James Cook's Homepage

Office: I'm stored near all the other mathematicians on the 4-th floor of DeMoss Hall.
My Fall 2012 semester office hours:

• Monday: 3:45-5:00,
• Tuesday: 8:00-8:45 and 12:05-2:05,
• Wednesday: 11:00-1:00,
• Thursday: 8:00-8:45 and 12:05-2:05,
• Friday: 3:45-5:00.

Current Teaching:

Differential Equations[teaching]

Complex Variables[teaching]

Physics I: Mechanics[teaching]

Applied Calculus[teaching]

Introduction to Classical Field Theory.[teaching]

Lecture Notes:
The files posted below are some of the lecture notes from 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,

1. Calculus I and II. Calculus II's chapters 15 , 16 , 17 , 18 , 19 were reformatted from earlier, inferior, word formatted notes.
2. multivariate calculus (pages 1-148) and multivariate calculus (pages 149-284) did not type up notes on integration or some vector derivative formulas.
3. linear algebra (2010 version) paired with Lay's text.
4. linear algebra (2009 version) paired with Insel,Spence, Friedberg's basic text.
5. advanced calculus (Fall 2011) based on Edwards, Munkrese, Burns and Gidea as well as notes from R.O. Fulp.
6. advanced calculus (Fall 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.
7. 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.
8. Mathematical Models in Physics: Relativistic Electrodynamics and Differential Forms (from NCSU)
9. complex analysis. Examples are given in the scanned version. The course went much further, these notes are unfinished.

Past Teaching:

1. College Algebra.
2. Applied Linear Algebra.
3. Linear Algebra.
4. Abstract Algebra II.
5. Transition to Advanced Mathematics.
6. Physics II: Electricity and Magnetism.
7. Introduction to Mathematical Physics.
8. Calculus I.
9. Calculus II.
10. Calculus III.
11. Advanced Calculus.
12. Topology and Geometry with Dr. Honore Mavinga (Spring 2012).
13. Advanced Classical Mechanics.
14. Supermath: an introduction.[a reminder to post something when time permits]
15. Computer Math: introduction to Mathematica.

Websites I visit:

1. WebAssign.
2. Mastering Physics.
3. MyMathLab for instructors
4. The ArXiV.
5. ABC Radio of NYC.
6. Mark Levin page.
7. mathstackexchange: a place to learn math and earn reputation.
8. mathoverflow: research math questions.

Links to websites that do the math for you:

1. Wolfram Alpha: careful, may be addictive.
2. Calculates the ref, rref, inverse and much more all while showing all the steps. very nice for problems without ugly decimals.
3. Eigenvector calculator, ugly numbers no problem. Also deals with complex case no problem. However, does not find generalized e-vectors.
4. Gram-Schmidt orthogonalizer: by Lawrence E. Turner of Southwestern Adventist University.
5. 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.
6. Behold, FREE 3D-grapher, nice resource, needs Java.
7. Riemann and other sum calculator/visualization tool.
8. GeoGebra demos. another free math program to learn.
9. This is how to use GeoGeobra. this website is just art, really pretty.
10. Mod P calculator; does modular arithmetic.
11. Conformal mapping experiments.
12. Complex exponential visualized.
13. Another nice demo for complex mapping.

Random Links:

1. AMS page for undergraduates: thinking about math gradschool?
2. journals for undergraduate research: links from BYU.gradschool?
3. how to write your first math research paper in under 5 minutes.
4. Sophisticated notes on your basic courses.
5. The "Graph" program I am fond of for creating figures in my notes.
6. Proof that the Pythagorean Theorem is false.
7. On topology and breakfast.
8. Some interesting math reading about maps of the globe.
9. radian measure, philosophy or quantitative question you be the judge.
10. fiber bundle article, general semi-technical.
11. learn this and teach me (tensor package for Mathematica)
12. USF, LU decomposition page, many viewpoints, Maple, Matlab and Mathematica. Broad online resource beyond just this topic.
13. I will Derive:math lyricism meets classic a pop tune.
14. list of the best online math videos sphere inside-out etc...
15. Qiaochu Yuan's wordpress nice expository writing about all sorts of math.
16. David Prager's Hiking Blog:
17. geometry of differential equations and Pfaff's Theorem.( bigger picture or see a proof of Pfaff's Theorem)

LaTeX (for mathematical documents):

1. just draw the symbol and it finds the LaTeX code for you, this is a nice idea!
2. the polynom-package for slick long-division in LaTeX, not w/o bugs, found error in calculus II notes as consequence.
3. LaTeX help wiki. Lot's of nice code.
4. LaTeX, more from a typesetting professional viewpoint.
5. on matrices in LaTeX.
6. LaTeX graphics, this looks tenable, start here when I try again.
7. advanced graphics tinkering in LaTeX, I'm not there yet, I may never get there...
8. LaTeX Beamer tutorial, slick LaTeX-based slides.

Online course notes and/or textbooks:
It's endless really. Seek and ye shall find.

