MAT 312/AMS 351 Syllabus

Spring  2004

SUNY at Stony Brook
Department of Mathematics
SUNY at Stony Brook

This course is an introduction to number theory and to group theory, together with some applications to codes and coding theory.

Attendance: Attendance will be taken at each class and each recitation, during the period from February 9 to April 2. Anyone who misses lecture or recitation, shows up more than 10 minutes late, or leaves early, more than twice during this period, will have their final grade reduced by one unit (e.g. from a B- to a C+).

Homework: Problem solving is a fundamental part of the course, and you are supposed to work hard on the homework assignments in order to succeed in the course. You are encouraged to discuss homework problems with other students. However, each student must write up the homework individually, in his/her words rather than merely copying someone else's. You will be required to turn in your homework assignment in the Tuesday recitation, following the week in which it was assigned. For example, the problems for the week 1/26-1/30 are due on Tuesday, February 3, in recitation. Late homework will not be accepted. No exceptions.

Warning about Calculators and Solution Manuals: Calculators and solution manuals can be of great assistance in helping you to learn the material, if used properly. If used improperly, they can actually cause great damage. Here is the proper way to use them, when you want to work on a problem:

First do the problem yourself, without touching the calculator or solution manual.

Then use the calculator or solution manual to check your work.

If the calculator or solution manual reveal any surprises, find a logical explanation for them.

Calculator abuse: When you first see a problem, your first response should be to think, not to punch buttons on a calculator; otherwise you are suffering from calculator abuse. Students with this syndrome lose out in the following ways:

They do not develop self-confidence in their own abilities to work the problems, which is essential for mathematical growth.

Mathematics is outside them, not part of them. You may have noticed that, if you write down a phone number, you are less likely to remember it. Similarly, calculator abusers often find themselves with poor memories for mathematics.

They do not learn to calculate well. Many courses in physics and the other sciences require students to be able to follow, and do, very complicated calculations.

In-class quizzes: There will be 3 short (15 minute) quizzes during the semester. These quizzes will be held in class on Thursdays. The quizzes will be held on 2/12, 3/4 and 4/15.

Examinations: There will be two in-class midterm tests, on Thursday, February 19, and Thursday, March 25. The final exam will be on Tuesday, May 18 from 11:00 am to 1:30 pm. Make sure that you are available at these times, as there will be no make-ups for missed mid-term exams. Calculators, books, notes, etc. are not allowed during exams. If you miss an exam for an acceptable reason and provide an acceptable written excuse, the relevant mid-term will be dropped' in computing your course grade. A letter stating that you were seen by a doctor or other medical personnel is not an acceptable document. An acceptable document should state that it was reasonable/proper for you to seek medical attention and was medically necessary for you to miss the exam (the note/letter need not state anything beyond this point). Incomplete grades will be granted only if documented circumstances beyond your control prevent you from taking the final exam. You must have ID to be admitted to exams.

Grading: your course grade will be based on your examination performance, quizzes, and homework, weighted as follows:

Midterm I 20%
Midterm II 20% 
 Final Exam 40%
 Quizzes  10%
 Homework  10%

Help: The Math Learning Center (MLC) is in S-240A of the math building. This is a place where students can go for help with pre-calculus and calculus material and where study groups can meet. The MLC is open 11am-9pm Monday through Wednesday,   11am-6pm Thursday and 11am-2pm on Friday. For more information on the Math Learning Center, please click here.

DSS advisory: If you have a physical, psychiatric, medical, or learning disability that could adversely affect your ability to carry out assigned course work, we urge you to contact the staff in the Disabled Student Services office (DSS), Room 133 Humanities, 632-6748/TDD. DSS will review your situation and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential.

Schedule (tentative): The following is the basic syllabus, but not all topics in each section will get covered. Please read the relevant parts of the book before class.

