### Welcome to Tom Roby's Math 3600 homepage! (Winter 2002)

(last updated: 5 February 2002)

• The Prime Pages includes numbers, research, and records. The Curois page includes a prime that is illegal and other numerology.

### Class Information

COORDINATES: Lectures meet Tues/Thur. 6:00--7:50 (#10595 01) in Science South 302.

TEXTS: Burton, David M. Elementary Number Theory (4th Ed.) McGraw-Hill, 1998.

WEB RESOURCE: http://seki.csuhayward.edu/3600.html will be my Math 3600 homepage. It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the quarter.

The breakdown of points is:

Midterm Final Quizzes Homework Participation Portfolio
25% 25% 20% 10% 10% 10%

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

Please read the sections from the book listed before the date of the first lecture on that material. To encourage this, I will give credit for emailing me with questions and statements about the assigned reading (see "Participation" below).

HOMEWORK: Homework will be given for each lecture, and all the homework assigned the previous week will be due the following Thursday. Please attempt all the problems by Tuesday, so that you can ask any questions you may have in class then. Except for routine computations, you should always give reasons to support your work and explain what you're doing. Not all the problems will be graded, but only a subset. Please write your solutions carefully.

You do not need to hand in the answers to question I've included in [square brackets], but you should do them to prepare for...

QUIZZES: There will be a short quiz at the end of class each Tuesday on the previous week's material. I will try to be very specific about what you should know, often by handing sheets of practice problems. Generally they will be comparable to easier problems I assign and to the examples given in the reading.

MIDTERM: Thursday, 7 February 2002 in class, Rearrange your schedule NOW if necessary.

FINAL: Tuesday, 19 March 2002 in class, Rearrange your schedule NOW if necessary.

PARTICIPATION: I expect you to generally show up prepared for class and willing to work. Please read the section(s) to be covered by the day before class, and send email to 3600@seki.mcs.csuhayward.edu with at least five (5) statements or questions about the reading. This will help me focus classtime where you need it most. The questions can be anything from "What does the following sentence from the text mean..." to "Why is it important that the derivative measures the slope?" But please be as clear as possible about where the confusion is. Questions like "What's a prime number?" or "I don't understand the Euclidean Algorithm?" are less useful than "I don't understand why 1 is not considered a prime number" or "Here's my attempt to compute the gcd of 343 and 182 using Euclid's algorithm, but I seem to get the wrong answer...". If you don't have any questions, then come up with five sentences that describe the main points of the reading. Twelve such emails over the course of the quarter will count as full credit. (Note that you need not send email before Review or Test Days.)

PORTFOLIO: Please organize your work neatly in some sort of binder (e.g., 3-ring), so that you can refer to all your classnotes, homework assignments, quizzes, exams, handouts, and emails on the reading. I will check them at the end of the term. This will not only help you during the class, but also later when you want to recall something you learned but can't quite remember. It gives you a permanent record of what you learned even if you sell your book (which I don't recommend).

MATERIAL: Number theory is one of the most beautiful subjects in all of mathematics. People's fascination with number paterns predates history and makes up the bulk of the knowledge that Euclid wrote down in his Elements . It has many problems that are easy to understand but fiendishly difficult to solve. Perhaps the most famous of these is "Fermat's Last Theorem", whose solution by Andrew Wiles after 350 years is one of the highlights of 20th century mathematics.

Many topics in number theory connect with and extend the pre-college mathematics curriculum in interesting ways. We will spend a lot of time solving equations, but the rules will be somewhat different than you are used to. This should help you gain a deeper understanding of why certain procedures you have learned in school (and may teach again later) work.

Our goal is to cover most of chapters 1--9 of Burton, culminating in Gauss's law of quadratic reciprocity. Other topics as time permits. I will continue to update the schedule below as the term progresses.

3600 LECTURE AND ASSIGNMENT SCHEDULE
Section: Topic Lect. Date Homework problems Due
PS#0: Bases & Mods 1/8 T P1-P6 1/10 R
§ 2.1: Division Algorithm 1/10 R p. 19: 2,3,5,8 1/17
§ 2.2 Divisibility & GCD 1/10 R p.25: 2ad,3 1/17
§ 2.3: Euclid's Algorithm 1/15 T p.31: 1,2abc,4ac,8 1/24
§ 2.4: ax + by = c 1/15--17 p. 38:1,2,3,7; Week2: P1--P5 1/24
§ 3.1: Primes & FTA 1/24 R p.44: 4,5,7,11,12; p.50: 1-3 1/31
§ 3.2-3: Primes 1/29 T p.50: 12b,13a, 14; p. 59: 2,3 1/31
§ 4.1-2: Mods 1/31 R p.68: 2,4,8,9; 2/7
§ 4.3: Divisibility tests 1/31 R p.73: 6b,8,10,11 2/7
§ 4.4: CRT 1/31 R p. 82:1--5,8 2/7
REVIEW FOR MIDTERM 2/5 T (Attempt Practice Midterm by today) .
MIDTERM EXAM: 2/7 R
§ 5.1-3: Fermat's Thm. 2/12 p. 96:1,4ab,12 2/23
§ 5.4: Wilson's Thm. 2/12 p. 101: #3,4,9,10a 2/23
§ 6.1: Tau & Sigma 2/14 p.109: 2,3,7,9; 2/23
§ 7.1-2: Phi (Totient fn.) 2/19 p.133: 1,4ab,8,9a,11a 2/28
§ 7.3: Euler's Thm 2/19-21 p.138: 1a,4,7,9; 2/28
§ 8.1: Orders 2/21 p.161: 1a,3,12 2/28
§ 8.2: Generators 2/26 p.167: 2,3,4a,10; 3/7
§ 8.4: Indices 2/26-8 p.177:2bc,3ad,12,17 3/7
§ 9.1: Euler's Criterion 2/28 p.183: 1b,3,4,7 3/7
§ 9.2: Legendre Symbol 3/5 p.194: #1abc,2abc,5; 3/14
§ 9.3: Quadratic Reciprocity 3/5-7 p.200: #1abc,3,5,14 3/14
§ 9.4: Composite mods 3/7 p.205: #2ab,4 3/14
Spillover Day 3/12
ABC Conjecture 3/12
REVIEW DAY 3/14 R (Attempt Practice Final by today)
FINAL EXAM 3/19 T

### NEWS & NOTES

Here are pdf versions of the assignment that was given out on day 1 and the practice midterm.

What are the next two terms of the following sequence: 0, 1, 10, 2, 100, 11, 1000, 3, 20, 101, ---, --- ?