Number Theory 1 [2018s]

Welcome! 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 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).

Shuffling in to view is the Individual Optional Project, which is due [if you choose to do it] at 2PM, on Friday, 10Aug2018, at the beginning of class/party.
In one convenient location: All 9 NT quizzes so far (pdf), [Tuesday, 07Aug2018]
Class-C, a paper-and-hensel exam, provided hours of entainment.
The amusing Class-B is present. Available is the nifty-cool Home-B.
The delightful Home-A was followed by the cute Class-A (pdf).
By Monday, 09July, please read the Ring basics, which has the defns of Group, Ring Field, as well as zero-divisor, unit, and the especially important notion of irreducible and prime elements.
In pamphlet Multiplicative Functions (pdf) you need to know defns of the divisor-count, divisor-sum and Euler-phi fncs, and formulas for them.
But you may ignore (and probably should) the rest of the material, for the time being.
By Thursday, 05July, please have fully-understood (grokked) Algorithms in Number Theory (pdf). It uses LBolt iteratively to compute the GCD of a list of integers, together with a Bézout-list.
Page 2 uses LBolt to solve linear congruences, e.g: Find all x where 33x is mod-114 congruent to 18.
While microquizzes are typically unannounced, here are the first three:
Microquiz on Thursday, 05Jul2018, testing Lightning-bolt, and basic modular arithmetic.
Microquiz on Friday, 06July, testing Iterated-Lightning-bolt, modular arithmetic, Math-Greek alphabet (pdf).
Microquiz on Monday, 09July, testing Iterated-Lightning-bolt, modular arithmetic, and the Fund. theorem of Arithmetic (e.g, its proof using Bézout multipliers).
By Tuesday, 03July please learn the Euclidean Algorithm, in the form of the Lightning-bolt algorithm (pdf), [so called, because the update-rule looks like a lightning-bolt]. Here is a practice sheet for LBolt (pdf), with LBolt answers (txt),

Please read W:NT through the end of section titled “Fermat”.

Author:	James K. Strayer	Edition:	2002
ISBN:	1577662245	Publisher:	Waveland (Reissue edition, blue & purple cover)