Office: DeMoss Hall 3291.

Note there is a complete schedule posted further down this page which shows both office hours and my teaching schedule.

- (Math 321) Linear Algebra.
- (Math 132) Calculus II.
- (Math 495) Short Course on Topology.
- (Math 495) Lie Groups for Undergraduates.
- (Physics 231) University Physics I

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]
- 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 422) 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

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.

- The ArXiV.
- ABC Radio of NYC.
- Mark Levin page.
- mathstackexchange: a place to learn math and earn reputation.
- mathoverflow: research math questions.

- 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.
- 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.
- GeoGebra demos. another free math program to learn.
- This is how to use GeoGeobra. this website is just art, really pretty.

- 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.
- fiber bundle article, general semi-technical.
- learn this and teach me (tensor package for Mathematica)
- USF, LU decomposition page, many viewpoints, Maple, Matlab and Mathematica. Broad online resource beyond just this topic.
- I will Derive:math lyricism meets classic a pop tune.
- list of the best online math videos sphere inside-out etc...
- Qiaochu Yuan's wordpress nice expository writing about all sorts of math.
- David Prager's Hiking Blog:
- geometry of differential equations and Pfaff's Theorem.( bigger picture or see a proof of Pfaff's Theorem)

- 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.

It's endless really. Seek and ye shall find.

- many links to free online books, nicely organized.
- Calculus without limits ( for Karch)
- LEGAL free books galore.
- Edward Frenkel's webpage. links to excellent YouTube videos on advanced calculus. Note the elegant and superior use of the chalkboard at this world-class academically excellent institution.
- Multivariable Calculus by George Cain and James Herod of GA Tech.
- Multivariable Calculus Online from ETSU under a NSF grant, browser tinkering probably required.
- Videos from Multivariable Calculus from Michael Hutchings of Berkeley
- MIT's open courseware Multivariable Calculus page
- Jerry Shurman's notes from Reed College on multivariable calculus (a little beyond calculus III in places).
- Multivariable Calculus Visualization project, backed by NSF, has applets to play with.
- Tools for multivariable calculus from Rhode Island University (parametrics and sphericals).
- Eric Carlen's multivariable notes from GA Tech.
- multivariable calculus from SUNY Albany by Carlos Rodriguez, unusual comments on bivectors. Maple-based.
- 10 animations to visualize key elements of multivariable calculus. Maple-based.
- Calculus Problems and Solutions, some really nice problems on a variety of topics. From UC at Davis
- Gilbert Strang's Calculus Text from the MIT website. this is a deep and quite comprehensive look at introductory calculus.
- link to more links, the resources posted for calculus are staggering.
- click Robert Ash's Real Analysis book site
- PDF Titles nice link site, has hundreds of books.
- Introduction to PDEs Peter J. Olver's site, much to learn here!

- nice modern physics notes from a UVA professor Michael Fowler. If you want to read about special relativity or quantum mechanics from a quasi-technical standpoint this might be a good starting point.
- HYPERPHYSICS: some good students have found this a useful resource for conceptual exploration.
- Waves on a string demo: PHET project at Colorado.
- Nice page on the math and physics of various sorts of waves.
- a guide to study in theoretical physics. (superstringtheory.com is a good website for accurate info on strings from a relatively non-technical viewpoint, truth of matter is there is no purely intuitive theory of physics, we need math, a correct description is necessarily technical. If you've had my classes you know I take this viewpoint in most venues, notation is to be embraced not skirted)
- Journal of Mathematical Physics, a journal full of things I'd like to know and/or calculate.

- 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.

My thesis is in the area of supermathematics. However, recently my interests have turned to two main areas:

- generalized complex variables: (produced several talks and one paper so far)
- differential geometry of low-dimensional manifolds: (no clear project yet, just reading)

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 1-12-2016.