SeLo: Sets and Logic [2020t]

Resources

Current: Please work-through W: Euclidean algorithm (up through “Extended Euclidean...” but skip the proofs) and work-through W: Modular arithmetic (through “Applications”).
Current: The Euclidean algorithm can be conveniently applied in table-form; I call this form “Lightning Bolt ” because the update-rule looks like a lightning-bolt (used thrice). Please read the Lightning-bolt algorithm (pdf), learning the algorithm, but skipping the proofs.
Suggestion: Print out on paper (yes, actual paper), the practice sheet for LBolt (pdf) and fill-in the tables. This type of question for the first exam, Sept.23, so you should practice.
Near Future: 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.
Future: Here are examples of fusing congruences (txt) using LBolt.
Everybody loves the Euler-Fermat thm. Available is Using EFT to solve 102⁷⁰ + 1 =113= b³⁷ (txt), from Prof. William Stein's book. Algorithms in Number Theory (pdf) [you will be responsible just for the Iterated Lightning-bolt part, page 1]
The PList: Problem List for SeLo (pdf), [Thursday, 24Sep2020]
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs about which you can post to our Archive.
Exams/notes from previous incarnations: Spr.2020, Aut.2019, Aut.2018, Spr.2017, Aut.2013, Spr.2012, and Aut.2011 [which also has Autumn 2009 and Spring 2008].
This will help you decide if my teaching-style is the right style for you.
In one convenient location: All 0 SeLo quizzes so far (pdf),
In this quizzes link, please have read the binomial/multinomial conventions on page 2, together with Operations on Sets..
A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
Optional: Ring Basics.
The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
The 2020t Selo syllabus is in progress.
Distant Future: Our Primer on cardinality.
Past: This week, please memorize the Math-Greek alphabet (pdf).
Past: Please work through Set-builder notation (up through “Equivalent predicates...”).

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).

Time	Computer	Memory/telepathy	Blackboard	Spur-OTM-Probs
Chase	Atharva	Sienna	Nathan	Bhaskar

Tips on writing proofs

"How To Write Proofs" (html), by Prof. Larry W. Cusick, [INTERMEDIATE]. Examples mostly from Elem. Number Theory; some from Calculus.
Prof. Christopher Heil's page (pdf) [4 pages, INTRO]. A well written survey of the structure of proofs. Has one example of induction (recursion).
“How to write proofs: a quick guide” by Prof. Eugenia Cheng (pdf) [17 pages, INTRO]. Good, friendly. She is stricter than I in the ordering of steps in a proof. Conversely, her write-up is lax in places where I am strict:
- Always use a word/phrase, and never a comma, for then; e.g then or necessarily or we discover to our delight that .
- She has proof snippets in her examples, but remember that your proofs must be written as a sequence of complete, grammatical sentences, correctly punctuated, structured into coherent paragraphs.

Sets and Logic

General Info

Resources

Tips on writing proofs