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

Modified:
Sunday, 01Mar2020
Printed:
Friday, 05Jun2020

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

Spr2020: MHF3202 3E07 (18129) Sets.&.Logic MWF5 [11:45-12:35] Matherly 006

now [30Apr2020] with interesting fun (D3(iii)) addition; can you solve it? ...

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

...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
.

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.

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

- 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) now has solutions! Folks indicated that IP-B 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 fun Class-A now has all solns.

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

Home-A now has solns.

In class we used a geometric induction-argument to prove the two-dimensional version.

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 readLightning-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* (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).

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.

- Given time, can you solve most of the problems on this self-evaluation of prerequisite knowledge?
- Read throughly and understand
*Book of Proof*(see above) up through page 24, Venn diagrams. - Work through Set-builder notation (up through “Equivalent predicates...”).
- Please start reading: Pigeonhole Principle (PhP).

The various Math czars who help out:

Time | Computer | Memory/telepathy | Spur-OTM-Probs | Phone |
---|---|---|---|---|

Jonathan S. | Teegan B. | Yasmeen G. | Blake W. | Chris P. |

- "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, forthen

; e.gthen

ornecessarily

orwe 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.

- Always use a