5: 5, 6,16, 19, 20, 21, 22, 23a, 25, 26, , 27, 28

Section 2.6: 5a, 6e, 8c, 8f, 9, 10c, 16, 18, 22

Section 3.1: 1, 2, 4,5, 6, 7, 11, 15, 17, 23, 28, 31, 33, 45

Section 3.2: 2b, 2c, 3, 5a,6a, 10, 11, 13a, 14b, 17, 23, 24, 28, 35

Section 3.3: 7, 8, 9 a, 9b, 10a, 10b, 12, 14, 15, 18, 23, 24

Section 3.4: 1, 3, 6, 10, 11, 16, 17, 18, 20(a, b), 26, 28.

Section 4.1: 1(a, e, h), 2(a, b, f), 3, 4, 5, 6, 7, 8, 13, 14.

Section 4.4: 5, 6, 7, 8, 25, 26, 27, 30, 32, 35.

Section 4.5: 2, 4, 10, 15, 16.

Section 5.1: 1(a, b), 2(b, c), 5, 7(a, b, e, f), 8(c, d), 9, 10, 12, 16, 19, 21, 22, 24.

Section 5.2: 1(a, b), 2, 3, 5, 6, 8, 9, 10, 11, 12, 15(a, c), 18, 19.

Section 6.2: 1, 2, 3, 7, 8, 10, 12, 15 (Replace "homomorphism" with "isomorphism".), 19.

Section 7.1: 15, 16, 17, 18, 19, 20.

Section 7.2: 1, 4, 7, 11, 12, 13b, 14d, 16, 17, 18, 19, 20.

Section 8.1: 3e, 5, 7, 8, 9, 15 (replace epimorphism with isomorphism).

Section 8.2: 3, 6, 10, 14, 15, 16, 21.

Section 8.3: 1, 2, 3a, 5, 6, 7, 11 (Assume problem 9 to solve 11.).

Section 8.4: 1 (c,e), 2 (a,c), 4, 7, 15, 17a, 18, 19, 20, 21, 23, 24.


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Last updated on 11 May 2006.