SeLo: Sets and Logic [20120g]

End-of-semester SeLo Individual Project D (IP-D)

[Problems (D2(C)) and (D3) are challenging. Don't delay, said the Wise Person...] Prof.

...was due, emailed to me, squashATuflDOTedu, as a PDF! no later than 5PM, Tuesday, 28Apr2020.

The SeLo Project must be carefully typed, but diagrams may be hand-drawn and scanned into the PDF.

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

The guidelines on the Checklist

(pdf, 3pages) are written for a team take-home, but are nonetheless are helpful for scoring well on an individual take-home.

Resources

Current: The nifty-diffty Primer on cardinality. [Wedn., 15Apr2020]
While not required for our course, the Primer on Polynomials has further information on Algebraic Numbers, for the Curious Ambitious Student.
The interesting IP-B (Individual-Project B), folks told me, was challenging.
All B-teams have emailed me their Home-B. Thank you.
The PList: Problem List for SeLo (pdf), has hyperlinks in the Table-of-Contents and the Index. [Sunday, 08Mar2020]
Our SeLo syllabus (pdf) has clickable links.
[Copied from our Teaching Page at Usually Useful Pamphlets.] The Checklist (pdf, 3 pages) has important ingredients of good mathematical writing. It also has some of the abbrevs that I use in grading. See also Studying (pdf).
Our Class-A was entertaining.

Relevant to the tiling question is the cool Blake-3 problem: It has a nice question about tilability-of-unions.

One question on Home-A generalized the geometric induction-argument (for the two-dimensional version) that we did in class.
Example Pictures of Lmino Tilings (txt).

Helpful for the first part of (A3), were these graph-papers: trianglepaper.6.pdf and trianglepaper.4.pdf and triangledots0.4.pdf.

Possibly helpful: hexpaper.5.pdf and hexpaper.3.pdf.

Being a visual exam, there is an induction-proof essay, with images, giving a soln to all Zoid-tiling problems (PDF). We also have pictures of 3-mino tiling (txt).

Finally, students in a previous SeLo class generated this picture of zoid-tiling of a 3^k triangle, when k =3= 0, as well as a zoid-tiling of a 3^k triangle, when k =3= ±1.
Look Pa! All 5 SeLo quizzes so far (pdf), [Friday, 21Feb2020].
We use two, free, online texts: The Book of Proof, by Richard Hammack.
And: Transition to Higher Mathematics: Structure and Proof, by Bob A. Dumas and John E. McCarthy.
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs about which you can post to our Archive.
The Math-Greek alphabet (pdf).
The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
Please 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]
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.

Also available are Past courses with notes, exams and links.
Optional, but useful: Please skim Ring Basics.

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).

Assignment for Add/Drop week

Time	Computer	Memory/telepathy	Spur-OTM-Probs	Phone
Jonathan S.	Teegan B.	Yasmeen G.	Blake W.	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.