Our Teaching Page
has important information for my students.
(It has the
Notes, Exams and Links
from all of my previous courses.)
The Teaching Page has my schedule,
LOR guidelines,
and Usually Useful Pamphlets.
One of them is the
Checklist (pdf)
which gives pointers on competant mathematical writing.
Further information is at our
class-archive 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 class-participation grade.
This will help you decide if my teaching-style is the right style for you.
Structure and Proof) work through pages 11-17.
Our two, free, online texts
(you can freely download the PDFs to your computer)
are these:
Main textbook:
The
Book of Proof
(BoP),
by Richard Hammack.
Secondarily, we will use
Transition to Higher Mathematics: Structure and Proof
(SaP),
by
Bob A. Dumas
and
John E. McCarthy.
Current: Please work-through W: Euclidean algorithm (up through “Extended Euclidean...” but skip the proofs) and work-through W: Modular arithmetic (through “Applications”).
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.
Find all x where 33x is mod-114 congruent to 18.
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
Autumn 2021, SeLo:
The Spring 2021, SeLo, page:
Autumn 2020, SeLo, page, for two online (due to COVID) sections:
The Spring 2020, SeLo, page:
...was due, emailed to me, squashATuflDOTedu, as a PDF! no later than 5PM, Tuesday, 28Apr2020.
The SeLo Project must be carefully typed, but diagrams may be hand-drawn and scanned into the PDF.
The various SeLo czars who helped:
Time | Computer | Memory/telepathy | Spur-OTM-Probs | Phone |
---|---|---|---|---|
Jonathan S. | Teegan B. | Yasmeen G. | Blake W. | Chris P. |
Autumn 2019, SeLo:
Essay (V3) had you label the vertices a dodecahedron. You may have found it convenient to print out the edge-graph of a dodecahedron for your vertex-label diagrams.
Available is a template, for folding-together a 3D-dodecahedron.
The various Math czars who help out:
Time | Computer | Memory/telepathy | Blackboard | Spur-OTM-Probs |
---|---|---|---|---|
Chase | Atharva | Sienna | Nathan | Bhaskar |
Autumn 2018, SeLo:
Author: | Daniel J. Velleman | ISBN-13: | 978-0521675994 |
Year: | 2006 | Publisher: | Cambridge University Press |
SeLoidal czars who aided the course:
Time | Computer | Spur-OTM-Probs | Phone-list |
---|---|---|---|
Kailey S. | Jeremy M. | Joey, Mario, Patrick | Aerin B. |
Computer-generated pictures of Lmino Tilings (txt), illustrating a geometric induction-argument.
The domino-tiling sequence on 2xN leads to the roots of the problem.
The nifty Class-B graced its way into existence on Wedn., 24Oct2018.
Part of the Spring 2017 SeLo page:
Math czars:
Time | Computer | Blackboard | Spur-Probs | Phone-list |
---|---|---|---|---|
Leah | Leah | Christopher P. | Nicholas C. | Lizzie(Donna) |
This was followed by the cute Class-V.
Folks thrilled to Class-W and its comforting question about Lminos, with which the cognoscenti were already familiar.
Useful info from the Spring 2014, SeLo, page:
A section of the the Autumn 2013 SeLo page:
February! Folks rushed to post solutions for their colleagues to admire.
The cheerful individual component, Class-V (pdf) [Wedn., 23Oct.] was well-received by the Mathematical Intelligentsia, appreciating its tight connection to Home-V.
Class-W (pdf) the individual component, revealed itself on Wednesday, 20Nov..
Helpful Math czars.
Time | Computer | Chalk | ES-Probs | Phone-list |
---|---|---|---|---|
Rico | Corey | Sam-C | Alex | David |
Part of the Spring 2012 SeLo page:
The various Math czars who help out:
Time | Computer | Chalk | Blackboard | ES-Probs | Phone-list |
---|---|---|---|---|---|
Annie | Sofia | Stewart | Ian | Christopher M. | Alejandra |
Give us more Zinc, Tin, Silver and Gold! —5 atoms; that's just not enough!All this followed the nifty Home-X (pdf), which was due by noon, on Tuesday, 28Feb2012, slid completely under my office door.
