Goto: Prof. King's page at Univ. of Florida.
Or: JK Homepage.

Modified:
Friday, 12Nov2021
Printed:
Friday, 21Jan2022

Page:
http://squash.1gainesville.com/Include/thispage.shtml

See the Teaching Page for Usually Useful Pamphlets.

Sets & Logic. Guides students on how to read/produce proofs, learning some of the language of modern Mathematics. My section will focus on problem-solving; both Putnam and USAMO problems will be used as examples. Both

(theoretical) Linear Algebra. Matrices, determinants, Gauss-Jordan algorithm, eigenvalues/vectors, matrix diagonalization, various matrix decompositions.

Sets and Logic, 2021Autumn.

Guides students on how to read/produce proofs, learning some of the language of modern Mathematics. My section will focus on problem-solving; both Putnam and USAMO problems will be used as examples.

Intro/Elem. Complex variables . How is complex differentiability connected to power-series expansion?

Sets and Logic. Guides students on how to read/produce proofs, learning some of the language of modern Mathematics. My section will focus on problem-solving; both Putnam and USAMO problems will be used as examples. Both

Elem. Differential Eqns.

Linear, separable, autonomous DEs, intro to Differential Operators,
for the bright, motivated, hard-working student. Time permitting, we'll
introduce the *Matrix Exponential* as a way of solving interconnected
linear DEs.

Prospective DiffyQ students
should **seriously review** High-School mathematics
(eqns of lines, parabolas; quadratic formula; sum of a geometric
series)
before or during Add/Drop.

Sets and Logic, 2020Autumn.

Two sections, taught online due to COVID-19.

Guides students on how to read/produce proofs, learning some of the language of modern Mathematics. My section will focus on problem-solving; both Putnam and USAMO problems will be used as examples. Both

Sets and Logic, 2020g.

Elem. Differential Eqns, 2020g

Linear, separable, autonomous DEs, intro to Differential Operators,
for the bright, motivated, hard-working student. Time permitting, we'll
introduce the *Matrix Exponential* as a way of solving interconnected
linear DEs.

Prospective DiffyQ students
should **seriously review** High-School mathematics
(eqns of lines, parabolas; quadratic formula; sum of a geometric
series)
before or during Add/Drop.

Abstract Algebra 1 . An introduction to

Sets and Logic, 2019t.

Number Theory & Mathematical Cryptography .

This is a special topics course and is only offered once every 3 years or so. Also... NT&Math-Crypto counts as an Upper-division math-elective.

Elem. Differential Eqns., 2019g.

Sets and Logic . Helps students to read and produce proofs, and learn the basic language of modern Mathematics.

Elem. Differential Eqns. Linear, separable, autonomous DEs, intro to Differential Operators, for the bright, motivated, hard-working student. Time permitting, we'll introduce the Matrix Exponential as a way of solving interconnected linear DEs.

Number Theory 1, of Summer-B 2018. Modular arithmetic, Chinese Remainder Thm, Legendre/ Jacobi symbols, Quadratic reciprocity, Fermat's SoTS thm, Lagrange 4-square thm, overview of Multiplicative Fncs.

Combinatorics II:

Continuing with *Graph Theory*,
proceeding to *Generating-Functions*, followed by some more advanced material.
Depending on student interest, we may cover some Combinatorial Game Theory.

Elem. Differential Eqns. Linear, separable, autonomous DEs, differential operators, for the bright, motivated, hard-working student. Possibly, the Matrix Exponential method for solving interconnected linear DEs.

Combinatorics I: Methods of counting, enumeration, bijective proofs.

The 1^{st} semester (Autumn)
will progress up to Graph Theory.

The 2^{nd}
semester (Spring 2018)
will start with *Generating-Functions*, continue with Graph Theory,
and some more advanced material.
Depending on student interest, we may cover some Combinatorial Game Theory.

Elem. Differential Eqns. Linear, separable, autonomous DEs, intro to differential operators.

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 modern Mathematics.

[Sabbatical in Autumn 2016.]

On sabbatical in Autumn 2016.

Number Theory 1, of Summer-B 2016. Modular arithmetic, Chinese Remainder Thm, Legendre/ Jacobi symbols, Quadratic reciprocity, Fermat's SoTS thm, Lagrange 4-square thm, basic cryptography (Diffie-Hellman, RSA). Assumes no previous knowledge of Number Theory.

(theoretical) Linear Algebra. Matrices, determinants, Gauss-Jordan algorithm, eigenvalues/vectors, matrix diagonalization, various matrix decompositions.

Number Theory & Mathematical Cryptography .

(theoretical) Linear Algebra. Matrices, determinants, Gauss-Jordan algorithm, eigenvalues/vectors, matrix diagonalization, various matrix decompositions.

Elementary Differential Equations MAP2302 section 5609 : Beginning differential eqns for the bright, motivated, hard-working student.

Elementary Differential Equations MAP2302 section 4689 : Beginning differential eqns for the bright, motivated, hard-working student.

There will be a test of prerequisite knowledge on Friday, 23Aug..

Sets and Logic. Helps students to read and produce proofs, and learn the basic language of modern Mathematics. There will be a test of prerequisite knowledge on Friday, 23Aug..

Combinatorics II , will start with the clever notion of Generating Functions.

Number Theory & Cryptography . This course is an introduction to coding theory in general, and Mathematical Cryptography in particular. It does not assume a previous Number Theory course, only asking that the student do a bit of reading before the semester begins. (The webpage has a few suggestions.)

