SeLo: Sets and Logic [2022g]

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).

Resources

The eagerly awaited Individual Optional Project (IOP-D) is available. It was due, typed, stapled, slid completely under my office door (402 Little Hall, northeast corner, top floor) no later than 2PM, Thursday, 21Apr2022.
A proof of the Chinese Remainder Theorem (pdf) [CRT] with many additional details. Proves that Euler phi is a multiplicative fnc. Here are some An example of using CRT to count roots of a polynomial.
Current: 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.
Here are examples of fusing congruences (txt) using LBolt.
Everybody loves the Euler-Fermat thm. Available is Using EFT to solve 102⁷⁰ + 1 =113= b³⁷ (txt), from Prof. William Stein's book.
Our last topic is a bit of Number Theory grab-bag (pdf). (I wrote this for a NT class, so we'll need to jump around in it, and skip parts.)
Our Class-C was given by Jake, when PK was on the injured list.
[Thank you Jacob, for the solns you posted.]
The eagerly awaited Class-B generated a lot of Mathematical Thinking.
The delightful Home-B is online for your team-solving pleasure.

If you want, for your Home-B:
A dodecahedron (do+dec = 2+10 = 12) has a planar edge-graph (of a dodecahedron); convenient, for vertex-label diagrams.
For those of you who like manipulables, we have a template, for making a 3D-dodecahedron.
Current: Our Primer on cardinality.
In addition to proof by raster scan, we can prove that NxN is equinumerous with N via Boustrophedon, which can even be pronounced!
Current: A std proof of the Inclusion-Exclusion principle (pdf), together with Candy-Store, Derangement and Stirling-number examples.
The PList: Problem List for SeLo (pdf) has hyperlinks in the Table-of-Contents and the Index. [Sunday, 17Apr2022]
Available is a magnified PList.
Look Ma! Abbreviations-to-learn, and: All 8 SeLo quizzes so far (pdf), [Monday, 18Apr2022].
Shouts of Joy greeted the beguiling Class-A (pdf), whetting people's appetite for further SeLo insights. Flowers and gold coins were tossed on the stage by an appreciative audience, as crowds gathered to cheer the elegance of the exam.

Newspaper headlines across the country proclaimed, Class-A, a triumph!, splashed across the front page in 19-point font. It has everything!, gushed one audience member, Mystery!, Sophistication!, Suspense!. Avid readers everywhere are looking forward to the next installment.
Our nifty Home-A was due at BoC [Beginning-of-Class], stapled on Monday, 14Feb2022 with All Team Members present.
Now available is Home-A.
Optional: Ring Basics.
An Introduction to Isomorphism, via Gambling. It asks: Why 2, when 76 seems correct?
Truth-table displayer:
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs about which you can post to our Archive.
Current:

Please work-through W: Euclidean algorithm (up through “Extended Euclidean...” but skip the proofs) and work-through W: Modular arithmetic (through “Applications”).

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.
An introduction to Hall's Marriage (Matching) Lemma.
Example: A cute proof that e is irrational.
Really Cool: The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
Fun, challenging problems: IMO and USAMO and HMMT and Putnam.
Past: The Math-Greek alphabet (pdf).
2022g SeLo syllabus.

Assignment for first week of SeLo: (See above, for the materials referred to.)

To help you self-evaluate, take 65 minutes to solve as many problem as you can, on this test of high-school mathematics, with a touch of calculus.
Learn the Math-Greek alphabet.
Work through BoP, sections 1.1 through 1.9. Write-up (but do not hand-in) at least 3 HW problems from pages 1-14.
Read Set-builder notation (up through “Equivalent predicates...”), becoming comfortable with the notation.
In PList:, read pages 1-6, memorize abbreviations in Appendix: Notation.
In SaP (Structure and Proof) work through pages 11-17.
Important: For us, the (double-bar N) symbol ℕ={0,1,2,...}; i.e zero is a natural number, a natnum. This is also the convention in SaP but, unfortunately, not the convention in BoP.
So when you read ℕ in BoP, replace it with ℤ₊={1,2,3,4,...}; the set of positive integers; the posints.

Sets and Logic

Resources

General Info

Examish stuff

Ending in style