Modern Algebra Syllabus Fall 2007

Instructor: Dr. Ron Smith
Office: 120 Science
Phone Office: 784-5283
Phone Home: 784-6473

Office hours:

MWF 1-2:30 and TTh 9:30-12. For a 20 minute appointment, just sign up on the sheet outside my office door or call me. You do not need to sign up in advance, but if you will please sign when you come, the time will be reserved for you. Also, if someone is in the office and you are signed up, please make your presence known!

Materials:

The required text is Contemporary Abstract Algebra, Sixth edition, by Joseph A. Gallian. You will also need a programmable calculator. In class, we will be using the TI 83.

Scope:

This course will introduce the student to axiomatic algebra and its major structures, namely groups, rings, integral domains, and fields.

Objectives:

The student will

Be exposed to the basic structures of modern algebra--groups, rings, and fields.
Do computations in the context of specific examples of each of these structures.
Read and write proofs in the context of specific examples as well as in abstract settings.

Expecations for the student:

An algebra student will ...

Schedule at least 1 to 2 hours outside of class each day for studying algebra.
Read each section and work each example with paper and pencil.
Look at problems besides those assigned to discover why the author asked the question.
Prepare homework to hand in before class starts, including putting the name, class, homework number, and date on the outside.
Come to class on time every day and stay the entire period,
Have paper and pencil out on the desk at the beginning of class ready to work.
Sit beside a partner with whom you will discuss algebra during class.
Turn off electronic communication during class.
Rest and eat before or after, but not during, class.
Check all homework answers with the book and others, but write them up without copying.

Expectations of the Professor:

I promise to ...

Start and end class on time, or within 3 minutes of the scheduled time.
Be prepared for class every day.
Grade and return homework and exams within 2 class days.
Treat every student with respect.
Learn each student's name.
Answer every question in a respectful, truthful manner.
Post homework assignments with clear due dates.
Be available in my office during office hours, and give priority to anyone signed up.
Grade all exams myself, completely, equitably, and clearly. Daily homework will be graded by an assistant. Not every homework problem turned in will be graded.
Do my best to make every minute of every class a learning experience.

Grades:

You will need 87.5% for an A, 75% for a B, 62.5% for a C, and 50% for a D. Grades will be based on homework, exams, a notebook of proofs, and extra credit. Your final grade is the percentage of the total possible.

Notebook of Proofs (200) You are expected to polish your 10 best proofs and present them in a notebook. Each will receive up to 20 points according to the rubric that accompanies the syllabus. A first draft containing at least five proofs is due Friday, October 12. I will make comments only. A final draft containing at least 5 proofs is due Friday, October 26, and the final notebook is due Friday, December 7 (one week before final exams). The proofs may be based on work or problems done in class, but should be problems of your own choosing.
Homework (~300) Approximately 17 homework assignments will be given at 20 points apiece. Homework assignments will typically be due 2 class days from the day they are given. Written homework is due at the beginning of class on the due date. Late homework will not be accepted. Papers will be returned in the labeled rack beside my office door. After one week, unclaimed papers may be discarded. The two lowest homework scores will be ignored.
Exams (300) There are two midterm exams and a comprehensive final @ 100. Exams may be taken late provided arrangements are made prior to the exam. If, in the opinion of the instructor, missing an exam would not be unavoidable, 90% of the exam score will be recorded. The final exam will be in Room 114 Science at 10:00 Monday, December 17.

Food

If I bring food to the classroom, I will bring enough for everyone. I expect the same courtesy from students. Please do not eat personal snacks/meals in the classroom. If you have a medical condition requiring food, please make arrangements with me.

Electronics

The use of cell phones, pagers, or other electronic devices intended to facilitate communication between students must not be used during lectures or exams.

Incompletes

Incompletes for the course require signing a contract for making up work, and must be initiated by the student.

Academic Integrity:

Honesty is a prerequisite for being a competent person. If you copy solutions to problems from any source, you are required to acknowledge the source. This includes copying from friends or old homework/test files. Working together for inspiration and asking for hints is allowed on everything but exams. However, writeups must be your own. For more on this subject, see the college policy printed in the handbook.

Disabilities:

Any student who, because of a disabling condition, may require special arrangements in order to meet course requirements should contact the instructor as soon as possible to make necessary accommodations.