Part of the Spring 2011 SeLo page:
Classroom czars who helped out:
ES-Probs | Computer | Time | Chalk | Blackboard | Phone-list |
---|---|---|---|---|---|
Mallory | Corey | David S. | Esther | Kristen | Blanko |
(∃ another photo at bottom of page)
Better than getting bitten by a rabid squirrel!
, was
the general consensis.
(A minority opined
Comparable to rabid-squirrel bites —but with
less fur...
)
Here is part of the Autumn 2009 SeLo page:
The various Math czars who helped out:
Computer | Time | Phone-list | Chalk |
---|---|---|---|
Marc | Sigrun | Cara | John |
Individual-Project Home-E was due 1PM, Friday, 11Dec2009, carefully typed, but diagrams may be hand-drawn.
The fascinating SeLo-D (pdf) got rave reviews; the Crowd Clamored for More! [Wed, 18Nov.]
Some examples of computer generated Lmino tilings (txt).
We had the stimulating SeLo-C (pdf) in class on Wed, 28Oct.
Hopefully, Eager Mathematicians rush to post Solutions….
the empty sum,
empty product
empty max
empty gcd?
Indexed and non-indexed big-operators.
Decimal notation and repeated decimals
.
Binomial and multinomial coeffs. Proof of Fermat's Little Thm by induction. Using a binomial coeff to count the number of ways of choosing N objects out of T distinguished types.
There was a makeup SeLo-B (pdf) for those with a legitimate reason for missing the original; please post solns.
We: Started Quantifiers and reviewed Free variables and these functions: d(), sigma(), EulerPhi(), floor(), ceiling(). Discussed notations for tuples/sequences, gcd of tuple or set, relation between contrapositive, converse and inverse of a stmt.
We start Propositional logic (also called sentential logic ). Play with the Venn-diagram self test, noting that this page uses B' to mean the complement of B, which we generally write a B^{c}. [ASIDE: Please read our general terminology (pdf).]
We'll also look at the
Euclidean Algorithm
(i.e, the Lightning Bolt algorithm
).
The
LBolt frame (pdf)
has seven practice problems on page 1
[LBolt answers (txt) are available],
and six
make your own problem
on page 2.
Please grok completely how to easily solve a linear congruence (pdf).
We proved that Primes has arbitrarily long gaps. We proved Euclid's thm that there are infinitely many primes.
Having defined the arithmetic progression AP(s,G) := [s + GZ], we stated Dirichlet's thm for coprime APs. We noticed that Euclid's thm is the special case AP(0,1) of Dirichlet's. We proved Dirichlet's for AP(-1,4), and Prof. King gave an exercise to prove the same for AP(-1,3), and AP(-1,6).
We defined Modular arithmetic and proved that addition/subtraction and multiplication are preserved, mod N.
David Gale's Game of
chomp
in Wikipedia.
Doron Zeilberger's Three-rowed Chomp
.
John posted some solns to our prerequisite mini-exam SeLo-A (pdf).
Please take a gander at our Syllabus (txt) and Past courses with notes, exams and links.
Material from the Spring 2008 SeLo page:
Author: | Keith Devlin | ISBN: | 978-1584884491 |
Year: | 2003 | Publisher: | Chapman & Hall/CRC |
The Math czars who helped out.
E-Probs | Computer | Phone-list | Chalk | Blackboard | Time |
---|---|---|---|---|---|
Karly & Josh | Michael | Kyle | Vincent | Ben | Ross |
Many folk finished Class-D (pdf) early, so as to go home and read about Completeness in Chapter 5. I invite you to post solutions to our archive.
Voila a practice exam for Class-D (pdf). It is quite similar to, but longer, the actual Class-D.