1. Clicking ▼&► to (un)fold the tree menu may facilitate locating what you want to find. 2. Videos embedded here do not necessarily represent my viewpoints or preferences. 3. This is just one of my several websites. Please click the category-tags below these two lines to go to each independent website.
Due to the new embedding mechanism implemented by YouTube, it becomes too difficult for me to carry on the web project on this site all by myself. I decided to stop all the scheduled editing works here for the time being. The project will resume only when a substantial help appears. This web project does need help. Please help spread the word if you can. Bye for now. Take care!
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source: James Cook 2016年1月19日
Matrix Lie Groups
You might also call this a course in Naive Lie Groups. The focus is on matrix group examples and a minimum of background in topology and manifold theory is needed. In particular, we follow Stillwell's text "Naïve Lie Groups"
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source: James Cook 2015年8月11日
Matrix Groups: crash course 2015
Here I give a series of little talks that walk you through my notes from reading Tapp's "Matrix Groups for Undergraduates". We see a good amount of detail about the complex linear matrices or quaternionic linear matrices which are special matrices of real numbers which encode the multiplication of complex or quaternionic matrices. Then, the later part of the talks outlines the rudiments of Lie Theory of Groups and Algebras in the context of matrices. Here probably too much detail is missing, so don't be discouraged if it's hard to follow. Finally we do some sight-seeing about the classification theory of compact connected Lie groups and the theory of maximal tori.
I assume the audience has some experience with manifold theory or differential geometry and a willingness to learn some group theory on the fly. Almost everything I say in these talks is also found directly in Tapp where you will also find further discussion and much more depth. Ideally, these videos might convince you to study further.
Matrix Groups: Part 1 13:42 In this talk we cover pages 1 to 4 of my notes where the K-notation for K=R,C,H is explained and the general linear group of nxn matrices over K is defined. We also begin to explain mapping which embeds nxn complex matrices in 2nx2n real matrices. Part 2 20:16 Part 3 15:26 Part 4 13:47 Part 5 16:52 Part 6 13:34 Part 7 13:47 Part 8 5:18 Part 9 21:28 Part 10 7:09 Part 11 9:12 Part 12 7:54 Part 13 25:32 Part 14 11:01
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source: James Cook 2015年3月24日
Lie Algebra: talks paired with Erdmann and Wildon's text
not much to see here. At some point I hope to make a proper series of videos. Basic Lie Algebras is one of the most interesting and pure applications of linear algebra. It's a great playground to hone your skills in theoretical linear algebra. Erdmann and Wildon's text is a good place to start.
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source: James Cook 2015年8月24日
Complex Analysis of 2015
This is the playlist for lectures captured from Math 331 of Liberty University of Lynchburg VA during the Fall 2015 semester. This course follows part of Gamelin's Complex Analysis. This introduction to complex analysis is intended for someone who has completed the calculus sequence and has some experience with proof. However, there is no real analysis prerequisite so we do not chase all the rabbits... just some. Anyway, see: http://www.supermath.info/Complex.html.
In a nutshell, we study complex number models, basic topology and limit theory in the complex plane, nth roots of unity, the complex exponential, log, sine, cosine, cosh, sinh, the CR equations and the relation of complex-linearity of the differential, holomorphic functions, conformal functions, basic idea of analytic continuation, Riemann Sphere, harmonic functions and conjugates, Green's Theorem complexified, Cauchy integral theorem and formulas, Goursat Theorem, Lioville Theorem, basic theory of complex power series, Laurent series, residue theory, techniques of complex integration, conformal mapping and fluid flow (perhaps from Fisher's text which is available as a Dover edition) , Mandelbrot and Julia set, and select topics TBD in part by interest of students.
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source: James Cook 2017年2月2日
Math 495: PDEs and Geometry
These are videos gathered from a Math 495 course I'm running in the Spring 2017 Semester. We're looking at some assorted topics which we don't usually cover in the required DEqns course then we'll turn to differential geometry in a few weeks. Many meetings I don't have a video here since we're working on a paper in this meeting time. The PDE part is largely based on Haberman's 3rd edition PDE book and the 4th edition of Nagle Saff and Snider's introductory Differential Equations text.
