Trigonometry | 
 enlarge | Authors: I.m. Gelfand, Mark Saul
Publisher: Birkhaeuser Boston
Category: Book
List Price: $29.95
Buy New: $22.36
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Rating:  7 reviews
Sales Rank: 42844
Media: Paperback
Edition: 1
Pages: 229
Number Of Items: 1
Shipping Weight (lbs): 0.7
Dimensions (in): 8.9 x 6 x 0.5
ISBN: 0817639144
Dewey Decimal Number: 516.242
EAN: 9780817639143
Publication Date: June 8, 2001
Availability: Usually ships in 1-2 business days
Condition: BRAND NEW
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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 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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| Customer Reviews: Read 2 more reviews...
 A fascinating treatment of trigonometry. September 24, 2004
N. F. Taussig (Bronx, NY)
46 out of 49 found this review helpful
This text, which is designed as a supplement to a trigonometry course, is noteworthy for the clarity of its explanations, the connections it draws between trigonometry and other mathematical topics, its many challenging problems, and its numerous worked and illustrated examples. Of particular interest are the appendices to the later chapters in which the authors relate trigonometry to Pythagorean triples, use sequences of trigonometric functions to approximate pi, and introduce Fourier series.
After reviewing the geometry of the triangle, the authors cover right triangle trigonometry, the relationship between trigonometry and the geometry of the triangle, unit circle trigonometry, trigonometric formulas and identities, graphs of trigonometric functions, and inverse trigonometric functions. The authors make every effort to explain why the results hold and how to use them. Rather than presenting a self-contained treatment, the authors make every effort to connect trigonometry with other branches of mathematics, thereby providing the reader with many fascinating insights.
The problems are designed to be challenging. The reader who diligently studies the numerous worked examples in the text and works through the problems will acquire considerable knowledge of the subject. Solutions to the problems are not provided in the text.
I also highly recommend the other texts in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Functions and Graphs (Dover Books on Mathematics).
Terrific! October 6, 2006
Clifford Stoll (Berkeley, CA United States)
25 out of 29 found this review helpful
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 first half of the sine curve is exactly 2?"
Aaah. Now *that's* a great trig book!
Outstanding Math Text June 14, 2006
L. D. Rafey (Ft. Walton Beach, FL)
29 out of 35 found this review helpful
I rarely compose reviews even if I happen to really appreciate a book. But THIS is one of those rare exceptions!Gelfand (who also happens to rank among the 20th Century's most renowned and prolific Mathematicians ... I noticed that no reviewer has mentioned this little fact) has written an exceptionally clear and concise, easy to read and to digest text concerning Trigonometry with advancement to higher education in mind. The perfectly logical format and development is novel, very inspiring, coaxing the reader to read on and on and one truly begins to learn right from the first sentence. The reader requires little in the way of prior knowledge and yet, I am convinced, will come away with an enthusiasm for this subject (and hopefully for Mathematics in general).
I am a member of a Mathematical Honor Society and of the Mathematical Association of America but I must confess that I was a poor math student, had some very poor teachers and, thanks to some inspiring individuals along the way, managed to discover the real magic and beauty of Math before it was too late (although I have spent the better portion of my professional life compensating for the failures of my former teachers!).
This text represents the way Math should be taught in schools. I believe that any frustrated math student will benefit from this text (and probably the other texts also by Gelfand).
Innovative, clear, well written trigonomety textbook April 6, 2007
George C. Johnson (Gainesville,Georgia)
4 out of 6 found this review helpful
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 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.
Trigonometry is all about triangles! August 20, 2008
Benjamin R. Rimmer (Minneapolis Minnesota)
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.
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