James Cook's Homepage
Office: I'm stored near all the other mathematicians on the 4-th floor of DeMoss Hall.
Note there is a complete schedule posted further down this page which shows both office hourse and my teaching schedule.
Linear Algebra (MATH 321)
Differential Equations (MATH 334)
University Physics I (PHYS 231)
Special Topics in Elementary Differential Geometry (MATH 497).
- College Algebra.
- Applied Calculus
- Applied Linear Algebra.
- Linear Algebra.
- Abstract Algebra II.
- Transition to Advanced Mathematics.
- University Physics I
- Physics II: Electricity and Magnetism.
- Introduction to Mathematical Physics.
- Calculus I.
- Calculus II.
- Calculus III
- Advanced Calculus (2009).[needs update, have revised course twice since then]
- Complex Analysis
Special Topic 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.
[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).
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,
Websites I visit:
- Calculus I and II. Calculus II's chapters
19 were reformatted from earlier, inferior, word formatted notes.
- My calculus III notes contain many pictures and hand-written calculations. These tend to make the files bigger. For students taking Math 231, there is a master file which has a table of contents which navigates the file. That feature is lost as I divide these for better download size. If you are my student then please save a copy of the file posted in Course Content for your convenience as the semester progresses.
- multivariate calculus (pages 1-28)
- multivariate calculus (pages 29-39)
- multivariate calculus (pages 40-53)
- multivariate calculus (pages 54-82)
- multivariate calculus (pages 83-90)
- multivariate calculus (pages 91-107)
- multivariate calculus (pages 108-121)
- multivariate calculus (pages 122-132)
- multivariate calculus (pages 133-148)
- multivariate calculus (pages 149-160)
- multivariate calculus (pages 161-174)
- multivariate calculus (pages 175-202)
- multivariate calculus (pages 203-217)
- multivariate calculus (pages 218-230)
- multivariate calculus (pages 231-242)
- multivariate calculus (pages 243-257)
- multivariate calculus (pages 258-284)
- multivariate calculus (Ch. 6: integration a)
- multivariate calculus (Ch. 6: integration b)
- multivariate calculus (Ch. 6: integration c)
- multivariate calculus (Ch. 7: vector 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. Have not typed notes for Laplace transforms and PDE material at this time.
- The ArXiV.
- ABC Radio of NYC.
- Mark Levin page.
- mathstackexchange: a place to learn math and earn reputation.
- mathoverflow: research math questions.
Links to websites that do the math for you:
- 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.
- Behold, FREE 3D-grapher, nice resource, needs Java.
- Riemann and other sum calculator/visualization tool.
- GeoGebra demos. another free math program to learn.
- This is how to use GeoGeobra. this website is just art, really pretty.
- Mod P calculator; does modular arithmetic.
- Conformal mapping experiments.
- Complex exponential visualized.
- Another nice demo for complex mapping.
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:
- 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.
- 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.
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.
Fall 2013 Meetings:
- (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.
Spring 2014 Meetings:
It is likely we will attend the MAA-local section meeting is at James Madison University April 25-26.
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 hope the generalization of the Laplace equation due to Spencer is actually a new idea in this study, but I'm not entirely certain of that at this time and date (8-17-2013).This summer (2013) I worked out several general proofs which are not included in the report with Spencer/Minh/Bailu, I hope to write those up sometime this semester (Spring 2014) and at minimum post it on the ArXiV. Bailu and I discovered new examples and a possible future direction for the project in Fall 2013, we hope to continue as time permits in Spring 2014.
- 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 I may be ready to sheperd a student in this direction by Spring of 2014. 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 1-12-2013.