I am not currently employed as a residential professor at a university. However, I intend to maintain this page and perhaps add a course when I find a little time...

I'm putting together a little minicourse on spectral graph theory.

I'm hosting these pages to assist with Math 530 and Math 510 at Liberty University. Ideally these courses serve students seeking an MAT degree with a Mathematics concentration.

I only include teaching here,

- Abstract Algebra II: Playlist on You Tube: and Course Website.
- Topology and Analysis: Playlist on You Tube: and Course Website.
- Calculus II: Playlist on You Tube: and Course Website.
- Linear Algebra: Playlist on You Tube: and Course Website.

These papers result from work done in conjunction with undergraduates in recent years.

- Introduction to A-Calculus. This introduces A-Calculus and covers the basic theory of differentiating and integrating with respect to an algebra variable.
- Theory of Series in the A-Calculus and the N-Pythagorean Theorem with Daniel Freese. This paper covers the abstraction of calculus II to A-Calculus.
- Introduction to the Theory of A-ODEs with Nathan BeDell. Covers abstraction of main calculational techniques in real DEqns to the A-Calculus. Here we actually derive new ways to solve problems I teach in Math 334.

- Doing Algebra over an Associative Algebra by Nathan BeDell.
- Logarithms Over a Real Associative Algebra by Nathan BeDell.
- Generalized Trigonometric Functions over Associative Algebras by Nathan BeDell.

- The ArXiV.
- mathstackexchange: a place to learn math and earn reputation.
- mathoverflow: research math questions.
- News streamed from California (12-3pm EST).
- My You Tube Channel (has playlists for most recent courses I've taught).
- easy way to save You Tube videos. feel free to save mine, I care not.

The files posted below are lecture notes from some previous courses that I've taught. I usually update the course notes each time I teach. I post these here for reference sake. My apologies for the errors. If you would like the source LaTeX for these notes feel free to ask, I'm happy to share, my email is jcook4 at liberty.edu.

- Elementary Differential Geometry:[summer 2015, 1/3 done]
- Linear Algebra [notes for Spring 2015]
- Guide to Gamelin [notes on Complex Analysis from Fall 2014]
- More than Complex Variables [notes on Complex Analysis from Fall 2018 in which I did some A-Calculus]
- Multivariable Calculus [notes from Calculus III (updated Fall 2014)]
- Differential Equations [notes updated Spring 2014]
- Differential and Integral Calculus of One Variable [notes for Calculus I (updated Fall 2013)]
- Advanced Calculus [notes from Fall 2013]
- Applied Linear Algebra [notes from Math 221 from Fall 2012]
- Oldschool Calculus I and II [notes from Calculus I and just the first part of II (updated Fall 2011)]
- Transition to Advanced Mathematics [notes from Spring 2009]
- Mathematical Models in Physics [notes from Ma 430 at NCSU]

- (Math 121) College Algebra.
- (Math 221) Applied Linear Algebra.
- (Math 321) Linear Algebra.
- (Math 421) Abstract Algebra
- (Math 422)(2017) Abstract Algebra II
- (Math 422)(2009) Abstract Algebra II.
- (Math 200) Transition to Advanced Mathematics.
- (Physics 231) University Physics I
- (Physics 232) Physics II: Electricity and Magnetism.
- Introduction to Mathematical Physics.
- (Math 126) Applied Calculus
- (Math 131) Calculus I.
- (Math 132) Calculus II.
- (Math 231) Calculus III
- (Math 334) Differential Equations (MATH 334)
- (Math 307) Number Theory.
- (Math 497) Special Topics in Elementary Differential Geometry.
- (Math 331) Complex Analysis
- (Math 332) Advanced Calculus
- (Math 495) Special Topics in Geometry
- (Math 450) Math Capstone Course.

If a student wishes to learn material past the standard core course at my school and it happens that their interest aligns with my own then I try to set up a Math 495 course with an appropriate title. In order to justify such a course the student needs to have a very solid academic history.

The notes below are older versions.

