This is a 1-semester course for folks interested in Mathematical Cryptography (major topic) and other aspects of Coding: Data Compression and (time permitting) Error-correcting codes. We may also cover one example of an Isomorphism code.
It is accessible to anyone who has Sets&Logic knowledge, whether or not you've take that course. I would like you to know:
What a prime number is, and What mathematical induction is and What an equivalence relation is. Also helpful is how to “add two numbers mod N”, and what the Euler phi function is.
Good choices [all these books are in Marston Science Library, on campus] for a bit of self-study are:
Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).
In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.
:: High-school knowledge
(formula for a line between two points, the Quadratic Formula,
intersecting a line with a parabola, etc.), and some
:: Sets&Logic ideas
(Equivalence relations, partial orders, binary operators,
induction, pigeon-hole principle, cardinality).
:: Mathematical maturity
(Do you remember your basic calculus stuff? Do you remember how
to sum a geometric series?)
:: Math-Greek alphabet (pdf),
which we will use in class frequently.
The Euclidean algorithm can be presented in table-form; I call this form the Lightning-bolt algorithm (pdf), because the update-rule looks like a lightning-bolt (used thrice). Here is a practice sheet for LBolt (pdf).
The first page of
Algorithms in Number Theory (pdf),
uses LBolt iteratively to compute the GCD of a list of integers,
together with its list of Bézout multipliers.
Page 2 uses LBolt to solve linear congruences:
Find all x where 33x is mod-114 congruent to 18.
Lightning Boltalg).
Pythagorean triples(a,b,c) of positive integers for which
Pythagorean Triples (pdf)at Usually Useful Pamphlets.
Various math czars who help out.
Time | Computer/Proj | Blackboard | Humor | E-Problems | Phone |
---|---|---|---|---|---|
? | ? | ? | ? | ? |
The Web
Authors: | Jeffrey Hoffstein, Jill Pipher, J.H. Silverman | ISBN: | 978-0-387-77993-5 |
Year: | 2008 | Publisher: | Springer |
Marston: | QA268 .H64 2008 | Electronic: | Chap. 1 and Chap. 2, Diffie-Hellman, etc. (Free for UF students) |
The IP (pdf), is due, slid u n d e r my office door (Little Hall 402, Northeast corner) , no later than 2PM, Thur., 25Apr2019.
The project must be carefully typed, but diagrams may be hand-drawn.
At all times have a paper copy you can hand-in; I do
NOT accept
electronic versions.
Print out a copy each day, so that you always have the latest version to
hand-in; this, in case your printer or computer fails.
(You are too old for My dog ate my homework.
)
Please follow the guidelines on the Checklist (pdf, 3pages) to earn full credit.