SeLo: Sets and Logic [2020t]

Resources

Our Primer on cardinality. [Tuesday, 01Dec2020]
The PList: Problem List for SeLo (pdf), [Thursday, 19Nov2020]
Beautifully designed [but unexpectedly eventful], our Exam-A (PDF) now has solns to all problems; useful for studying.
Our Exam-B (PDF) went smoothly, and now has all solns; useful for studying/learning.
A free site, Merge PDF, for merging multiple PDFs into one. I've used this and it worked fine. There are other free ones on the web as well. Use whatever works for you.
A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
Past: Please work-through W: Euclidean algorithm (up through “Extended Euclidean...” but skip the proofs) and work-through W: Modular arithmetic (through “Applications”).
Past: 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.30, so you should practice.
Past: 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.
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].
Future: Everybody loves the Euler-Fermat thm. Available is Using EFT to solve 102⁷⁰ + 1 =113= b³⁷ (txt), from Prof. William Stein's book.
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.
Past: The Math-Greek alphabet (pdf).
Past: Be comfortable reading/writing Set-builder notation (up through “Equivalent predicates...”).
Optional: Ring Basics.
Fun, challenging problems: IMO and USAMO and HMMT and Putnam.

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).

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