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SeLo 2022g
LinA 2022t
SeLo 2021t
Plex 2021t
SeLo 2021g
DfyQ 2021g
SeLo 2020t, both sections
Combinatorics 2017-2018
Algebra.1 2019t
NT&Crypto 2019g
MHF3202 1079 (18207) Sets.&.Logic MWF4 [10:40-11:30] ONLINE
MHF3202 139A (18209) Sets.&.Logic MWF5 [11:45-12:35] ONLINE
Sets and Logic
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
General Info
Please take a gander at
Past courses with notes, exams and links.
Resources
-
Our Primer on cardinality.
[Tuesday, 01Dec2020]
![[Image: Updated]](Images/updated.gif)
- The PList:
Problem List for SeLo (pdf)
has hyperlinks in the
Table-of-Contents and the Index.
[Sunday, 03Jan2021]
- A std proof of the
Inclusion-Exclusion principle (pdf),
together
with Candy-Store, Derangement and Stirling-number examples.
- Past:
Please work-through
W: Euclidean algorithm
(up through “Extended Euclidean...” but skip the proofs)
and work-through
W: Modular arithmetic
(through “Applications”).
- Past:
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.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 mod-114 congruent to 18.
-
Does Zero = One? (pdf).
Here are some
proofs poofs about which
you can post to our Archive.
-
Future:
Everybody loves the Euler-Fermat thm.
Available is
Using EFT to solve
10270 + 1 =113= b37
(txt), from Prof. William Stein's book.
- 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.
- Past:
The Math-Greek alphabet (pdf).
- Past:
Be comfortable reading/writing
Set-builder notation
(up through “Equivalent predicates...”).
- Optional:
Ring Basics.
-
Fun, challenging problems:
IMO and
USAMO and
HMMT and
Putnam.
Examish stuff
-
Beautifully designed
[but unexpectedly eventful due to my unfamiliarity with Canvas],
our Exam-A (PDF).
-
The engaging Exam-B (PDF)
went smoothly.
-
The
Individual End-of-Semester Project
was administered via Canvas.
- 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.
In case you want it,
this free
[as of 21Dec2020].
site
converts PDFs to PNGs.
- 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].
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).
JK Home page