1. many links to free online books, nicely organized.
2. Calculus without limits ( for Karch)
3. LEGAL free books galore.
4. 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.
5. Multivariable Calculus by George Cain and James Herod of GA Tech.
6. Multivariable Calculus Online from ETSU under a NSF grant, browser tinkering probably required.
7. Videos from Multivariable Calculus from Michael Hutchings of Berkeley
8. MIT's open courseware Multivariable Calculus page
9. Jerry Shurman's notes from Reed College on multivariable calculus (a little beyond calculus III in places).
10. Multivariable Calculus Visualization project, backed by NSF, has applets to play with.
11. Tools for multivariable calculus from Rhode Island University (parametrics and sphericals).
12. Eric Carlen's multivariable notes from GA Tech.
13. multivariable calculus from SUNY Albany by Carlos Rodriguez, unusual comments on bivectors. Maple-based.
14. 10 animations to visualize key elements of multivariable calculus. Maple-based.
15. Calculus Problems and Solutions, some really nice problems on a variety of topics. From UC at Davis
16. Gilbert Strang's Calculus Text from the MIT website. this is a deep and quite comprehensive look at introductory calculus.
17. link to more links, the resources posted for calculus are staggering.
18. click Robert Ash's Real Analysis book site
19. PDF Titles nice link site, has hundreds of books.
20. Introduction to PDEs Peter J. Olver's site, much to learn here!

Physics:

1. 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.
2. HYPERPHYSICS: some good students have found this a useful resource for conceptual exploration.
3. Waves on a string demo: PHET project at Colorado.
4. Nice page on the math and physics of various sorts of waves.
5. 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)
6. Journal of Mathematical Physics, a journal full of things I'd like to know and/or calculate.

Departments, Organizations and Contests:

1. NCSU department of Mathematics.
2. 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.
3. American Mathematical Soceity.

Fall 2012 Meetings:
Each of these meetings was fairly local to Lynchburg. Several students attended these meetings with me last semester. In addition, the math department organized a trip to the MAA conference which was attended by about half our department. Maybe we'll find a meeting in Spring 2013... ask if interested.

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

Links of interest to past and present students:

Old NCSU webpage, many solutions posted.

Previous LU course webpages

Research and Personal Interests:
Current work with undergraduates: This summer/semester I intend to investigate two questions:

1. generalized complex variables: with Bailu, Minh and Spencer
2. supermanifolds with Kryptonite? with Spencer

For the most part, the work on generalized complex variables is not new. Quaternions, bicomplex numbers, Clifford Analysis all bump into our investigation and these subjects have a rich and lengthy history.

Wikipedia article on dual numbers

split complex numbers from Wikipedia

Clifford Algebras from Wikipedia

In any event, I hope we can add some new insight in our approach. If we can clarify our current work in the next week or two then I hope to present the generalized complex variables project together with Minh and Spencer at the SUMS meeting at JMU in late September. Our project uses primarily linear algebra and a few basic ideas from advanced calculus. It involves replacing traditional numbers with some sort of number which is abstractly related to the real numbers.The abstract numbers have the structure of a real, finite-dimensional, vector space over the real numbers.

In contrast, the project about supermanifolds requires background in real analysis, linear algebra, abstraction, advanced calculus and manifold theory. However, it also relies at it's base on the concept of replacing the real or complex number system with grassmann numbers. The difficulty arises from the fact our grassmann numbers are infinite dimensional over the reals. Instead of finite-dimensional vector space we must deal with an infinite-dimensional Banach space.

Tentative reading (working on access, put these here to remind me...)

1. click invertibility of elements over infinitely generated BG algebras,1990
2. click cayley hamilton for supermatrices, 1994
3. click super cayley hamilton equation, 1999
4. click meaning of anticommuting variables, 1987
5. click DeWitt supermanifolds and infinite ground rings, 1989
6. click deformations of SRS, 1992
7. click DEqns, Frobenius theorem, local flows, 1985
8. click add to differential analysis in infinite diml. spaces, 1986
9. click glimpse at infinite diml holomorphy, 1974
10. click foundations of complex analysis, a google book link, 2003
11. click theory of operator algebras, 1997, a book.
12. click superanalysis II, integral calculus, 1984
13. click survey of hypercalculus, 2011
14. click geometric nonlinear functional analysis, 2000
15. click early grassmann paper, 1970
16. click hypercomplex analysis, 2009

From previous semesters: My apologies to the undergraduate who reads through the pages linked below. There is a fair amount of jargon mixed in 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 (testbetter@yahoo.com).

1. My Thesis
2. Talk at AMS meeting at NCSU, Raleigh NC, April 5 2009
3. 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.
4. Some motivations for supermathematics from physics.
5. How I first learned of supersymmetry
6. Superfields; some technical motivations for supermathematics from physics.
7. Noncommuative superspace (digression from other items)
8. Random physics topics I enjoy.
9. Supermath, just the math. (good source of open problems for ambitious undergraduates in math)
10. An invitation.

DISCLAIMER:
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 1/2013.