MATH 430-01 Applied Algebra (Ellis) -- IIT Applied Mathematics

MATH 430-01 Applied Algebra (Ellis) Spring 2011

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Instructor: Robert Ellis	Office: E1 105c	Email:	Office phone 567-5336
Lectures	MW 11:25am-12:40pm	E1 122
Office Hours	T 12:45pm-1:45pm (430 priority) R 2:35pm-3:35pm (230 priority)			Appointments and emailed questions are welcome
Textbook	Gallian, Contemporary Abstract Algebra, 7th edition
Resources tailored for the textbook	Text-based and online Flashcards, advice for learning proofs, advice for learning abstract algebra, overview slides for Chapters 1-6, computer exercise software for 7^th edition

First day handout (pdf) (course contract & exam schedule)

Exams
Spr `11	Exam 1	Exam 2		Final
Date	W 2/16 exam key	W 4/6 see Blackboard		T 5/3 8-10am
Practice Exams
Term	Exam 1	Exam 2	Exam 3	Final
Fall `08	exam, key	exam, key		exam key
Fall `06	exam, key	key	exam, key	exam, key
Example Reading Quizzes See Fall `08 course page

Homework Due Dates
Homework cover sheet (use this for each homework or hand-write something similar).

Due

Random Quiz Reading¹ (flashcards help prepare)

Daily Activities³

Group Homework²

T 5/3

Final Exam

Cumulative but with somewhat more weight on material since Exam 2. Best starting place to study is previous exams; also review group activities for a source of examples. Be familiar with all major results in Chapters 0-11.

Final Exam

There will be 3 types of proofs: (1) transforming one definition into another (e.g., Ex2#13); (2) those needing definitions/citing a major theorem plus one minor observation (e.g., Ex2#12); and (3) those requiring some serious thought (e.g., Ex2#15). Think of these proofs as C, B, and A-level, respectively.

W 4/27

No quiz.

Chapter 11 finite Abelian groups exercise; highlights of rings, integral domains, and fields

T 4/26

Proofs practice with Cory@ARC 5:30-7:00pm

Focus material:

GA 10A Question 3; GA 10B Questions 1-3; HW 11 proofs; Exam 2 proofs; Final `08 proofs; Final `06 proofs

M 4/25

Chapter 10, last page of GA10B

Chapter 11, pp.218-222

Quiz 10C/11A

GA 10B: Group Homomorphisms

Chapter 10 Theorems

HW 12

Chapter 10: 4, 6, 12 (Hint: cite theorem(s)), 18, 22 (cf. Ch9#37,65), 30, 32, 48, 56

W 4/20

Chapter 10

Exam 1 rewrite due (Do not alter original exam. Non-collaborative, no ARC, web, etc.; text, notes &hw ok.)

Quiz 10B: Chapter 10

GA 10B: Group Homomorphisms

Chapter 10 Theorems (10.1,10.2)

T 4/19

Proofs practice with Cory@ARC

Focus material:

GA 9C Question 4; Cauchy`s Theorem for Abelian groups (Thm. 9.5); Chapter 9 Exercises 65, 37; HW 10 proofs

M 4/18

New groups starting 4/18, after submission of HW 11

Chapter 10

New groups starting 4/18, after submission of HW 11

Quiz 10A: Chapter 10

GA 10A: Group Homomorphisms

New groups starting 4/18, after submission of HW 11

HW 11

Chapter 9: 4, 6, 10, 16, 24, 32, 46, 54, 56, 64

W 4/13

The quiz will come directly from GA 9C

Quiz 9C: Chapter 9

GA 9C: Normal Subgroups and Factor Groups (due M 4/18)

T 4/12

Proofs practice with Cory@ARC

Focus material:

GA 9A and 9B proofs, HW 10 proofs

M 4/11

The quiz will come directly from the second half of GA 9A

GA 9A: Normal Subgroups and Factor Groups (due W 4/13)

GA 9B: Normal Subgroups and Factor Groups (due W 4/13)

Chapter 9 Theorems

2^nd attempt on all group activities through 5C are due at 11:25am

W 4/6

Exam 2 Chapters 4-7 & beginning of Chapter 8 (cf. HW 9)

T 4/5

Proofs practice with Cory@ARC

Focus material:

Chapter 5 (Permutations): GA5A, GA5B, GA5C, Chapter 5 Theorems

Chapter 6 (Isomorphisms): automorphisms and inner automorphisms, esp. pp3-4 of GA6B, and pp4-6 of Ch6 Theorems

M 4/4

Chapter 9

Quiz 9B: Chapter 9

GA 9A: Normal Subgroups and Factor Groups (due W 4/13)

Chapter 9 Theorems

HW 10

Chapter 8:

12, 18, 24 (i.e., prove), 34, 44, 58, 62, 64

W 3/30

Chapter 8 and

pp.178-180 of Chapter 9

Quiz 8B/9A: Chapter 8/9

GA 8B: External Direct Products (due M 4/4)

GA 9A: Normal Subgroups and Factor Groups

Chapter 9 Theorems

T 3/29

Proofs practice with Cory@ARC
Focus material: GA 7B questions (2), (5); GA 8A question (6); HW 7-8 proofs

HW 9 (Due 5pm, mailbox).

Chapter 7:

6, 8	Prove that the cosets you list are distinct

12, 14, 18, 24, 34, 48

Chapter 8: 4, 6

M 3/28

Chapter 8

Quiz 8A: Chapter 8

GA 8A: External Direct Products (due W 3/30)

GA 8B: External Direct Products (due M 4/4)

Chapter 8 Theorems

W 3/23

Chapter 7

Quiz 7B: Chapter 7

GA 7B: Cosets&Lagrange`s Thm (due M 3/28)

Chapter 7 Theorems

Truncated Icosohedron

T 3/22

Proofs practice with Cory@ARC
Focus material: GA 6B question (9), page 6 of Ch6 Theorems, and HW 6 proofs.

