Linear Algebra Internet Archive

[Desiderato Chouinard]

Thistextbook is a comprehensive united course in linear algebra and analytic geometry based on lectures read by the author for many years at various institutes to future specialists in computational mathematics.

It is intended mainly for those in whose education computational mathematics is to occupy a substantial place. Much of the instruction in this speciality is connected with the traditional mathematical courses. Nevertheless the interests of computational mathematics make it necessary to introduce large enough changes in both the methods of presentation of these courses and their content.

One place to start, if you are an undergrad, is Miles Reid's book Undergraduate Algebraic Geometry. Not everyone likes it, but I do, and routinely recommend it to both undergrads and beginning grad students.

(By the way, I work in algebraic geometry, arithmetic geometry, modular forms, elliptic curves, and related topics mentioned in the comments above. I think that viewing things as difficult, or the most difficult, etc., area of math is not very helpful. If you are interested in something, and motivated to learn it, try learning it! Just keep your common sense about you, make sure you do well in your regular classes too, and ideally find a nearby faculty member, grad student, post-doc, or even just more experienced undergrad to act as mentor. Also, although algebraic geometry, once it gets going, relies on other areas of math for background, including various areas of algebra, topology, and geometry, you can try getting into it directly, and then use it as motivation to learn something about those other areas.)

I guess it is technically possible, if you have a strong background in calculus and linear algebra, if you are comfortable with doing mathematical proofs (try going through the proofs of some of the theorems you used in your previous courses, and getting the hang of the way you reason in such proofs), and if you can google / ask about unknown prerequisite material (like fields, what $k[x, y]$ stands for, what a monomial is, et cetera) efficiently...

...but you will be limited to pretty basic reasoning, computations and picture-related intuition (abstract algebra really is necessary for anything higher-level than simple calculations in algebraic geometry).

Both of these books are designed to be easy on the reader when it comes to prerequisites, unlike most other books who are written for "pros", a.k.a. "people with a lot of background in Abstract Algebra". I think / hope that your knowledge in Calc. + Linear Algebra is enough for this to get you going (but be warned, it might be pretty hard to understand all the new concepts in one go, so take it easy :) ).

In the nineteenth century there were various expansions of the traditional field of geometry through the innovations of hyperbolic geometry, non-Euclidean geometry and algebraic geometry. Hermann Grassmann was one of the more advanced innovators with his anticipation of linear algebra and multilinear algebra that he called "Extension theory" (Ausdehnungslehre). As recounted by David E. Rowe in 2010:

At the Summer meeting of the American Mathematical Society on August 15, 1894, Schlegel presented an essay on the problem of finding the place which is at a minimum total distance from given points.[3]

My grandfather had a PhD in math. When he died, he left a lot of math textbooks, which I took. These include things like Van der Waerden's 2-volume algebra set from the 1970s, "Studies in Global Geometry and Analysis" by Shiing-Shen Chern, a series called "Mathematics: it's content, methods, and meaning," and many more.

I'm keeping about 20 of them, but there are 103 which I don't want to keep, but which I don't know what to do with. I obviously don't want to throw them away, and I don't really know what will happen to them if I donate them to the giant used-books depository in downtown Baltimore (called "the book thing," where people drop off and pick up used books for free). I'd like to donate them to some math collector or math library. But maybe there are just too many used antique math books floating around.

David, Older mathematics books can be surprisingly rare.

An option is to sell them on Advanced Book Exchange (abe.com). I would be happy to help you triage your books. I did this once for the daughter of a philosopher who had a large mathematics book collection. It did not take long on the telephone. Dan

If any of them are out of copyright, the internet archive (www.archive.org) might want to scan them to put them online. There are lots of other scanned math books on the site right now. I really love this one even though I can't read any of it:

I would suggest scanning them all and donate them to "the" "internet" book library (for example, a thepiratebay.se); many people would be grateful and the legacy of your father shall be preserved. And one hopes that the laws shall eventually change so that it becomes legal (and maybe is already legal in some countries)..

