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SeLo 2020t, both sections
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MHF3202 1079 (18207) Sets.&.Logic MWF4 [10:4011:30] ONLINE
MHF3202 139A (18209) Sets.&.Logic MWF5 [11:4512:35] ONLINE
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.
Resources

Our Primer on cardinality.
[Tuesday, 01Dec2020]
 The PList:
Problem List for SeLo (pdf),
[Thursday, 19Nov2020]

Beautifully designed
[but unexpectedly eventful],
our
ExamA (PDF)
now
has solns to all problems; useful for studying.

Our
ExamB (PDF)
went smoothly, and now has all solns; useful for studying/learning.
 A free site,
Merge PDF, for merging multiple PDFs into one.
I've used this and it worked fine. There are other free ones on the web as well.
Use whatever works for you.

A std proof of the
InclusionExclusion principle (pdf),
together
with CandyStore, Derangement and Stirlingnumber examples.
 Past:
Please workthrough
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
and workthrough
W: Modular arithmetic
(through “Applications”).
 Past:
The Euclidean algorithm can be conveniently applied in tableform; I
call this form “Lightning Bolt ”
because the updaterule looks like a lightningbolt (used thrice).
Please read
the
Lightningbolt algorithm (pdf),
learning the algorithm, but skipping the proofs.
Suggestion:
Print out on paper (yes, actual paper), the
practice sheet for LBolt (pdf)
and fillin the tables. This type of question for the first exam, Sept.30, so you
should practice.
 Past:
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.
 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].

Future:
Everybody loves the EulerFermat thm.
Available is
Using EFT to solve
102^{70} + 1 =113= b^{37}
(txt), from Prof. William Stein's book.
 The famous
Online Encyclopedia of Integer Sequences, and
some
W: OEIS history, and a
video with a challenge at the end.
 The
2020t Selo syllabus.
 Past:
The MathGreek alphabet (pdf).
 Past:
Be comfortable reading/writing
Setbuilder notation
(up through “Equivalent predicates...”).
 Optional:
Ring Basics.

Fun, challenging problems:
IMO and
USAMO and
HMMT and
Putnam.
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).
 "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 writeup is lax in places where I am strict:
 Always use a word/phrase, and never a comma, for
then
;
e.g then
or necessarily
or
we 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.
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