Math 222 -- Course Info
Last modified: Wed May 2 22:01:35 CEST 2001
This web page will be updated during the course of the
semester
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Reader.
Exam Schedule
- Exam 1 - Wednesday, February 28, in class: Sample Exam, Some Sample Exam Solutions, Exam solutions.
- Exam 2 - Wednesday, April 25, in class: Sample Exam, Exam
solutions.
- Final Exam - Monday, May 7, 1:45 -- 3:45, in FITZ 356: Sample Final, A Sample Final
Solution,.
Course Handouts
Related Materials (not required)
Take-Home Quizzes
Course Assignments and Schedule
Warning: The future is
subject to change.
The dates the quizzes are given might
change.
The syllabus will be updated during the cousre of the
semester.
- WEEK 1 - January 17 - 19
Wed. - 1.1: Introduction, 1.1, Start Appendix F: Mathematical
Induction
HW -- 1.1: 4-7, 14,15,17 (16 is a bonus
problem)
Fri. - Appendix F: Mathematical Induction
HW -- Appendix F:
2,4,6,7,9,11,12,14
- WEEK 2 - January 22 - 26
Mon. - 2.1: Complex Numbers.
HW -- 2.1:
3,7,9,11,15,17,21,23,26,27 29,31,36
(there is a misprint in 27;
see errors in book above),
Wed. - 2.1: Complex Numbers and problems 31 and 36.
Fri. - 2.2: Complex Roots
HW - 2.2: 1, 13, 23, 27, 19, 21, 28,
5, 8, 15 (do them in that order)
NOTE: In #'s 19 and 21, it
should be assumed that ``w'' is a cube root of unity
Take-home
Quiz 1 Given Out - Due on Wednesday
- WEEK 3 - January 29 - February 2
Mon. 2.2: Finish Complex Roots.
Wed. - 2.3: Solvability by Radicals and Algebraic Expressions
HW
-- 2.3: 1-17 (odd)
Fri. - 2.4: Ruler and Compass Constructions
HW - 2.4: 6,9, 11,
12, 13, 16, 19,21,23
First Group Projects 2.4 # 1 and 5 assigned
- WEEK 4 - February 5 - February 9
Mon. - 2.4: Finish Ruler and Compass Constructions
Wed. - 2:5: Orders of roots of unity,
Take-home Quiz 2 Given Out
-- Due Monday
HW - 2.5: 3,5,9,11,13,15,18
Fri. - 3.1: The cubic Formula and 3.2: More on solvability by
radicals
Start 4.1: Modular Arithmetic
HW - 3.1: 1,5,10,11
- WEEK 5 - February 12 - February 16
Mon. - Answer questions on 2.4 and finish 4.1.
HW - 4.1: 3, 6 and
7 (only with respect to #3), 9, 11, 15, 21 (21 was assigned in class
but not on the web -- my error).
Wed. - 4.2: The Euclidean Algorithm and start Modular
Inverses
4.2: 1, 2, 3, 5, 21, 22, 23, 25.
Fri. 4.2: Finish Modular Inverses
HW - 4.2: 11, 13, 17, 7, 15
(try in the above order)
Next Group Projects 4.2: 24 and 26,
30.
- WEEK 6 - February 19 - February 23
Mon. - 5.1: Start the binomial theorem
Homework 5.1:
1,5,7,15.
Take-home Quiz 3 Given Out -- Due Friday
Wed. - 5.2: Fermat's Theorem
HW - 5.2: 1,3,7,9,12.
Take-home
Fri. - Finish 5.2: orders of roots. Hopefully a group project
HW
- 5.2: 17, 22, 25, 27. solutions
Practice
Exam available.
- WEEK 7 - February 26 - March 2
Mon. -- Some group projects, and review.
Wed. -- In class exam.
Fri. -- The handout on RSA (applied example), the handout on rings
and fields and start 6.1: Fields and Polynomials.
HW -- the
problem of the RSA handout, problems 1-5 on the ring handout and 6.1:
5,7,18,21.
