SeLo: Sets and Logic [2019t]

Quantifiers ∀ and ∃ (“for all” and “there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.

There is no partial credit when it comes to Explosives and Quantifiers.

-JLF King

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).

General Info

Resources

Our Home-U is now available. Related to the exam are Pictures of Lmino Tilings (txt), to illustrate a geometric induction-argument.
In one convenient location: All 7 SeLo quizzes so far (pdf), [Friday, 20Sep2019]
In this quizzes link, please have read the binomial/multinomial conventions on page 2, together with Operations on Sets..
The PList: Problem List for SeLo (pdf), [Friday, 06Sep2019]
A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs about which you can post to our Archive.
Our SeLo syllabus/calendar. [11Sep2019]
Exams/notes from previous incarnations: Aut.2018, Spr.2017, Aut.2013, Spr.2012, OR Aut.2011 [which also has Autumn 2009 and Spring 2008].
Future: Please glance at Ring Basics.
Future: The highly-unfinished Primer on cardinality.
The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
[Old] Have learned the Math-Greek alphabet (pdf).
[Old] Have read and throughly understood Set-builder notation (up through “Equivalent predicates...”).
[Old] Have read and throughly understood the Euclidean algorithm (up through “Extended Euclidean...”) and Modular arithmetic (through “Applications”). From our Teaching Page, have read
Lightning-bolt algorithm (pdf) [pages 1-3. You are not responsible for pages 4,5];
practice sheet for LBolt (pdf) [print on paper and work through several examples];
Algorithms in Number Theory (pdf) [you are responsible just for the Iterated Lightning-bolt part, page 1]

Time	Computer	Memory/telepathy	Blackboard	Spur-OTM-Probs
Chase	Atharva	Sienna	?,	?

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.

SeLo Individual Project [SIP]

There will be a (possibly optional) SeLo Project, to be done individually. It will be due, slid u n d e r my office door (Little Hall 402, Northeast corner) , by 2PM, Thursday, 05Dec2019 The project must be carefully typed and carefully proofread.

For the typesetting, one possibility is the (free) mathematics-typesetting language . It can be learned in a week. (It is the archival language of the American Mathematical Society.)

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.