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MHF3202 3E06 (17450) Sets.&.Logic MWF4 [10:4011:30] Lit235
Sets and Logic
Quantifiers
∀ and
∃
(“for all”
and
“there exists”)
are like nitroglycerin, in that one little misstep leads to the whole
thing blowing up in your face.
There is no partial credit when it comes to Explosives and Quantifiers.
JLF King
General Info
Please take a gander at
Past courses with notes, exams and links.
[See “Examish stuff”, further below.]
Resources

The popular
Quiz Fantabulous!
as a nice productive way end our pandemic Zoomester; it now has the essay.
 Current:
Our Primer on cardinality.

Elegant E
was everyone's favorite, as it answered that burning light bulb question...
[Hopefully
SeLoticians will post solns answering the other questions.]
 Current, Always: Solve problems
(working with a classmate is fine, and encouraged)
the challenging
PList:
Problem List for SeLo (pdf).
It has hyperlinks in the
TableofContents and the Index.
 Computergenerated 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.]
 Current:
A std proof of the
InclusionExclusion principle (pdf),
together
with CandyStore, Derangement and Stirlingnumber examples.
 Current:
Ring Basics.
 Cognoscenti marveled at
the straightforward induction proof on
Daffy quiz D.
 SeLoCitizens were entertained by
Goofy quiz C
starting off with a binomialidentity, and finishing with a nice Induction proof.
Cognoscenti cheerfully garnered CPpoints by posting solutions
(not just answers) to our SeLo Archive.
 Scholars showered the keyboard with roses,
admiring the
Pleasant quiz B
with its elegant PHP proof.
 Folks appreciated that our first
Enjoyable quiz A
had no essay question.
[Future quizzes will have proofs on them, and
students will need to upload a (typically, small) essay as a PDF.]
 Current:
The Euclidean algorithm can be presented in tableform; I
call this form the
Lightningbolt algorithm (pdf),
because the updaterule looks like a lightningbolt (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 33x is mod114 congruent to 18.
 Past:
Please workthrough
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
and workthrough
W: Modular arithmetic
(through “Applications”).
 The famous
Online Encyclopedia of Integer Sequences, and
some
W: OEIS history, and a
video with a challenge at the end.

Optional:
Everybody loves the EulerFermat thm.
Available is
Using EFT to solve
102^{70} + 1 =113= b^{37}
(txt), from Prof. William Stein's book.

Fun, challenging problems:
HMMT and
IMO and
USAMO and
Putnam.
 Past: Peruse
Does Zero = One? (pdf).
Here are some
proofs poofs about which
you can post to our Archive.
 Past:
Practice: Binomials, complex arithmetic
 Past:
Memorize the MathGreek alphabet (pdf).
 Past:
Become comfortable reading/writing
Setbuilder notation
(up through “Equivalent predicates...”).
 SeLo syllabus
[Monday, 12Apr2021]
.
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
classarchive URL
(I email this private URL directly to students).
Prof. King's
Mastery of Zoom.
[Source unknown]
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