Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1)
by Tom M. Apostol
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Book Summary Information
Author: Tom M. ApostolEdition: Hardcover
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1967-06
ISBN: 0471000051
Number of pages: 666
Publisher: Wiley
Book Reviews of Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1)
Book Review: A Bona Fide Masterpiece ... With One Reservation.
Summary: 4 Stars
The name above should read: Old-Time Math HOBBYIST!
Sorry about that! Oh, the vagaries of aging ... to the review of Apostol One:
Oh, the memories!
Young mathematicians, kindly grant an old-timer the license of your tolerance. I thank you in advance for your patient forebearance. Sigh, ... the memories ... good ones, to be sure:
The time ... Autumn 1973. The place ... The University of Chicago. The event ... Yours truly in "Mathematicians' Calculus Class" ... ! Back then, they did not call it Honors Calculus, as I believe they do today. Also, it was The U of C, rather than UChicago, as it is now.
Then, as now, you arrived at The U of C and spent your first week of orientation taking placement tests. By some unbelievable miracle, I placed into The U of C's very tippy-top math class for entering freshman. Most of my classmates had a perfect 800 SAT math score. The few that did not have the perfect 800 had like a 790, 780, 770. Hey, close enough, right? Me? Not in that league. I got by on determination alone and nothing else. There were only two sections of this class, and each section had no more than 15 people in it. The point is that only the best of the best of the best even qualified to sit in that class in the first place.
Back then, they used Apostol for that class. Nowadays, I believe, they use Spivak; however, I'm not entirely sure about that.
Anyway:
This book was then, and remains today, a veritable GEM for anybody truly and intensely interested in mathematics for its own sake and not merely as a tool to use for some profession or another. That's why they (The U of C Mathematics Faculty) called our class "Mathematicians' Calculus Class," and, again, Apostol One was the textbook they chose for that class.
Tom Apostol of Caltech wrote the definitive introductory calculus book FOR MATHEMATICIANS back in 1966. When I studied from it, it had only been out for 6-7 years or so and was only used at no more than six mathematics departments in the entire country. I believe they used Apostol Volume One (We didn't know it as Tommy 1 a way back when) at Caltech (of course!), Princeton, The U of Chicago, I believe at Michigan. I'm not sure of the other place or two. It's been nearly 40 years.
The Chairman of the U of C Mathematics Department back then chose this book, because he and the faculty truly believed that:
This is THE CALCULUS BOOK for anyone aspiring to become a mathematician and, indeed, a pure rather than an applied mathematician.
The writing is clear and concise. The treatment is rigorous. The emphasis is on proofs. The problems range from a little challenging to hard as hell.
Those of you with a true gift for mathematics (If you are using this text you have been deemed to have that gift, or you would not be using it for your class, I assure you!), will relish reading this fine classic in mathematical didactics.
Notice, I only gave Apostol One four stars and listed a reservation in the title to this review. Here's why:
This book is TECHNICALLY BRILLIANT ... BUT !!! ... it is rather a bit dry, as most mathematics texts seem to be. (Parenthetically-speaking, IMHO, the driest and most terse of all such books is Walter Rudin's "Analysis" [The shortened title!])!
What, indeed, does Apostol One lack?
THE PASSION, PROSE AND PURITY of teaching offered to us by Professor Spivak! Spivak veritably scintillates with excitement! That empassions its readers! THIS is how to teach mathematics ... and any other subject for that matter. The purists will not approve of Spivak's delivery and will prefer Apostol's. Hey, live and let live, I say. I'm cool with that. To each their own. Personally, I genuinely believe that Spivak's passionate (albeit literary) approach to teaching is the way to go.
The ultimate calculus book intended for aspiring mathematicians would be, IMO, an admixture of both Apostol One and Spivak that blends the best features of both tomes into one supremely marvelous course text!
Said book, to my knowledge, does not yet exist. The solution? Why, read BOTH Apostol One AND Spivak, of course!
Lastly, our sophomore-year text for "Mathematicians'-Track Mathematics" at The U of C back in The Day was, you guessed it, Rudin's "Analysis." Yawn ... !
All in all, Professor Tom Apostol's Calculus, Volume One, is truly a masterpiece. Buy it. Read it. Love it.
Be aware of one caveat, however: This book is aimed at a mathematically-sophisticated audience; i.e., students who have either genius-level intellects or lots of mathematics experience.
The determined non-genius can read this book and genuinely benefit from it by dint of determination. I am that kind of person myself. If I can enjoy it, many of you can too ... provided that you have either the genius or the determination. I got by on the latter. You can too: "Ya gotta wanna!" If you do, you're in for a real treat with Apostol One.
Thanks again, young mathematicians, for putting up with the ramblings of this old-timer. Down the line, when I finally do retire, I'm going to study the bejeeziz out of these wonderful mathematics books just for the ever-lovin' hell of it ... and have a stone-cold blast doing so! Sooner than you think, you, too, will be along in years and have very fond memories of things like this. Trust me, you really will. You'll see.
Happy Mathematics for many years to come. My best to all of you. Read and enjoy this book. Tell a friend about it too. I salute you!
U of C Old-Timer
More Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) reviews:
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