Tom Roby's Math 3240 Home Page (Fall 2010)|
Questions or Comments?
COORDINATES: Classes meet Tuesdays and Thursdays
2:00-3:15 in MSB
215. The registrar calls this Section 001, #14260.
PREREQUISITES: Math 2710 (Transition to
Theory: A Lively Introduction with Proofs, Applications, and Stories,
by James Pommersheim, Tim Marks,
and Erica Flapan
(Feb. 2010), ISBN=978-0-470-42413-1.
WEB RESOURCES: The homepage for this course is
SOFTWARE In trying to understand properties of integers, we
will often want to generate some data. Doing some computations by
hand is generally good for learning, but having software that can do
bigger computations or check your works is very useful. One free
source on the web
is WolframAlpha. For a
full-fledged progamming environment, check out the free open-source
computer algebra system
GRADING: Your grade will be based on one midterm exam, one
final exam, homework, &
The breakdown of points is:
| HW || Quizzes || Midterm || Final |
|20% ||20% || 25% ||35% |
MIDTERM EXAM: Will cover all the material to that point in
the term. It is currently scheduled for TUESDAY 26 October.
Please let me know immediately if you have a conflict with that date.
There are no makeup exams.
QUIZZES: Quizzes will be given roughly once every two
weeks, on the weeks when HW isn't due.
HOMEWORK: Homework will be done in groups of
roughly four students, with only one set of solutions handed in per
group. I've started a list
of HW Policies here,
currently a list of seven.
Many of the assignments will reference Handouts available
here, though I've also put some direct links in below:
Here are the assignments:
- hw1.pdf (#4(d) and due date revised)
- hw3.pdf (3(a) revised)
- hw4.pdf (due date corrected to
10/22; F_5 corrected in 3d)
- hw5.pdf (1(b) group initials corrected
You may find some homework problems to be
challenging, leading you to spend lots of time working on them and
sometimes get frustrated. This is natural. I encourage you to work
with other people in person or electronically. The
HuskyCT site for this class has
discussions boards you can use for this purpose (though I$may not check
them regularly). It's OK to get significant help from any resource, but
in the end, please write your own solution in your own words, even if
someone else in your group is the scribe for a given problem.
Copying someone else's work without credit is plagiarism and will be
dealt with according
policy. It also is a poor learning strategy.
CONTENT: Number Theory is a fascinating
subject. It's richness and beauty has captured the imagination of the
greatest mathematicians from antiquity to the current day. Once
thought to be some of the purest (read "most useless") branch of
mathematics, it is now one of the most important: Many of the most
important cryptographic systems, including some crucial to everyday
web commerce, are based on deep unsolved problems in number theory.
DISABILITIES: If you have a documented
disability and wish to discuss academic accommodations, or if you would
need assistance in the event of an emergency, please contact me as soon
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.
We will sometimes spend classtime doing things in
groups, presenting mathematics to one another, or having interactive
discussions. There will not be time for "cover" all material in a
lecture format so you will need to read and learn some topics on your
own from the book, web sources, (or otherwise).
SCHEDULE: The following is a the start of a tentative
schedule, that I will update throughout the semester.
3240 (STILL BEING REVISED) LECTURE AND ASSIGNMENT SCHEDULE |
| Prologue & Ch. 1
|| Overview of Number Theory
|| Read Ch. 2 on Mathematical Induction for Quiz
|| Divisibility in Z
|| QUIZ on Math Induction
|| Common Divisors; Euclid's algorithm
|| Bezout's relation and GCD
|| Quiz Rewrite due FRIDAY 9/10 3:00PM; HW#1 due MONDAY 9/13 3:00PM.
|| Computations in mods
|| Units, residues, divisibility tests in Z
|| Quiz #2 on divisibility, simple mod computations.
|| More divis. tests in Z; Congruences obstructions to
|| Factorization and primes in Z
|| HW#2 due Fri 9/24 @3:00PM
|| Unique Prime Factorization in Z and in R[t]
|| Linear systems of congruences
|| Quiz #3 on divisibility tests & primes
|| Congruences in R[t]; sums of two squares in
|| Powers in mods: Thms of Fermat & Euler
|| HW #3 due Fri 9/24 @3:00PM
|| Quiz #4
|| Orders and repeating decimals
|| Attempt Practice Midterm by 10/21R
|| Catchup & Review Day
|| HW4 due 22 Oct, 3PM
TUESDAY 26 OCTOBER 2010 MIDTERM EXAM |
|| RSA Encryption
|| Applications of CRT: Phi is multiplicative
|| When is -1 a square (mod p)? Gaussian Integers
|| HW5 due 5 Nov, 3PM
|| Arithmetic in Z[i]
|| More Z[i], sums of two squares
|| Squares in Z/p
|| Counting sums of two squares in Z/p
|| Take home Quiz 6 (due 11/30)
22-26 NOVEMBER THANKSGIVING BREAK, NO CLASSES |
|| Proof of QR via counting "points on spheres"
|| Finish proof of QR
|| HW6 due 3 Dec, 3PM
|| Jacobi symbols & Solovay-Strassen Test
|| Read Squares
Mod p, III, , § 4
|| More applications of Square Patterns
|| Read Square Applications
I & II
SUNDAY 12 DECEMBER 4:00PM: REVIEW SESSION IN MSB 215 (Attempt Review Problems by today)|
TUESDAY 14 DECEMBER 1:00PM: FINAL EXAM IN MSB 215
Conrad has an Expository
paper website with lots of useful handouts, some of which we will
use during the semester. (He also provided the most of the links below.)
A current list of known
Mersenne primes, ordered by the (prime) exponent. Click
here to join GIMPS
(the Great Internet Mersenne Prime Search).
A discussion of
Euclid's algorithm. There are links to other items from
number theory at the bottom of the page.
with Jean-Pierre Serre, one of the most prominent
number theorists of the 20-th century.
Here's an Online Mind
Reader. Can you figure out how it works?
NEWS & NOTES
Back to my home page.
a Practice Midterm (typos
Roby's Rules for Rewrites .
the wiki for Math
453 at UICC (Fall 2008), where the students filled in an outline
of webpages created by the instructor. Perhaps you'll find the
explanations here useful?
a Review & Practice Final