- Calculus I and II. Calculus II's chapters 15 , 16 , 17 , 18 , 19 were reformatted from earlier, inferior, word formatted notes.
- Calculus III: multivariate calculus.
- Lecture Notes for Applied Linear Algebra (2012 version)
- linear algebra (2010 version) paired with Lay's text.
- linear algebra (2009 version) paired with Insel,Spence, Friedberg's basic text.
- advanced calculus (Fall 2011) based on Edwards, Munkrese, Burns and Gidea as well as notes from R.O. Fulp.
- advanced calculus (2009-2010) based on Edwards primarily with more focus on applications, included chapter on variational calculus. Missing examples found here. These notes were compiled from one offering of the course as well as several independent studies given in subsequent semesters.
- (2013)advanced calculus, DEqns, manifolds a series of discussions with several students over the summer "break" DEqns and limits Multivariate MVT Contraction Mapping, Newton's Method tensors, wedges, multilinear algebra tensors remix, differential forms manifolds and tangent spacesthese conversations partly inspired the 2013 revision of the Advanced Calculus course.
- (2010)advanced calculus with some analysis from Rosenlicht's Introduction to Analysis text. From a focused hybrid 332/422 course with a student who went on to graduate school.
- Mathematical Models in Physics: Relativistic Electrodynamics and Differential Forms (from NCSU)
- complex analysis. Examples are given in the scanned version. The course went much further, these notes are unfinished.
- differential equations (first order ODEs, n-th order problem, systems, series) also concerning the connection between Green's functions and the transfer function.

- Sage: when in Sage mode you can't be stopped. Notice, you can do Sage online without installing anything locally.
- Wolfram Alpha: careful, may be addictive.
- Calculates the ref, rref, inverse and much more all while showing all the steps. very nice for problems without ugly decimals.
- Eigenvector calculator, ugly numbers no problem. Also deals with complex case no problem. However, does not find generalized e-vectors.
- Gram-Schmidt orthogonalizer: by Lawrence E. Turner of Southwestern Adventist University.
- matrix multiplier: it's ok, but, has annoying adds
- complex number polar form finder: it's ok, but, has annoying adds
- automatic algebra website by Daniel R. Collins: check your skill under time pressure. Fun!
- cycle notation generator by James Hamblin (check notation against your text before getting too carried away)
- subgroup lattice and cayley table generator, by John Jones, I have crashed it before, but usually it's a great resource.
- euclidean algorithm for integers thanks to W.J. Cook of Appalachian State U. (aka Bill)
- euclidean algorithm for polynomials thanks to W.J. Cook of Appalachian State U. (aka Bill)
- phase plane plotter for autonomous system of ODES: pplane plotter, nice and simple
- slope field plotter, via geogebra, beautiful
- Riemann sums illustrated (also visualizes other things if explore)
- really nice calculus III graphing applets, includes some vector fields along a surface as well as cross-sections. This is the best I've seen of this type.
- parametric plotter needs flash, worked for me 8-8-17.
- 3D-plotter pretty, allows number of different plotting methods and can add vector fields etc... lots of options.
- GeoGebra demos. another free math program to learn.
- This is how to use GeoGeobra. this website is just art, really pretty.

- paper on Killing's work: by J. Coleman
- generatingfunctionology: by Herbert S. Wilf
- A Russian Teacher in America: Andrei Toom's amazing criticism of modern "education"
- Five Stages of Accepting Constructive Mathematics: Andrej Bauer
- Lockhart's Lament: on the abuse of math.
- some quotes pulled from Edward Frenkel's "Love and Math".

- Gudermannian function the "transcendent angle" a less known bridge between complex and hyperbolic functions
- Jacobi's Formula: differentiating determinants and such...
- Rigged Hibert Space: as in, it's not fair, nature is rigged
- phasors: not the dangerous kind
- Smith normal form: how to make row reduction harder, add column operations...
- finitely presented abelian groups Chapter 10 Christopher Cooper's really clear notes.
- homogeneous equation over system of equations on ring: a basic module theory calculation.
- when is there just units or zero divisors Question by Bill on Math Overflow
- link to online copy of Lam's Lectures on Modules and Rings, a Springer GTM
- geometry of differential equations and Pfaff's Theorem.( bigger picture or see a proof of Pfaff's Theorem)
- introductory survey of supermanifolds lots of helpful insights.
- Question and Answers about multivariable calculus and differential forms
- The local functors of points of supermanifolds: L. Balduzzi, ,C. Carmeli, R. Fioresi
- Venn Diagrams Wikipedia article with some interesting history and context for Venn Diagrams.
- Venn Diagrams and Circles from the Math Stack Exchange
- Big List of Fun Almost Facts: see the first answer. It is based on the IE formula.