Combinatorics I , with many methods of counting. Note: I give test of prerequisite knowledge during Add/Drop. A practice exam is on our webpage.

Calculus III Careful treatment of multi-dimensional calculus. Note: I give test of prerequisite knowledge during Add/Drop. Our webpage has a practice exam.

Euclidean Geometry. A proof-based course covering a superset of: Theorems on Triangles (centroid, in-center, circum-center, ortho-center, Euler-line, Simson-Line), circles (Central-angle thm, Power-of-a-point), ruler/straightedge contructions and dissections of polygons. Matrix multiplication will be introduced for easy descriptions of transformations preserving Euclidean theorems. Time permitting, elem. Projective Geometry will be introduced, since many PG thms are also EG thms.

Sets and Logic. Helps students to read and produce proofs, and learn the basic language of modern Mathematics. There was a test of prerequisite knowledge on Wedn, 11Jan.; our webpage has a practice exam.

(theoretical) Linear Algebra. Matrices, determinants, Gauss-Jordan algorithm, eigenvalues/vectors, matrix diagonalization, various matrix decompositions.

Sets and Logic . Helps students to read and produce proofs, and learn the basic language of modern Mathematics.

Modern Analysis II . The continuation of a full-year course in Real Analysis. Time permitting, we will learn some Ergodic Theory (dynamical systems) this semester. Its undergrad number is

Number Theory & Mathematical Cryptography: [

Modern Analysis I . A full-year course in Real Analysis. It uses the highly-regarded

Baby Rudintext. Time permitting, I hope to discuss a bit of Ergodic Theory (dynamical systems) in the 2

(Abstract) Linear Algebra .

Calculus II . Careful treatment of 1-dimensional calculus, with emphasis on Taylor's theorem and Taylor series.

Ergodic Theory

Ergodic Theory

Sets and Logic . Helps students to read and produce proofs, and learn the basic language of modern Mathematics.

Advanced Calculus for Engineers and (Physical) Scientists [ACES] Introductory Real Analysis on Euclidean Spaces. One might say that it is

Advanced Calculus (Theoretical) [ACT] Introductory Real Analysis on Metric Spaces. For students who plan to do graduate work in mathematics, this is the AdvCalc course to take.

Abstract Algebra 1 . An introduction to

Sets and Logic . Helps students to read and produce proofs, and learn the basic language of modern Mathematics.

Number Theory & Elliptic Curve Cryptography
is an undergraduate Special Topics course which is also appropriate for
graduate students who have not had extensive Number Theory.
This course does **not** require
MAS4203 as prerequisite. All that is necessary is some
preparatory reading
from a free online NT text.
What we cover will be partly determined by *students' interests*.

The central theme is Number Theory and codes of various kinds:
Diffie-Hellman protocol,
Huffman coding,
Ziv-Lempel,
Meshalkin isomorphism code,
Elliptic Curve Codes.
We will discuss various algorithms, such as
*repeated-squaring*,
and Shank's
*Baby-step Giant-step* method for computing a Discrete logarithm.

Computational Linear Algebra . Matrices, determinants, Gauss-Jordan algorithm, eigenvalues/vectors, matrix diagonalization, various matrix decompositions.

My section of this course will have a **test of prerequisite
knowledge** on
Monday, 27Aug2007.
The course webpage has a *Sample Exam*.

Number Theory 1, of Spring 2007. Modular arithmetic, Chinese Remainder Thm, Legendre/ Jacobi symbols, Quadratic reciprocity, Fermat's SoTS thm, Lagrange 4-square thm, basic cryptography (Diffie-Hellman, RSA). Assumes no previous knowledge of Number Theory.

Computational Linear Algebra . Matrices, determinants, Gauss-Jordan algorithm, and various matrix decompositions.

Number Theory 2 & Cryptography: A continuation of my NT1 with an emphasis on Mathematical Cryptography. Course NT1 is

Advanced Calculus This is an introductory Real Analysis course. One might say that it is "Calculus done right", with rigorous definitions and proofs. If time permits, we'll do an introduction to Metric Spaces.

Introduction to Number Theory, 1 , Spring 2006. This course is an introduction to elementary number theory. It assumes no previous knowledge of number theory.

Numbers & Polynomials . Textbook:

Moore Method, meaning that students prove all theorems, with enlightened guidance from the Professor.

(theoretical) Linear Algebra . MAS4105.

Abstract Algebra 1 An introduction to Groups, Rings and Fields.

For the academic year Autumn 2004 through Spring 2005 I was on Research Leave.

Prof. King will be on Research Leave for Autumn2004-Spring2005 and will not be teaching. (He does plan to be present!, working on a writing project.)

Probability & Potential Theory 2 MAP6473 MWF 7 in FLO100. (Griffin-Floyd Hall.)

Elementary Differential Equations MAP2302 section 3145 : Beginning differential eqns for the bright, motivated, hard-working student.

Probability & Potential Theory 1 MAP6472 MWF2 in LIT217.

Calculus III Careful treatment of multi-dimensional calculus.

Abstract Algebra 1 An introduction to Groups, Rings and Fields.

Elementary Differential Equations Beginning differential eqns for the bright, motivated, hard-working student.

Numbers&Polynomials Axioms of the real-number-system. Class is run Moore-method, with students collaborating to find the proofs.

Honors Calculus III Careful treatment of multi-dimensional calculus.