Which Textbooks Were Your Most Memorable?

[andytoh]

I asked my differential geometry professor, and he said Spivak's Calculus on Manifolds and Dugundji's Topology. He said those books gave him the foundation that shaped him into what he is now.

Please mention your most inspiring textbooks, which you swear by to this day.

 

[andytoh]

"Elementary Topology" by Gemignani. Not very well-known, nor advanced. But it is the textbook that I read long time ago that made me finally realize that I love math. The book is too easy for me now, but it has great sentimental value for me.

"Tensors and Manifolds" by Wasserman will probably be my bible for the future--I haven't finished it yet.

 

[3trQN]

I didn't have a maths textbook until recently (and I am in my late 20's), which is "Practical Techniques by Jordan & Smith".

I have Calculus made easy by Thomson which is just fun fun to read, not at all like a standard text.

Having studied chem a bit i think "Phys Chem P.W.Atkins" was my book of preference there, never was a huge fan of organics.

 

[mathwonk]

spivaks calc on manifolds also formed, as a full time teacher in 1971 or so, the basis for my understanding of advanced calc, but it was courant's diff calc vol1 that lifted me as a college freshman in 1960, into the higher level of math once and for all, after a first glimpse in high school from allendoefer and oakleys "principles of mathematics".

I also like Mumfords first three preliminary chapters ("redbook") on algebraic geometry, and Beauville's Complex Algebraic Surfaces.

but mostly i only began to really learn math at an advanced age (about 32) when i was already a little beyond the level of textbooks and more into learning from professors. I read a lot of textbooks by Widder, Lang, Rudin, Royden, Halmos, Zariski, Herstein, Artin, Munroe, Spanier, Ahlfors, Kamke, Hausdorff, Hilbert, ... preparing for research, but I didn't understand them. Grad school at Brandeis and later Utah, was eye - opening.

So I never really learned anything from a textbook that even approximates what I got from live teachers like Herb Clemens, David Mumford, Phillip Griffiths, Boris Moishezon, Hugo Rossi, Robert Seeley, Ron Stern, Maurice Auslander, Alan Mayer, Bernard Teissier, Arnaud Beauville, Robert Varley, Pete Bousfield, Ed Brown Jr., Johnny Wahl, Mike Schlessinger, Lynn Loomis, David Kazhdan, Frans Oort, Mike Artin, Robin Hartshorne, John Tate, Raoul Bott, Mike Spivak, Paul Monsky, Ken Chakiris, Bob Friedman, Dave Morrison, Ron Donagi, Barry Mazur, Janos Kolla'r, Miles Reid, Heisuke Hironaka, and many others (Enrico, Maurizio, Fabrizio, Fabio, Sevin, Gerald, ...).

A human being who understands the subject can often tell you more in one sentence than you can get from reading a whole chapter of a book.

 

[mathwonk]

i also like euclids elements, goursats course in analysis, and anything by arnol'd, e.g. his diff eq books.

 

[mathwonk]

recall the words of niels abel, "study the masters, not the pupils".In this vein, I recommend the worlds best precalculus book, Euler's "Introduction to the Analysis of the Infinite".

 

[MadScientist 1000]

I would say Baron's Guide to Calculus and Baron's Guide to Trignometry, which I studied from in 7th grade.

 

[mathwonk]

which is more or less the opposite to my advice, and abels.

 

[andytoh]

Different people have different tastes and different levels of study.

MadScientist's popular-type books are what gave him the greatest leap in mathematical understanding and appreciation in his youth. Those easy books might not be suitable for him anymore, but they are what assisted him the most during his development in math.

My "Elementary Topology" by Gemignani is too easy for me now, but it has great sentimental value for me, for it was what look me from the boring life to mathematical heaven.

 

[MadScientist 1000]

Hey! I still am in 8th grade... You speak of me as if I am some 150 year old guy...

By the way, much of Euler seems outdated. It seems much more logical for me to not go very deep into Euler and make Minskowi Geometry a long term goal of mine.

 

[mathwonk]

young mad scientist, you cannot simutaneously claim youth and foolishness and also disdain the advice of your elders. If you have the moxie to tell a senior research scientist his recommendations are "outdated", even though you apparently have not read them, you have to take your chances.

to put it simply, euler is a lot less outdated than barron's trigonometry.

 

[complexPHILOSOPHY]

I love you, mathwonk!

I am new to mathematics so my favorite texts so far is, Herstein's "Topics in Algebra" (recommended to me by you beautiful PFers) and Fraleigh's "A First Course in Abstract Algebra". I have only recently started working through them but I am finding that I really enjoy the elegance and beauty behind the logic of algebraic systems. Fraleigh is a larger book and slightly less advanced than Herstein's, however it covers roughly the same topics and has a lot of diagrams and pictures which is good for my introduction to algebra. Herstein is full of content and brilliant logic which I can't wait to start to understand more deeply.

A passion for theoretical physics made me want to do math but my exposure to abstract mathematics has developed a new passion for pure math itself (perhaps as much as my passion for physics).

 

[mathwonk]

well i can understand that, as i have often inspired strong emotions, but it seems to date those wishing to rend me limb from limb still outnumber those finding me lovable.

 

[redrzewski]

I'm a big Shankar fan.

https://www.amazon.com/dp/0306450356/?tag=pfamazon01-20

As well as his Quantum Mechanics book are extremely well written and insightful.

(I look at physics as a great way to learn lots of cool math).

 

[neurocomp2003]

Perko's DE and DynSys, GaryFLakes CBN, Lewis Theory of Computation, Bondy's Graph Theory, O'Rourke' Computational Geometry. Bauer and Nobel: ODEs

 

[DeadWolfe]

Birkhoff and Maclane's Modern Algebra was memorable, as was anything by Artin I've ever read.