JK Contradance calling
L0 Contradance program
L1 Contradance program
L2 Contradance program
L3 Contradance program
L4 Contradance program
L5 Contradance program
Michael Dyck's Contradance Index
Complex Vars 2017g
NT & Math Crypto 2016g
Don't just stand there, -Read Something!
students have rated me
and the comments, ahem, vary.
(At least I rank better than Attila the Hun… -his teaching
was terrible -no wait, that was Ivan …)
discusses this phenomenon.]
TG: Wed22-25Nov. Evals: Nov21-Dec08
SB: Sat.Mar.3-10. Evals: Apr.14-Apr27
For UF students there is free tutoring at the
UF Teaching Center
For a fee, some
UFMath grad students tutor.
In all of my courses,
attendance is absolutely required
(excepting illness and religious holidays).
All classes have a
Past, Present and Future courses.
Number Theory 1
of Summer-B 2018.
Chinese Remainder Thm,
Legendre/ Jacobi symbols,
Fermat's SoTS thm,
Lagrange 4-square thm, basic cryptography (Diffie-Hellman, RSA)
Intro/Elem. Complex variables
How is complex differentiability connected to power-series expansion?
Sets and Logic
Helps students to read and produce proofs, and learn the basic language of
[Sabbatical in Autumn 2016.]
All courses, with Notes, Exams and Links
Usually Useful Pamphlets
(pdf, 3 pages)
has important ingredients of good mathematical writing. It
also has some of the abbrevs that I use in grading.
Here is my
general terminology (pdf).
If you don't know it already, it is crucial that you learn the
Math-Greek alphabet (pdf),
which shows how I use it in class, and on pamphlets; it also has
my special symbols, e.g, the Golden ratio, or the Riemann zeta fnc.
Three authors at UC Davis wrote
Some Common Mathematical Symbols and Abbreviations (with History)
(pdf) which has a nice list of symbols,
with the presumed introducer of
each. I don't use all of these symbols/phrases in class.
A very few of
them, I use slightly differently from how the above link shows.
For email to each other, here are
mathematical conventions for the QWERTY keyboard,
as well as a partial list of
mathematical notation for Maple.
- Have you ever wondered:
Does Zero = One? (pdf).
Poofs by Induction,
Combinatorial Poofs, even
Poofs from Complex Analysis.)
- Two pages on
Converting eventually-periodic numerals to
Number theory stuff
The Euclidean algorithm can be presented in table-form; I
call this form the
Lightning-bolt algorithm (pdf),
because the update-rule looks like a lightning-bolt (used thrice).
Here is a
practice sheet for LBolt (pdf).
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.
Here are examples of
fusing congruences (txt)
Everybody loves the Euler-Fermat thm.
Using EFT to solve
10270 + 1 =113= b37
(txt), from Prof. William Stein's book.
- A proof of the
Chinese Remainder Theorem (pdf) [CRT]
with many additional details. Proves that Euler phi is a multiplicative fnc.
Here are some
Also, an example of
using CRT to count roots of a polynomial.
- Partial Theorem List (pdf)
for Number Theory.
- Special case of Dirichlet's Thm (pdf),
showing that there are infinitely many primes in -1+6Z.
Also, for SeLo,
comments on the exposition.
- Pythagorean Triples (pdf).
- Mersenne primes and Even Perfect numbers
Congruences in Number Theory (pdf).
- Elementary facts about
Fibonacci Sequences (pdf).
The Fibonacci Speedup (txt) shows how
to use repeated squaring
and modular arithmetic to rapidly compute the last two digits of the
1024th Fibonacci number.
Multiplicative Functions (pdf)
and convolution of number-theoretic functions, such as Euler-phi.
Generating functions and Mobius inversion (pdf)
to counting irreducible polynomials over a finite-field.
- Proof (a picture needs to be adjoined) of
Quadratic Reciprocity (pdf).
In particular, proofs of the Eisenstein and Gauss Lemmata.
- Finite fields have cyclic multiplicative groups (pdf).
This also proves the Primitive Root Thm, and Korselt's Thm characterizing the
- Hensel's Lemma (pdf),
for a lifting a mod-p root of a polynomial, to be a root mod pn.