- problem lists nice set of problems on wide range of math
- AMS page for undergraduates: thinking about math gradschool?
- journals for undergraduate research: links from BYU.gradschool?
- how to write your first math research paper in under 5 minutes.
- Sophisticated notes on your basic courses.
- The "Graph" program I am fond of for creating figures in my notes.
- Proof that the Pythagorean Theorem is false.
- On topology and breakfast.
- Some interesting math reading about maps of the globe.
- radian measure, philosophy or quantitative question you be the judge.
- I will Derive:math lyricism meets classic a pop tune.
- list of the best online math videos sphere inside-out etc...
- David Prager's Hiking Blog:
- Singapore Math: a review by Cathy Duffy. This curriculum I recommend if you are serious about teaching your kids math. It is not easy much like most things worth doing.

- overleaf website (formly writelatex.com) this website is amazing. Although a local installation is faster, this allows us to share and jointly edit LaTeX documents.
- just draw the symbol and it finds the LaTeX code for you, this is a nice idea!
- the polynom-package for slick long-division in LaTeX, not w/o bugs, found error in calculus II notes as consequence.
- LaTeX help wiki. Lot's of nice code.
- LaTeX, more from a typesetting professional viewpoint.
- on matrices in LaTeX.
- LaTeX graphics, this looks tenable, start here when I try again.
- advanced graphics tinkering in LaTeX, I'm not there yet, I may never get there...
- LaTeX Beamer tutorial, slick LaTeX-based slides.
- Tikz introduction article: would be nice to learn...

- NCSU department of Mathematics.
- VT math contest, we need participants for the fall, contact me if you're interested. It just takes a Saturday morning and it's a great experience for any serious upperclassman in math.
- American Mathematical Soceity.

If you are interested in attending a local math meeting sometime this semester please let me know. I don't go as often now since the universities travel policy now requires me to rent a car rather than drive my own. Anyway, if you ask early enough we may find the time to make a trip a reality. Usually the department goes to the MAA meeting each Fall or Spring.

- (PaNTS XVIII): Palmetto Number Theory Series at Wake Forest University September 15-16, 2012.
- (SUMS)Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University on Saturday, September 29, 2012
- (MAA) The Mathematical Association of America Maryland-District of Columbia-Virginia Section, October 26-27, 2012.
- The 8th Annual UNCG Regional Mathematics and Statistics Conference, Saturday, November 3, 2012.
- (MAA) The Mathematical Association of America Maryland-District of Columbia-Virginia Section, November 1-2, 2013.
- (AMS/MAA) Joint Math Meetings, Atlanta Georgia, January 3-7, 2017.

My thesis is in the area of supermathematics. However, recently my interests have also turned to hypercomplex analysis which I refer to as A-Calculus. Projects I'm currently working on:

- a paper on inequalities in A-Calculus with Khang Nguyen
- a text on supercalculus in collaboration with R.O. Fulp
- a solution to various inverse problems in A-Calculus with Professor Elifalet Lopez Gonzalez
- a paper on elementary differential equations with William J. Cook of Appalachian University

I should mention, I do have many questions in supermathematics. However, you need to take all the required courses at LU before we can even properly begin to develop background so we can then discuss the questions. So, this means it is a rare student who has the option to attempt this. Ideally, I'll find some free time to distill the questions down to a form which doesn't require all the background. Sadly, at the moment, I am not there. So I recommend the other questions for the time being.

- My Thesis
- Talk at AMS meeting at NCSU, Raleigh NC, April 5 2009
- Talk at Mid-Atlantic Algebra Conference at NCCU, Durham NC, April 21 2007 The links below contain some rough comments about the topics which occupied my attention in graduate school in physics and math.
- Some motivations for supermathematics from physics.
- How I first learned of supersymmetry
- Superfields; some technical motivations for supermathematics from physics.
- Noncommuative superspace (digression from other items)
- Random physics topics I enjoy.
- Supermath, just the math. (good source of open problems for ambitious undergraduates in math)
- An invitation.

The content and opinions expressed on this website are not necessarily those of Liberty University. For more information as to the expressed opinions, beliefs and foundational core values of Liberty University one may consult the official website for details. The primary purpose of this site is to provide my students (and myself) with a permanent easy to find archive of coursework done under my supervision. Also, it serves as an advertisement for my math/physics research hence the site name. Any questions, comments or clarifications may be sent to testbetter@yahoo.com, Thanks.

Last Modified 5-4-2020.