James Cook's Homepage
Office: DeMoss Hall 3291.
Note there is a complete schedule posted further down this page which shows both office hours and my teaching schedule.
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.
- OLD (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
Independent Study Courses:
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.
[Daniel Freese and Jess Gregory, Spring 2016] studied elementary topology from Manetti's text, contraction mappings and existence theorems from Chapter 13 of Nagel Saff and Snider's DEqns text, and then we spent a few weeks discussing manifolds. At the conclusion we studied a bit about supermanifolds. See this video record of our meetings
[Daniel Freese and Bradley Hoogerwerf, Spring 2016] studied matrix Lie groups. We started with Stillwell's Naive Lie Group text, but, after a few weeks we transitioned to working through the first few chapters of Hall's Lie Groups, Lie Algebras and Representations. Playlist of our meetings .
[Daniel Freese, Fall 2015] plan to study A-calculus in depth to continue and refine work initiated with Bailu Zhang.
[R.M. Shumate, Spring 2015] plan to study topology from Munkres and Elementary Differential Geometry from Oneill.
[Bailu Zhang, Fall 2014] we are studying Cartan for Beginners by Thomas and Ivey as we hope to add some depth to our previous work on the calculus of A-algebras.
Spring 2014 I taught a special topics course on Elementary Differential Geometry from Barrett Oneiil's text. There were 7 students. Unofficially, Minh Nguyen worked on Lee's text on Smooth Manifolds and he gave an introductory talk on Coarse Geometry.
[Jesse Keyton, Fall 2013] Introduction to Topology (mostly Dr. Skoumbourdis' work here)
[Jesse Keyton and Michael Shumate] Abstract Linear Algebra.
[Spencer Leslie, Spring 2013] Introduction to Classical Field Theory. (actually, we only got to fiber bundles and connections, classical field theory is a bit past where we got). Spencer turned his focus to measure theory with Professor Skoumbourdis and a project in analytic number theory with Professor Ethan Smith.
[Spencer Leslie, Fall 2012] Supermath: an introduction. Worked through the basics of supermathematics including superanalysis and supermanifold theory.
[Spencer Leslie, Spring 2012] Topology and Geometry with Dr. Honore Mavinga (Spring 2012). (actually, I just listened to the topology in here, Professor Mavinga did the teaching from Willard's Topology text, then we covered several chapters from Conlon and in the start of the summer we worked through some Riemannian geometry from Burns and Gidea's text.)
[Scott Taylor, Spring 2010] Advanced Classical Mechanics (we looked at Saletan's Classical Mechanics, but then we diverged into Cantwell's text on Symmetry and Differential Equations).
Older Lecture Notes and Special Discusssions:
The notes below are older versions.
Websites I visit:
- Calculus I and II. Calculus II's chapters
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
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.
Links to websites that do the math for you:
- 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.
LaTeX (for mathematical documents):
- 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)
Online course notes and/or textbooks:
- 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!
Departments, Organizations and Contests:
- 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.
Past Meetings with Students:
- 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.
Links of interest to past and present students:
Old NCSU webpage, many solutions posted.
Previous LU course webpages
Research and Personal Interests:
My thesis is in the area of supermathematics. However, recently my interests have turned to two main areas:
In summer 2012 some meetings with Minh Nguyen prompted the intiation of the research project on the calculus over an algebra. After numerous meetings with Minh, Spencer joined us in about July of 2012. Finally, a bit later Bailu joined in an did some explorations with Maple. In total I'm pleased with the result our group found and it is to be published in a Springer conference proceeding which documents some of the reports given at The 8th Annual UNCG Regional Mathematics and Statistics Conference, Saturday, November 3, 2012. In short, we solved the problem to our satisfaction for any associative semi-simple algebra over the real numbers. Much of what we discovered was known to researchers in the 1950's and we were pleased to discover good agreement. We believe the generalization of the Laplace equation due to Spencer is actually a new idea in this study.Bailu and I have developed material beyond the publication and I hope to complete and extend the (currently unpublished 8-14-15) material during the Fall 2015 semester with the help of Daniel Freese.
- generalized complex variables: (produced several talks and one paper so far)
- differential geometry of low-dimensional manifolds: (no clear project yet, just reading)
For future students I have several questions from our study of calculus on associative algebra which are still open. I have no clear questions for diffential geometry at this time, but if you are interested in that direction of study we can probably find something to work on. If you are interested in undergraduate research (with me) then visit me sometime so we can talk about your background and future plans. Thinking beyond work at LU, it's wise to seek an REU (Research Experience for Undergraduates, funded by the NSF) as soon as possible, don't assume you need all the math courses. There are some REU's that seek students who are between Freshman and Sophomore year. In recent years, we've had math students participate in REU-type programs at Penn State and NCSU.
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.
From previous semesters: My apologies to the undergraduate who reads through the pages linked below. There is a fair amount of jargon mixed into some of them. I would be happy to explain in more detail any item or phrase you find curious. To the expert who is for whatever reason bored and perusing this site I welcome corrections and/or questions via email (email@example.com).
- 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 firstname.lastname@example.org, Thanks.
Last Modified 1-15-2017.