Can anyone suggest pre algebra book for beginner. Would like to see something more than the worksheets offered online. I would prefer a book which would teach strong fundamentals concepts about beginning algebra. I would like to add it is for my kid who started middle school.
[Math] Pre Algebra book Recommendation
algebra-precalculusbook-recommendationreference-request
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The classic reference is David Hestenes' New Foundations for Classical Mechanics which is by one of the early developers of geometric algebra.
You may find it easier to learn geometric algebra from Geometric Algebra for Physicists by Doran and Lasenby though (I certainly did). The link is to a sample version of chapter 1.
A reference that I've never looked at is Geometric Algebra for Computer Science which details the geometric algebra approach to computer graphics, robotics and computer vision.
As for prerequisites - certainly some familiarity with linear algebra. For the 'geometric calculus' component a first course in multivariable calculus would be sufficient. Since the big developments in geometric algebra in the 1980s were by physicists, many of the examples tend to be physically motivated (spacetime algebras, relativistic electrodynamics etc) and a passing familiarity with (special) relativity, rigid body dynamics and electromagnetism would be useful (though certainly not essential).
Although I couldn't provide the sequence you request, I can point two references that can be of great help in gaining a bic-picture view of higher mathematics: The Princeton Companion to Mathematics and Mathematics: Its Content, Methods and Meaning.
Here is a description of the first out of Tim Gowers's web page:
"This is a book I am editing with the help of June Barrow-Green and Imre Leader, which could be thought of as "Mathematics: A Very Long Introduction". It has the aim of being a genuinely useful reference work in mathematics. This is a difficult aim, since mathematics is hard enough to explain at the best of times, and even more so if one has limited space. Is there any point in trying to summarize algebraic geometry in ten pages, for example? Probably not, but the articles in the PCM don't try to summarize , so much as to provide an initial overview and perspective. I like to think of them as "prequels" to textbooks -- things you would read to get an idea of why you were bothering to learn some concept that your lecturer seems to take for granted is interesting. Strenuous efforts have gone into making the book as accessible as possible, which I hope will have been worth it when it comes out, all going well, some time in the first half of 2008."
Hopefully that sounds enticing. (The second book runs somewhat along the same lines).
You mentioned OCW resources, I am sure you will know how to use those after you've gained your motivation and are ready to dive right into the subjects!
Best Answer
From the Chicago Undergraduate Mathematics Bibliography:
Gelfand/Shen, Algebra
Gelfand/Glagoleva/Shnol, Functions and graphs
Gelfand/Glagoleva/Kirillov, The method of coordinates
These three little white books come from the Soviet correspondence school in mathematics, run by I. M. Gelfand for interested people of all ages in the further reaches of the USSR. Rather than trying to be artificially "down-to-earth" in the way Americans do, Gelfand simply assumes that you can understand the mathematics as it's done (and avoids the formal complexities mathematicians are inured to). YSP and SESAME give these out by the carload to their students, who mostly love them. TMoC is notable for its intriguing four-axis scheme for making flat graphs of $\Bbb R^4$. Overall a fresh, inspiring look at topics we take for granted, and a good thing to recommend to bright younger students or friends (or parents!)
Cohen, Precalculus with unit circle trigonometry
[Rebecca Virnig] I used this book in high school and absolutely loved it. It's very skimpy on proofs, and really should not be used for that sort of insight. However, in terms of understanding how to apply various mathematical concepts it's wonderful. It has a large number of graphs, examples, and easy reference tables. It covers all the algebra, trig, and cartesian geometry that any good high school math sequence should deal with. I have used it for years as a reference book (e.g., what exactly is Cramer's rule again...) Solutions to a number of the problems are in the back, and the problems are not entirely applications.