Week Sections Notes Homework
1/26-1/30 1.1,1.2   1.1:3,5,6(ii), 1.2:1(i)(iii)(v)(use the method on page 13),2,3,6
2/2-2/6 1.3,1.4 Last day to add or drop a course without a W: February 6  1.2: 1(i)(iii)(v)(use the method on page 15);1.3: 4,6,7;1.4: 2(iv)(v)(show all your work), 8(show all your work). Also: Construct the addition and multiplication tables for Z5.
2/9-2/13 1.5,1.6 First quiz: Thursday, February 12, on everything up to and including page 44.  1.4: 5,6; 1.5: 1(i)(iii)(v), 2(ii), 5 (show all your work for these); 1.6: 2,6(i),12 (show all your work for these),3,7
2/16-2/20 review First midterm: Thursday, February 19, through section 1.6  1.6: 1(i)(iii) (show all your work for these), 8, 10, 11
2/23-2/27 2.1,2.2   2.1: 4, 7(i); 2.2: 2(ii)(iv)(v) (prove your assertions in this problem), 6, 11.
3/1-3/5 2.3 Second quiz: Thursday, March 4, on Chapter 2, up to and including page 98.  1.6: 5 (show all your work for this problem); 2.2: 8,9; 2.3: 2(d)(e),8, 9
3/8-3/12   4.1: 6 (show all your work); also write (123)(145)(162) as a product of disjoint cycles, also write (17)(16)(15)(14)(13)(12) as a product of disjoint cycles. Also find the inverses of these permutations. Make sure you know how to do problems 1 and 3, but don't hand these in, since the answers are in the back of the book. 4.2: 1,6,7 (show all your work for these problems), 4.
3/13-3/19 4.3   4.2: 10, 12, 13; 4.3: 1 (ii), (iv), (vi), (viii) (prove all your assertions carefully), 4, 8 (Answer these questions for #8: Why must c be the identity? What are the inverses of each of the elements (prove)? What is ff (prove)? Why can you now fill in the 1st, 3rd, 6th and 4th rows (prove)? What must the missing entries be (prove)?)
3/22-3/26 review Second midterm: Thursday, March 25, through section 4.3.
Last day to P/NC or drop a course: March 26
No homework due for next Tuesday. There will be a few problems assigned on Tuesday, due for next Thursday.
3/29-4/2 5.1 Both lectures this week will be on Tuesday (during the regular lecture time and during the recitation time). Recitation will be on Thursday, during the usual lecture time, in the Alliance Room.  Homework for Thursday, April 1: 5.1: 1, 2(iii)(iv) (show all work for these problems). Note: GL(n,R) is defined on page 183. The group operation for GL(n,R) is matrix multiplication. Homework for Tuesday, April 13: 5.1: Say G is a group, H is a subgroup of G, and x is an element of G. Show that the cyclic subgroup generated by x is contained in H if and only if x is in H. Then do #4, 6, 7, and 8. Show all your work for #8. When doing #8, recall that the order of an element of G_n must divide phi(n). (Sorry, I don't know how to make Greek letters on a webpage, I mean the Greek letter phi.)
4/5-4/9 Spring break; no classes in session 
4/12-4/16 5.2 Third quiz: Thursday, April 15, on section 5.1   5.2: 2,4,5; also understand #3, but don't hand it in, since the solution is in the back of the book. 5.3: 1 (prove your assertions), 3, 6.
4/19-4/23 5.3,4.4   5.3: 9 (in the hint, replace the phrase "any two elements" by "any two DIFFERENT elements", 10; 4.4: 1(ii)(iv) (prove your assertions), 3 (iv)(viii) (prove your assertions; Venn diagrams OK in part (iv)), 4, 5.
4/26-4/30 5.4   5.4: 3 (omit: "Show that f does not give a group code"), 5, 7 (omit: "Write down the two-column decoding table for f").
5/3-5/7 finish 5.4; review Last day of classes: May 7 
5/10-5/14 No classes Office hours: Tuesday 5/11 3:40-5:10, in 4-100B Math Building.
Thursday 5/13 2:30-4, in P-143 Math Building.
I may need to change these hours again; please check back at this webpage before coming!  
5/18   Final Exam Tuesday May 18, 11:00 am -1:30 pm., in the Alliance Room (our regular classroom). Covers the whole semester's work, with emphasis on material covered since the last midterm.