SeLo: Sets and Logic [20120g]

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).

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.

Assignment for Add/Drop week

General Info

Resources

The PList: Problem List for SeLo (pdf), [Tuesday, 07Jan2020]
Our SeLo syllabus (pdf) has clickable links.
The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
Near Future: Please read and throughly understood the Euclidean algorithm (up through “Extended Euclidean...”) and Modular arithmetic (through “Applications”).
Medium Future: 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]
A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
Exams/notes from previous incarnations: Aut.2019, Aut.2018, Spr.2017, Aut.2013, Spr.2012, OR 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.
Future: Please skim Ring Basics.
Future: The mostly-finished Primer on cardinality.

Time	Computer	Memory/telepathy	Spur-OTM-Probs	Phone
Jonathan S.	Teegan B.	?	?	Chris P.

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.

End-of-semester SeLo Individual Project (pdf)

...was due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than 2PM, Thursday, 23Apr2020.

The SeLo Project must be carefully typed, but diagrams may be hand-drawn.

For the typesetting, one possibility is the (free) mathematics-typesetting language LaTeX .

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.