- Notes-in-progress on
Fermat's SOTS (Sum-Of-Two-Squares) thm.
Slides showing how the Euclidean Algorithm writes a given N as a
Sum Of Two Squares (pdf).
Such an N is a
SOTS in the notes.
- A characterization of the
irreducibles elements in the ring of Gaussian integers (pdf).
- Liouville's Theorem (pdf)
on approximating reals by rationals.
Also: Hilbert's proof
that e is transcendental (pdf).
Bertrand's postulate (pdf)
and Chebyshev's thm, and other results on the density of prime numbers.
Binomial Coefficients (pdf).
Smith Normal Form and
Integer solutions to linear equations (pdf).
I janned up some emacs-lisp code for the
Miller-Rabin probabilistic primality test (txt).
PDF images of the
y2 = x3 -2x + 1.
These images were made with Gnuplot:
Here is a
(the light purple-reddish self-intersecting curve)
on the same surface.
- A Primer on Polynomials (pdf).
- Basic Algebra definitions (pdf).
[Currently this has some group-theory results, which need to be
- Solutions to problems in Gallian's text (pdf).
- Example of
Burnside's Lemma, for coloring the cube (pdf).
[This could also be filed under Combinatorics.]
- Algorithmic exposition of
Fund. Thm of Symmetric Polynomials (pdf).
- Voila! a proof of the
Eisenstein Irreducibility Criterion (pdf).
- Proof of
Fund. Thm of Finite Abelian groups (pdf).
- Here we explore
N×N determinants (txt) and
Cramer's “Rule”, i.e Theorem (txt).
proof of the Rank-Nullity Theorem (pdf),
and also a
proof that RREF is unique (pdf),
- Nullspaces of commuting transformations (pdf);
applies Linear Algebra to constant-coeff linear differential equations.
- An example of the
Gram-Schmidt orthogonalization algorithm.
Also, Rotation matrices in 3 dimensions (txt);
the general orthogonal matrix.
Linear Recurrence using matrices (pdf)
solves a fibonacci-like recurrence; it makes a cryptic
reference to Jordan Canonical Form.
Its method is to attempt to diagonalize a matrix.
a 2x2 diagonalizable matrix. And
a 3x3 matrix with only 2 dimenions of eigenvalues.
powers of a diagonalizable 4x4 matrix.
Finally, here are
examples showing Trace and char-poly are preserved under conjugation.
- The Triangular Matrix Lemma
[just page 4 in JCF] (pdf),
Cayley-Hamilton Theorem (pdf).
- A glance at
projections (pdf), and the dictionary game.
vert-and-hor shears generate SL2 (pdf).
- Distance between flats (pdf),
which will eventually compute the distance between two
arbitrary flats (translated subspaces).
Should you wish a letter of recommendation (LOR) from me,
I have certain
Although I prefer that you provide an LOR waiver form
(obtained from University/firm/granting-agency that you are
here is a generic LOR waiver (pdf).
For course-grades I use
A+ A A-
. . .
D+ D D-
The Registrar rounds an
to an A, and
to an E,
but I kept track of the higher grade when I
write letters of recommendation for students.
[NOTE: Although a D-
is passing, certain
University requirements need a
minimum grade of C;
students should check with their
College or Department.]
Students should read my
[N.B: At the end of each semester, I place graded final projects/exams
in a wallbin outside my office door.
Information System (ISIS) gives each student access to his
One of the greatest labour-saving inventions of today is tomorrow.
-Vincent T. Foss
Hard work has a future payoff. Laziness pays off NOW.
Warning: Dates in Calendar are closer than they appear.
Typesetting mathematics: TeX/LaTeX/ps/dvi
- "How To Write Proofs" (html), by Prof. Larry W. Cusick,
Excellent. Examples mostly from Elem. Number Theory; some from
- Prof. Christopher Heil's page (pdf) [4 pages, INTRO].
A well written survey of the structure of proofs. Has one example of
- “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 write-up is lax in places where I am strict:
- Always use a word/phrase, and never a comma, for
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.
The faculty union.
JK Home page