Tentative Course Outline:

Day	Date	Topic
1	9/5/07	Introduction
2	9/7/07	Logic
3	9/10/07	Div Algorithm; Greatest Common Divisor
4	9/12/07	Mod arithmetic; Check Digits
5	9/14/07	Induction
6	9/17/07	Equivalence Relations/Functions
7	9/19/07	1 Dihedral Groups
8	9/21/07	2 Definition of Group
9	9/24/07	Elementary Properties, Applications
10	9/26/07	3 Finite Groups; Subgroups
11	9/28/07	Examples
12	10/1/07	4 Cyclic Groups
13	10/3/07	Review
14	10/5/07	Exam 1. Chapters 0, 1, 2, 3, 4
15	10/8/07	5 Permutation Groups
16	10/10/07	Properties/Examples
17	10/12/07	Check Digit: Verhoeff.
18	10/15/07	6 Isomorphisms
19	10/17/07	Examples
20	10/19/07	Proofs
21	10/24/07	7 Cosets & Lagrange's theorem
22	10/26/07	Orbit/Stabilizer Examples
23	10/29/07	8. External Direct Products
24	10/31/07	Examples
25	11/2/07	Proofs
26	11/5/07	Review
27	11/7/07	Exam 2. Chapters 5, 6, 7, 8
28	11/9/07	The Proof
29	11/12/07	RSA Workshop
30	11/14/07	Continued
31	11/16/07	12 Rings
32	11/19/07	Prop & Examples
33	11/26/07	13 Integral Domains
34	11/28/07	Examples Integral Domains & Fields
35	11/30/07	16, 17 Polynomial Rings, Irreducibility tests
36	12/3/07	19 Vector Spaces
37	12/5/07	Continued
38	12/7/07	20 Extension Fields
39	12/10/07	23 Constructions
40	12/12/07	Review
41	12/14/07	Review
42	12/17/07	10:00 Final Exam

Guidelines for Homework:

Be neat!
- Use 8.5 x 11 loose leaf paper, one side only.
- Use pencil or a computer.
- Working problems on scratch paper first and recopying is a good strategy for catching mistakes as well as for being neat.
Fold papers together lengthwise to hand them in. Do not staple or tear, etc. The blank side of the paper is to be out. (See illustration below.)
On the outside at the top, provide the following information as shown in the illustration.
1. Name
2. Class(Modern Algebra)
3. Homework Number
4. Date that you turn it in
Clearly mark the section and number of each problem.
Include enough information on each problem so that the reader will know (a) what the book asked for, and (b) your response without referring to the book.
Respect the equal sign "=". Use this sign only when you mean that the expression on one side can be substituted into any statement containing the expression on the other side without changing the truth value of the statement.
Respect the equal sign "=". Use this sign only when you mean that the expression on one side can be substituted into any statement containing the expression on the other side without changing the truth value of the statement.
Avoid "Type" errors. Use the equal sign "=" to connect two expressions only when they stand for the same type of expression, e.g. two numbers, two functions, or two sets. Use implies "=>" to connect two statements when the truth of the first guarantees the truth of the second. Sometimes, you will need to use an explanatory phrase such as "Therefore", "Now we can see", or "From equations (1) and (2)... in order to express the relationship between two statements.
Write using complete sentences whenever possible.

Proof Assessment Rubric:

	5 Outstanding	4 Good	3 Marginal	1 Unsatisfactory
Logic	Logic is valid. Assumptions explicit. Contradictions clearly stated and shown. Compututation is appropriate, complete. Conclusion drawn. Result is general.	Logic is valid. Assumptions not explicit, or contradiction unclear. Computation is appropriate but not complete. Conclusion vague.	Main argument and computation are appropriate, but not necessarily correct. Question is partially answered.	Main argument invalid. Computation may be inappropriate, or question is not addressed.
Organization	Question is explicit. Ideas are linearly connected. No hand waving required. All variables named. Conclusion is clear and explicit.	Question is explicit. Ideas are linearly connected. Little hand waving required. Variables named. Conclusion is clear but may be implicit.	Question is clear. Ideas connected, but hand waving required. Variables may not be named. Conclusion missing or unclear.	Question not stated. Ideas not explicitly connected--loosely or randomly strung together, or there is no identifiable structure. Variables not named. Conclusion missing or unclear.
Problem Selection (If Applicable)	Challenging; requires significant intellectual resources; potential for a new or different understanding.	Requires modest intellectual work; complex computation, or some computation with interpretation	Requires modest intellectual work; computation with minimal interpretation.	Requires little or no intellectual work: e.g. Fill in the blank computation.
Citation	Source of problem explicit. Results used cited appropriately. Each hypothesis' use clearly indicated.	Source of problem explicit; Crucial result used but not cited. Each hypothesis use clearly indicated.	Source of problem explicit; Crucial result used but not cited. Some use of hypotheses not indicated.	Source of problem unclear, or no results cited. Use of hypotheses not clearly indicated.

Last Update: September 4, 2007
Ronald K. Smith
Graceland University
Lamoni, IA 50140
rsmith@graceland.edu