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Type of bind: Paperback
Dewey Decimal Number: 516.242
EAN num: 9780817639143
ISBN number: 0817639144
Label: Birkhäuser Boston
Manufacturer: Birkhäuser Boston
Quantity: 1
Page Count: 229
Printing Date: June 08, 2001
Publishing house: Birkhäuser Boston
Sale Popularity Level: 209371
Studio: Birkhäuser Boston
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Product Description:
Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. Like other I.M. Gelfand treasures in the program—Algebra, Functions and Graphs, and The Method of Coordinates—Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike.
From a review of Algebra, I.M. Gelfand and A. Shen, ISBN number 0-8176-3677-3:
'The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.... [The authors] have shown how to write a serious yet lively book on algebra.'
—R. Askey, The American Mathematics Monthly
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Rated by buyers 
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So I bought this book for some Trig class I signed up for at the last minute. I didn't know what to expect. I skimmed through the book and saw triangles everywhere. I figured that a few triangles should not be so difficult to figure out- the measurements and all. It's a skimpy little book, but there sure is a lot of info crammed in there. I studied hard. I had dreams of triangles floating around, suspended in the air. I could not get triangles off my brain. Day and night- triangles and more triangles. I think I just got sick of looking at triangles come final exam, because I went out and got hammered to get them off my mind just hours before the exam. I'm not BSing you either. To make a long story short, I took the exam while under the influence of alcohol. It worked, the booze got the triangles off my brain, but the timing was not good because I had to think about triangles in order to finish the darn exam. I had a perfect GPA until that Trig exam. I did manage to pull off an A- on the exam, which surprised the heck outta me. Now I try to not let triangles get the best of me anymore. I'm angry at them, but at the same time I understand them. Triangles deserve respect. Don't be boozin' before an exam. This was a good book and I recommend it highly. But some advice first; don't be square and let the triangles shape your mind- think outside the box and you'll do fine, circle the correct answers if you can, and come at problems from different angles.
Rated by buyers 
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Don't waste your time. It's books of this sort that bring disinterest and sleep to the eyes of teenaged minds. To think that the work of Euclid (now freely available on Google Books) has degenerated to this third-hand rendition of the foundation of natural existence is awe-inspiring. Like all other books in this class, the discusion never connects the reader to the idea that the symbolization of the relationships of the orientations of the boundaries of certain forms are universal and utterly fundamental. Instead, we get tossed a few line drawings, graphs, number types mixed with graphic symbols, and condescending ministration on whether we got it right or wrong. The author's idea of connecting trigonometry to other fields of math is to state profound meanings like "trigonometry is a part of precalculus, and is related to other precalculus topics". In one exercise, the author commands: "Using a protractor, measure the angles of the triangle as accurately as you can. Do your measurements add up to 180 degrees? Let us now turn our attention to circles." The missing parts of the discusion being: 1) Who invented the protractor? 2) Why do protractors always work, or do they? 3) Why bother measuring with a cheesy plastic nomograph when its the RELATIONSHIP that's of primary importance? 4) Should I be all OCD about measuring accurately because that's what Trigonometry is all about? 5) My measurements don't entirely add up to 180, why is that? 6) Why 180 degrees, and not 37 lurkmons, and can't I make up my own system of relationships? 7) Then what makes the relationship of orientation of certain extensions or boundaries universal? 8) How is it possible to add numbers to shapes, or did you just miss out on presenting to me a massive chunk of the development of the arithmetization of geometric thought? 9) Why are we doing all this? Is there a progression of thought process involved or should I just keep memorizing an apparently jumbled collection of methods extracted from all modes of mathematical approach at face value? 10) Is this a thinking sort of course? Or do I just follow instructions like a drone? Naaah... Let's just skip to circles. No wonder people despise how math is taught, and also, the teacher.
Rated by buyers -
The book is well written with clear descriptions, many examples and plenty of diagrams. The book also contains a large number of exercises and therein lies my gripe. There are absolutely NO SOLUTIONS. For self study this is of little use and I have had to revert to the Schaum's Outline for Trigonometry for practice. Two stars is perhaps a bit harsh but I think it important that potential purchasers notice that no solutions are provided for any of the exercises.
Rated by buyers -
I enjoyed this textbook, especially the way some subjects were so well explained. Not only does this text cover a good bit of material, but it also reveals the way in which the author thinks about this subject. I have noticed, both with this text and the previous two which I have commented on, that certain aspects of the subject become much more transparent or understandable when reexamined with a keener mathematical ability than, at least I possessed, when I was very first exposed to these subjects in high school. I had no special interest in math at that time. The limited reexposure one has to trigonomety and geometry as one learns new areas of mathematics in college doesn't seem to do justice to these foundation areas of math.
Rated by buyers -
Finally - a trig book that doesn't talk down to students. Gelfand treats his readers as intellegent, curious, and competent. This goes far ... especially with kids.
Most other trig books are written by educational consultants who view the subject as a odorous swamp that you have to slog through. They distract the reader with glitzy graphics and useless photos. No such chartjunk here. It's from someone who loves the subject, and places the mathematics first.
I feel like an avuncular mathematician is showing me the delights of trig ... indeed, he seems to revel in sines, cosines, and tangents. Several of the problems have tickled my 10 year old son: "Dad! Did you know that the area under the very first half of the sine curve is exactly 2?"
Aaah. Now *that's* a great trig book!
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