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Spr2022: MHF3202 17HE (16078) Sets.&.Logic MWF3[09:3510:25] LIT233(CE)
Sets and Logic
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).
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
responsible to get all
Notes / Announcements / TheWholeNineYards
from a classmate, or several.
All my classes have a
substantial
classparticipation grade.
Resources
 The eagerly awaited
Individual Optional Project (IOPD)
is available.
It was due, typed, stapled, slid completely under my office door
(402 Little Hall, northeast corner, top floor)
no later than
2PM, Thursday, 21Apr2022.
 A proof of the
Chinese Remainder Theorem (pdf) [CRT]
with many additional details. Proves that Euler phi is a multiplicative fnc.
Here are some
An example of
using CRT to count roots of a polynomial.
 Current:
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.
 Here are examples of
fusing congruences (txt)
using LBolt.
Everybody loves the EulerFermat thm.
Available is
Using EFT to solve
102^{70} + 1 =113= b^{37}
(txt), from Prof. William Stein's book.
 Our last topic is a bit of
Number Theory grabbag (pdf).
(I wrote this for a NT class, so we'll need to jump around in it, and
skip parts.)
 Our ClassC
was given by Jake, when PK was on the injured list.
[Thank you Jacob, for the solns you posted.]
The
eagerly awaited
ClassB
generated a lot of Mathematical Thinking.
 The delightful
HomeB
is online for your teamsolving pleasure.
If you want, for your HomeB:
A dodecahedron
(do+dec = 2+10 = 12)
has a planar
edgegraph (of a dodecahedron);
convenient, for vertexlabel diagrams.
For those of you who like manipulables, we have a
template, for making a 3Ddodecahedron.
 Current:
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!
 Current:
A std proof of the
InclusionExclusion principle (pdf),
together
with CandyStore, Derangement and Stirlingnumber examples.
 The PList:
Problem List for SeLo (pdf)
has hyperlinks in the
TableofContents and the Index.
[Sunday, 17Apr2022]
Available is a magnified PList.
 Look Ma!
Abbreviationstolearn, and:
All 8
SeLo quizzes so far (pdf),
[Monday, 18Apr2022].

Shouts of Joy
greeted the beguiling ClassA (pdf),
whetting people's appetite for further SeLo insights.
Flowers and gold coins were tossed on the stage by an appreciative audience,
as crowds gathered to cheer the elegance of the exam.
Newspaper headlines across the country proclaimed,
ClassA, a triumph!
, splashed across the front page in 19point font.
It has everything!
, gushed one audience member,
Mystery!, Sophistication!, Suspense!
.
Avid readers everywhere are looking forward to the next installment.
 Our nifty
HomeA
was due at BoC
[BeginningofClass],
stapled
on
Monday, 14Feb2022
with All Team Members present.

Now available is
HomeA.
 Optional:
Ring Basics.
 An Introduction to Isomorphism, via Gambling.
It asks: Why 2, when 76 seems correct?
 Truthtable displayer:

Does Zero = One? (pdf).
Here are some
proofs poofs about which
you can post to our Archive.
 Current:
Please workthrough
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
and workthrough
W: Modular arithmetic
(through “Applications”).
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.
 An introduction to
Hall's Marriage (Matching) Lemma.
 Example: A cute proof that
e is irrational.
 Really Cool:
The famous
Online Encyclopedia of Integer Sequences, and
some
W: OEIS history, and a
video with a challenge at the end.

Fun, challenging problems:
IMO and
USAMO and
HMMT and
Putnam.
 Past:
The MathGreek alphabet (pdf).

2022g SeLo syllabus.
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
Assignment for first week of SeLo:
(See above, for the materials referred to.)
 To help you selfevaluate,
take 65 minutes to solve as many
problem as you can, on
this
test of highschool mathematics, with a touch of calculus.
 Learn the MathGreek alphabet.
 Work through BoP, sections 1.1 through 1.9.
Writeup
(but do not handin) at least 3 HW problems
from pages 114.
 Read
Setbuilder notation
(up through “Equivalent predicates...”),
becoming comfortable with the notation.
 In PList:, read pages 16, memorize abbreviations
in Appendix: Notation.
 In SaP (
Structure and Proof
)
work through pages 1117.
Important:
For us, the (doublebar 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.
General Info
Please take a gander at
Past courses with notes, exams and links.
JK Home page