You're still in Eugene, right David? I'd take your books (or the list of books) up to Powell's bookstore in Portland to see what they think. They'd probably be happy to buy many of your books as long as they're not too common. They have a pretty serious technical books collection and as far as I can tell they make a lot of money selling rare math books on-line.

Another option would be to have an auction in Eugene, say, in the math department lounge. The Cornell math library used to auction off their old duplicate books that were no longer in frequent circulation. I got some really nice books for cheap at those auctions.

Except for purely local transactions, shipping cost is always a major concern in dealing with individual books or small collections (more so outside the US). But the market for advanced mathematics is limited everywhere, so be selective. It's true that most public or college libraries have too little shelf space and staff to deal with questionable freebies. I've often given away surplus books at all levels to colleagues and students, but there is no way to guarantee that these are really used. Some I've given away have on the other hand wound up being sold, as I later learned.

People stop by faculty offices here regularly and offer cash for current sellable editions of elementary textbooks; they pay well but are definitely picky. Even that market is changing rapidly due to e-books and the like.

If you haven't sold all of these books, i might be interested in purchasing some of them from you. I am a math major in college and planning on getting a PhD in Math. Currently i am building a library of math books. Thanks!

I'd like to install the Eigen3, which is a C++ template library for linear algebra. It should be available on a website link but strangely, I cannot open it. Is the website link broken, or is something wrong with my browser? I tried using Bing and Firefox but neither of them worked.

In the meantime you should still be able to get started, you can access the main pages on Internet Archive's Wayback Machine, e.g. the latest snapshot of the homepage can be found here, and you can still access the source code on github.

Electronic Journal of Differential Equations

Publishes research related to differential equations and their applications (ODE's, PDE's, integral equations, functional differential equations, etc.)

Electronic Journal of Linear Algebra

A publication of the International Linear Algebra Society (ILAS), publishes mathematical articles on matrix analysis and the various aspects of linear algebra and its applications

Journal of Nonlinear Science

Publishes papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena

Notices of the American Mathematical Society

The membership journal of the American Mathematical Society

AMS web account required

The function concept is a central idea of precalculus and beginning calculus and is used for modeling in the sciences and engineering, yet many students complete courses in precalculus and calculus with weak understandings of this concept. Students who are unable to construct meaningful function formulas to relate two varying quantities have little chance of responding to novel applied problems, or understanding key ideas of calculus such as derivative, accumulation and the Fundamental Theorem of Calculus. I will share data that reveals how students might construct these and other critical reasoning abilities and understandings for learning calculus. I will share the research developed Pathways Precalculus student materials and teacher resources that provide the context for this research, and are resulting in large gains in student learning of the function concept and other foundational ideas for learning calculus. Results from using Pathways materials at 5 large universities will be shared and contrasted with other popular approaches to teaching precalculus mathematics.

We consider swarm pursuit-evasion dierential games in the Euclidean plane where an evader is engaged by multiple pursuers and point capture is required. All the players have simple motion la Isaacs and the pursuers are faster than the evader. It is shown that in group/swarm pursuit, when the players are in general position, capture is eected by one, two, or by three critical pursuers, and this irrespective of the size N (> 3) of the pursuit pack. Thus, group pursuit devolves into pure pursuit by one of the pursuers, into a pincer movement pursuit by two pursuers, or cornering by three pursuers, who isochronously capture the evader, a mnage trois. The solution of the Game of Kind is obtained and critical pursuers are identified. Concerning the Game of Degree, the players' state feedback optimal strategies are synthesized and the Value of the game is derived.

Teaching mathematics for social justice centers mathematics as a tool for understanding the sociopolitical forces that shape the world around us. It addresses complex and sometimes controversial real-world issues (especially those related to economic and racial justice) through open-ended investigations. This approach to teaching is sometimes criticized as not being rigorous enough; and some also believe that mathematics is neutral and should not deal with controversial issues. In this talk, I will argue that addressing social justice issues in mathematics courses is timely and important; and that it can be rigorous and result in significant learning both of mathematics and the issues investigated. I will share examples of activities, assignments, and projects I have developed and used, and give some recommendations for beginning and sustaining this work.

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