M 3/21

Chapter 7

Quiz 7A: Chapter 7

GA 7A: Cosets&Lagrange`s Thm (due W 3/23)

GA 7B: Cosets&Lagrange`s Thm

HW 8. Show work, write complete explanations, etc.
Chapter 6: 2, 10, 12, 24, 28, 32, 38, 40, 44

Chapter 6 Computer Exercise: 1
(Include data collected. Answer all Make a conjecture prompts with separate responses.

W 3/9

No reading quiz

GA 6B: Isomorphisms

Ch6: Cayley`s Theorem

Ch6 Theorems

T 3/8

Proofs practice with Cory@ARC
Focus material: GA 6A (5)-(7), HW 6 proofs.

M 3/7

Chapter 6

Exam 1 rewrite due (Do not alter original exam. Non-collaborative, no ARC, web, etc.; text, notes &hw ok.)

Quiz 6B: Chapter 6

GA 6A: Isomorphisms (due M 3/14)

GA 6B: Isomorphisms

Ch6: Cayley`s Theorem

HW 7. Show work, write complete explanations, etc.

Chapter 5: 8, 14, 24, 36, 40, 46, 50, 52, 54

Chapter 5 Computer Exercises: 1

(include data collected)

W 3/2

Chapter 6 through p127

Quiz 6A: Chapter 6

GA 5C: Permutation Groups (Due M 3/7)

Chapter 5 Theorems

GA 6A: Isomorphisms

T 3/1

Proofs practice with Cory@ARC
Focus material: GA 4B, HW 5 proofs.

M 2/28

Chapter 5

Quiz 5B: Chapter 5

Build a tetrahedron

GA 5B: Permutation Groups (Due W 3/2)

GA 5C: Permutation Groups (Due M 3/7)

Chapter 5 Theorems

HW 6.

Chapter 4: 12, 14, 24, 28, 36, 40, 44, 52, 54, 62
Chapter 4 Computer Exercises: 1, 2 (include data collected)

W 2/23

Chapter 5

Quiz 5A: Chapter 5

GA4C: Cyclic groups (Due M 2/28)

GA5A: Permutation groups (Due W 3/2)

Chapter 4 Theorems

T 2/22 5:30-7

Proofs practice with Cory@ARC
Focus material: GA 4B, HW 4 proofs.

M 2/21

Chapter 4

Quiz 4C: Chapter 4

GA4B: Cyclic groups (Due W 2/23)

Chapter 4 Theorems

HW 5.

Chapter 3: 12, 14, 30, 44, 50, 58, 62

W 2/16

Exam 1 Chapters 0-3

M 2/14

Chapter 4

Quiz 4B: Chapter 4

GA4A: Cyclic groups (Due M 2/21)

W 2/9

Chapter 4

Quiz 3C/4A: Chapter 4

HW 4. Chapter 3: 4, 8, 18, 52

Ch 3 Computer Exercises: 3, 4

M 2/7

Chapter 3

Quiz 3B: Chapter 3

GA3B: Subgroups (Due M 2/14)

F 2/4

Due 3:15pm

HW 3. Chapter 2: 6, 8, 10, 12, 14, 18, 32, 34 (assume 31-32)
Ch 2 Computer Exercises: 2, 4

W 2/2

Blizzard

shoveling snow

decategorize snowflakes

M 1/31

Chapter 3

Quiz 3A: Chapter 3

GA 3A: Subgroups (Due M 2/14)

W 1/26

Chapter 2 (Groups)

Read first 2 pages of Chapter 3

Quiz 2B: Chapter 2

GA2B: Groups (Due M 1/31)

HW 2. Chapter 1: 6, 8, 14, 16
Problem A: Give an example of a glide reflection, composed of a nontrivial reflection and nontrivial translation, that is a plane symmetry of a bounded figure (such as the square). Label the operations and appropriate distances in a diagram, and give the equivalent reflection.
Problem B: Describe how to generate an infinite hexagonal lattice from a single hexagon and plane symmetries. Then describe the set of plane symmetries of the lattice.

M 1/24

Chapter 2 (Groups)

Quiz 2A: Chapter 2

GA2: Groups (due M 1/31)

W 1/19

Chapter 1 (Intro to Groups)
Flashcards for Chapter 0

Quiz 1: Chapter 1

GA1: Symmetry (due M 1/24)

Chapter 1 Plane Symmetries

HW 1. Chapter 0. 8, 10, 12, 14, 16, 24, 26, 32, 52;
Prove Theorem 0.7 parts 2&3;
Computer Exercises 2, 6 (give a clear, written solution)

W 1/12

Chapter 0 (Preliminaries)

Quiz 0: Chapter 0

See Blackboard for in-class proofs. Compare techniques to Joe Gallian`s excellent advice for learning proofs.

GA 0: Divisors (due W 1/19)

Chapter 0 Theorems and Proofs

1. Each day starting W 1/12 except for exam days the quiz dice will be rolled. On a 2, 3, 4, 5, or 6 a group reading quiz will be given covering the reading due that day.

2. Warning: Use of text editions other than the 7^th edition is at your own risk. (Full credit requires clear proofs, showing steps, clear explanation, etc.)
See the first day handout for instructions on working and submitting group homework.

3. Group activity worksheets are due for a participation grade. They will be graded for correctness, and you will have one chance for resubmitting incorrect work.

Page maintained by Robert Ellis / http://math.iit.edu/~rellis/