- WEEK 8 - March 5 - March 9
Mon. The handout on rings and fields
HW problems 1-5 on the ring
handout and 6.1: 5,7,18,21.
Wed. -- 6.1: Polynomials and Start 6.2: Factorization of
Polynomials
HW -- Problem 6 on the ring handout and 6.1:
1,3,4,11,22.
Fri. -- Answer questions and tell bad jokes. NO Homework.
-
Spring Break
- WEEK 9 - March 19 - March 23
Mon. -- 6.2: Factorization of Polynomials
HW -- 6.2: 3,5,10,12
(Hint: see #10), 13
Take-home Quiz 4 Given Out -- Due
Friday
Wed. -- Finish 6.2 and Handout of irreducible polynomials in
Q[x]
HW -- 1-3 on the handout.
Fri. -- 6.3: The Euclidean Algorithm (again)
HW - 6.3: 21, 1, 3,
7, 8, 9 (hint look at the zeros of x^n-1).
- WEEK 10 -- March 26 - March 30
Mon. -- 7.1: Galois Fields
HW -- 7.1: 11,12,18-21,25.
New
group Projects 7.1: 26,29.
Wed. - 7.1 and 7.2: Orders in Galois Fields:
HW -- 7.1: 1,2,5
and 7.2: 4 (hint look at problem 7.1.5).
Fri. - 7.2 and 7.3: More on orders:
HW - 7.2: 1,3,10,11 and 7.3:
2,3,5 (hint see problem 7.1.2),
7 (hint look at problem 7.1.5),
13 (where is a typo x^(p^v) should be x^(p^v-1)).
Take-home Quiz
5 Given Out -- Due Wednesday.
- WEEK 11 - April 2 -- April 6
Mon. Finish Chapter 7.
Wed. - 8.2: Permutations
HW -- Handout of
problems for 8.2 Solutions
Fri. - 8.2: Permutations II
HW -- 8.2: 1, 3, 6, 8, 9, 11, 13, 22,
30, 31
- WEEK 12 - April 9 -- April 11
Mon. - 8.4: Transposition and parity
HW --
8.4:1,3,7,9,11,12,13
Wed. - Two group projects
Answer lots of questions
Take-home Quiz 6 Given Out -- Due Friday
Fri. Easter break. No class.
- WEEK 13 - April 16 -- April 20
Mon. - Easter break. No class
Wed. - 9.1 and 9.2: Definition of a group, subgroup, order and
examples.
HW -- 9.1: 1-6, 35 and 9.2:1-4,7
Fri. - 9.1 and 9.2: More examples of groups
HW -- 9.2: 28, 37 and
9.3: 17, 19, 22
- WEEK 14 - April 23 -- April 27
Mon. - Catch up and review.
Wed. - In class exam.
Fri. - 9.4: Subgroups and cosets
Group Project 9.5 #12 and
#28.
Homework - 9.4: 1, 2, 6, 11, 13, 15, 28, 31, 32, 33 (should
be 12 not 15), 36, 41, 56 (HW need not be turned in)
Last day to
turn in HW
- WEEK 15 - April 30 -- May 2
Mon. - 9.5: Cyclic groups
Homework - 9.5: (for the first 4
problems just decide if it is cyclic or not) 2, 3, 4, 10, 13, 15, 16,
17 (HW need not be turned in).
Wed. Last group project, catch up and review.
- Final Exam, Monday May 7, 1:45 -- 3:45, FITZ 356.
- Material not covered this year.
9.3: Isomorphisms of groups
HW -- 9.3: 2, 3 (hint: write
out the tables and compare) 9-16
Parts of 10.1: Definition of normal subgroups, Examples S_3 and S_5
and Prop 10.11.
Homework - 10.1: 7,9 (only the first part: is H
normal in G?), 17,22,36
Isomorphisms of rings, characteristic 0 vs p, examples x^3-2 and x^5-1
over the rationals, Galois's theorem about solvable by radicals, the
example x^5 - 10x +5 over the rationals (For interested parties, I
suggest reading the handout, Introduction to
Galois Groups).
Correct above here
Not correct below here