SeLo: Sets and Logic [2018t]

End-of-semester SeLo (Individual Optional Project) IOP-D (pdf)

...will be due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than 2PM, Thursday, 06Dec2018

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 . 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.

General Info

If you want, for your IOP:
The edge-graph of a dodecahedron, for vertex-label diagrams.
A template, for making a 3D-dodecahedron.
The highly-unfinished Primer on cardinality. [Wednesday, 28Nov2018]
In one convenient location: All 9 SeLo quizzes so far (pdf), [Monday, 26Nov2018]
We went One-on-One with the cheery Class-C, and we Won!
The PList: Problem List for SeLo (pdf). [Friday, 19Oct2018]
The tilable Home-B (pdf) now has short-answers.
Being a visual exam, there is a visual soln to Zoid tiling (pdf) together with pictures of 3-mino tiling (txt). We already had Computer-generated pictures of Lmino Tilings (txt), illustrating a geometric induction-argument.

The domino-tiling sequence on 2xN leads to the roots of the problem. The second part of domino-tiling is solved on Home-B, but I have not yet typeset the solution presented in class for the first part.

The nifty Class-B graced its way into existence on Wedn., 24Oct2018. It had a nice question about tilability of unions.
The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
Please glance at Ring Basics. Have read and throughly understood Euclidean algorithm (up through “Extended Euclidean...”) and Modular arithmetic (up through “Applications”).
The cute Home-A has solns. It was followed by the highly-praised Class-A, much admired for its two-tone format, and the comic relief of the Three Stooges.
Please have learned the Math-Greek alphabet (pdf).
Have read and throughly understood Set-builder notation (up through “Equivalent predicates...”)
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs to post about...
Voila! our SeLo syllabus. Recall that events may necessitate date-changes of exams.
Nostalgic?, see Spring 2012 OR Autumn 2011 which also has Autumn 2009 and Spring 2008.

Time	Computer	Blackboard	Spur-OTM-Probs	Phone-list
Kailey S.	Jeremy M.	?	Joey, Mario, Patrick	Aerin B.

Tips on writing proofs

"How To Write Proofs" (html), by Prof. Larry W. Cusick, [INTERMEDIATE]. Excellent. 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.

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).

Author:	Daniel J. Velleman	ISBN-13:	978-0521675994
Year:	2006	Publisher:	Cambridge University Press