JK focus
Articles
Fonts
JK Contradance calling
Jonathan's dances
Dances/Composers (contradance)
Tunes/Bands (contradance)
L0 Contradance program
L1 Contradance program
L2 Contradance program
L3 Contradance program
L4 Contradance program
L5 Contradance program
testing Misc
Navigation
Schedule
Teaching
StanZas
Michael Dyck's Contradance Index
LORs
Pamphlets
PASTCOURSES
Footnote, good books
SeLo 2022g
LinA 2022t
SeLo 2021t
Plex 2021t
SeLo 2021g
DfyQ 2021g
SeLo 2020t, both sections
Combinatorics 20172018
Algebra.1 2019t
NT&Crypto 2019g
Aut2021: MHF3202 12A3(19805) Sets.&.Logic MWF4[10:4011:30] 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).
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
Resources
 The
Individual Project C
now has a guidedversion of the Infinite Hats problem. All three problems are nontrivial,
so Yoda says,
Delay, do not, young Jedi.
 Our Primer on cardinality.
 HomeB (PDF),
done individually, was due Monday, 29Nov2021
 The PList:
Problem List for SeLo (pdf)
has hyperlinks in the
TableofContents and the Index.
[Tuesday, 09Nov2021]
 An introduction to
Hall's Marriage (Matching) Lemma.
 An intro to the
Chromatic polynomial of a graph
(pdf);
a graphical example of deletioncontraction.
 The spiffy
The tilable ClassA (pdf)
was enjoyed by all. (Even by the person who has to grade it.)
Our HomeA (PDF)
was due date Wednesday, 20Oct2021.
 An Introduction to Isomorphism, via Gambling.
It asks: Why 2, when 76 seems correct?
 A cute proof of Irrationality:
e is irrational.
 Truthtable displayer:

Does Zero = One? (pdf).
Here are some
proofs poofs about which
you can post to our Archive.
 Tentative
2021t Selo syllabus.
 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.
 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:
Please workthrough
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
and workthrough
W: Modular arithmetic
(through “Applications”).
 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.
 Past:
A std proof of the
InclusionExclusion principle (pdf),
together
with CandyStore, Derangement and Stirlingnumber examples.
 The famous
Online Encyclopedia of Integer Sequences, and
some
W: OEIS history, and a
video with a challenge at the end.
 Optional:
Ring Basics.

Fun, challenging problems:
IMO and
USAMO and
HMMT and
Putnam.
 Past:
The MathGreek alphabet (pdf).
General Info
Please take a gander at
Past courses with notes, exams and links.
Assignment for first week of SeLo:
(See below, for the materials refered to.)
 Learn the MathGreek alphabet.
 In PList:, read pages 16, memorize abbreviations
in Appendix: Notation.
 In BoP (
Book of Proof
)
work through pages 114 and writeup
(but do not handin) at least 3 HW problems
from those pages.
 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.
 Start reading
Setbuilder notation
(up through “Equivalent predicates...”),
becoming comfortable with the notation.
JK Home page