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

Modified:
Sunday, 01Mar2020
Printed:
Saturday, 26Sep2020

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

MHF3202 1079 (18207) Sets.&.Logic MWF4 [10:40-11:30] ONLINE

MHF3202 139A (18209) Sets.&.Logic MWF5 [11:45-12:35] ONLINE

Please take a gander at Past courses with notes, exams and links.

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 occasionally use

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

- Current:
Please work-through
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
*and*work-through W: Modular arithmetic (through “Applications”). - Current:
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.23, so you should practice. -
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. -
Future:
Here are 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.Algorithms in Number Theory (pdf)

[you will be responsible just for the Iterated Lightning-bolt part, page 1] - The PList: Problem List for SeLo (pdf), [Thursday, 24Sep2020]
- 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**].This will help you decide if my teaching-style is the right style for you.

- In one convenient location:
All 0
SeLo quizzes so far (pdf),

*In this*.quizzes

link, please have read the binomial/multinomial conventions on page 2, together with Operations on Sets. - A std proof of the
Inclusion-Exclusion principle (pdf), together
with
*Candy-Store*,*Derangement*and*Stirling-number*examples. - Optional: Ring Basics.
- 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 is in progress.
- Distant Future: Our Primer on cardinality.
- Past: This week, please memorize the Math-Greek alphabet (pdf).
- Past: Please work through Set-builder notation (up through “Equivalent predicates...”).

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).

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 various Math czars who help out:

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

Chase | Atharva | Sienna | Nathan | Bhaskar |

- "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