Goto: Prof. King's page at Univ. of Florida.
Or: JK Homepage.

Page:
http://squash.1gainesville.com/Include/thispage.shtml

A bout of Nostalgia? See
past SeLo courses.

The various Math czars who help out.

Computer&Projector | CP-Probs | Time | Memory/Telepathy | Whiteboard |
---|---|---|---|---|

Brandon D. | Diego P. | everyone | ? | everyone |

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 responsibleto get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.

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

- The delightful
Home-A is available for
your cogitating-pleasure.

Typed and well-stapled, your team's write-up is due [with all team-members present] at beginning-of-class on Wednesday, 28Sep2022.

It's first page is the printed problem-sheet, with the blanks filled-in (handwritten is fine). - Computer-generated Lmino tiling appear in Pictures of Lmino Tilings (txt). The pictures start about a third of the way down the file. [The top of the file just comprises notes to me, on how to use the code.]
*Look Ma!*All 4 SeLo quizzes so far (pdf) [Wednesday, 14Sep]- The PList: (Problem List for SeLo has hyperlinks in the Table-of-Contents and the Index.) [Monday, 12Sep2022].
The Euclidean algorithm can be presented in table-form; I call this form the Lightning-bolt algorithm (pdf), because the update-rule looks like a lightning-bolt (used thrice). Here is a practice sheet for LBolt (pdf).

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 33*x*is mod-114 congruent to 18.- Prof. Gallian's home page. Has links to a modular-arithmetic calculator.
- Does Zero = One? (pdf).
Here are some
~~proofs~~*poofs*about which you can post to our Archive. - Optional: Practice: Binomials, complex arithmetic.
Near future: 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.Near future: 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 33*x*is mod-114 congruent to 18.- Optional: Examples of
fusing congruences (txt)
using LBolt.

Everybody loves the*Euler-Fermat thm*. Available is Using EFT to solve 102^{70}+ 1 =113= b^{37}(txt), from Prof. William Stein's book. - A std proof of the
Inclusion-Exclusion principle (pdf),
together
with
*Candy-Store*,*Derangement*and*Stirling-number*examples. - An Introduction to Isomorphism, via Gambling.
- What is Hall's Marriage (Matching) Lemma?
- Future: 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! - Optional:
Our Primer on Polynomials
has further information on Algebraic Numbers, for the
*Curious Ambitious Student*. - Future, optional: Number Theory grab-bag (pdf). (I wrote this for a NT class, so we'll need to skip parts.) Optional: A proof of the Chinese Remainder Theorem (pdf) [CRT], as a ring-isomorphism thm. Proves that Euler phi is a multiplicative fnc. An example of using CRT to count roots of a polynomial

Our two, free, online texts
(you can freely download the PDFs to your computer)
are these:

Main textbook:
The
Book of Proof
(**BoP**),
by Richard Hammack.

Secondarily, we will use

Transition to Higher Mathematics: Structure and Proof
(**SaP**),
by
Bob A. Dumas
and
John E. McCarthy.

Our Teaching Page
has important information for my students.
(It has the
Notes, Exams and Links
from all of my previous courses.)

The *Teaching Page* has **my schedule**,
LOR guidelines,
and Usually Useful Pamphlets.
One of them is the
*Checklist* (pdf)
which gives pointers on competant mathematical writing.
Further information is at our
class-archive URL
(I email this private URL directly to students).

- Ring Basics (pdf).
- Fun, challenging problems: IMO and USAMO and HMMT and Putnam.
- The famous On-line Encyclopedia of Integer Sequences, and some W: OEIS history, and a video with a challenge at the end.
- A free site,
Merge PDF, for merging multiple PDFs into one.
(I used this several years ago but have not tested it recently.)
There are other free ones on the web as well.

In case you want it, this free [as of 21Dec2020]. site converts PDFs to PNGs. -
#### 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).

- Optional: A cute proof that
**e**is irrational.

- Prof. King's
Mastery of Zoom
[
*except for the cigarette*]. [Source unknown] - An End-of-Semester
*Math Derivation*.

Assignment for first week of SeLo:
(See below, for the materials refered to.)

- To help you self-evaluate, take up to 90 minutes to solve as many problem as you can, on this test of high-school mathematics, with a touch of calculus (pdf).
- Learn the Math-Greek alphabet (pdf)
*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.- In
*PList:*, read pages 1-6, memorize abbreviations in*Appendix: Notation*. - Exams from previous
SeLo incarnations:
This will help you decide if my teaching-style is the right style for you.

- Autumn2022 SeLo syllabus. Please check exam dates w.r.t religious holidays and ROTC events.
- Read Set-builder notation (W) (up through “Equivalent predicates...”), becoming comfortable with the 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*.

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