Math books I'm glad I bought


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Math books I'm glad I bought

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Fev 17, 2017, 4:11 pm

Title: Probability on Trees and Networks
Author: Russell Lyons and Yuval Peres
Publisher: Cambridge University Press
Publication Date: 2016
Content: This is a research monograph in an area of advanced probability that doesn't just involve constructing complicated abstract arguments to justify something that seemed intuitively true to begin with. Many of the results are rather unexpected. The book does rely on measure-theoretic probability, but the results and discussion seem like they would be largely accessible to someone without that background. Within its area, the book appears to be encyclopedic. The authors are prominent specialists and skilled expositors. This book is available for free in electronic form on the authors' website.

Physical Description: The book is a thick hardback with a glued (but, at this moment, unbroken) binding. There are lots of illustrations that seem to have been printed very precisely. The printing, in general, and the paper used are both excellent.

Fev 17, 2017, 4:29 pm

Title: Mathematics of Quantization and Quantum Fields
Author: Jan Derezinski and Christian Gerard
Publisher: Cambridge University Press
Publication Date: 2013
Content: I acquired this book during my search for the Holy Grail of a details-oriented quantum theory book that is wholly acceptable to mathematicians. It's more advanced than many others that I've acquired during this quest, so it may end up sitting unread on my shelf for a long, long time, but we'll see. I used camelcamelcamel to alert me to when the Amazon price of this book dropped to about 25% of its usual price, so it doesn't represent a huge financial investment. (It's amazing how much Amazon pricing for a book varies over time.)

Physical Description: The first copy sent to me by Amazon had a torn dustcover. The replacement copy Amazon sent had its cloth binding pretty well bashed in on one corner, but I've got better things to do with my time than continually rewrapping books and taking them to the UPS Store, so I kept it. (I wonder if this was Amazon's passive-aggressive way of getting back at me for getting a bargain!) Glued binding, nice paper, sharp printing (but maybe a wee bit on the light side).

Fev 17, 2017, 4:46 pm

Title: Mathematics: The Loss of Certainty
Author: Morris Kline
Publisher: Oxford University Press
Publication Date: 1980
Content: What's the proper word for Kline? Gadfly? Contrarian? Anyway, he was a mathematician who was quite critical of the mathematics profession. In general, I find that there's often something to be gained (besides the undeniable entertainment value) from controversial works. On my third or fourth scouring of OUP's website searching for something, anything, to buy during their 40% off sale in December, I settled on this book. I'm only up to about the dawn of the Enlightenment in my reading so far; I think things will get juicier when we get to around 1900.

Physical Description: Evidently printed on demand. The printing is kind of muddy, but I find that more palatable for cheap narrative works like this than for expensive works of technical mathematics.

Editado: Fev 17, 2017, 7:31 pm

Title: Numerical Recipes : The Art of Scientific Computing
Author: William H. Press
Author: Brian P. Flannery
Author: Saul A. Teukolsky
Author: William T. Vetterling
Publisher: Cambridge University Press
Publication Date: 1986
Content: This book saved my life so many times during my professional life that I long ago lost count. This is the original book, and all the examples are in FORTRAN, with the PASCAL translations as an appendix in the back. At the time it was published, you could send away for a floppy disk to get either set of code. When a later version with examples in C was published, I rushed to get the floppy disk of that as well.

Physical Description: Hardcover. I'm the original owner, and it's been treated with respect.

Several others to be added are included here:, for my own reference. What an excellent idea for a thread!

Fev 17, 2017, 7:27 pm

Title: The Mathematical Theory of Communication
Author: Claude E. Shannon
Author: Warren Weaver
Publisher: University of Illinois Press
Publication Date: 1949
Content: This small publication was responsible for the beginnings of the world as we know it. Everything, from information theory, and entropy, to communication theory, started here. Claude Shannon was one of the rare human beings that I am in awe of.

Physical Description: Original was painstakingly photocopied from a library book. Second copy purchased a few years ago, in paperback form.

Fev 20, 2017, 11:35 am

Title: Introduction to Metamathematics
Author: S. C. Kleene
Publisher: Van Nostrand
Publication Date: 1962
Content: One of the best individually-run math websites is Peter Smith's website In addition to a well-maintained blog and material related to his various books, Smith has put together a "Teach Yourself Logic" guide which includes reviews of many logic books. The first book listed in the guide's appendix on "Big Books" is Kleene 1952 (of which my 1962 copy is a reprint). Smith's praise for this book was the last straw that got me to buy it. I've only just started it, but it seems pretty neat.

Physical Description: Last year, I bought a near fine copy used for about $70. Even with 50 years of aging, it is so much more beautiful than a typical 2017 Springer math book that it is a cause for celebration (thinking of the past) or mourning (thinking of the future).

Fev 20, 2017, 11:40 am

>4 Lyndatrue: "What an excellent idea for a thread!"

Thanks. It's a shame that this group has been so quiet for so long. The more contributions the merrier! (And not everyone has to have the same bee in their bonnet about the physical book that I do!)

Fev 21, 2017, 4:43 pm

Title: The Probabilistic Method
Author: Noga Alon and Joel H. Spencer
Publisher: Wiley
Publication Date: 2016
Content: Roughly speaking, the Probabilistic Method proves the existence of a mathematical object (usually combinatorial or number-theoretical) by proving rigorously that it has positive probability of existing. It is one of those curious examples of how an indirect approach to a mathematical problem can sometimes end up being the most convenient. (Detouring into the complex plane to calculate certain definite integrals of real-valued functions of real variables is another prominent example.) This book and its previous editions have about 1600 citations on Mathematical Reviews, which is quite high. The contents are quite accessible to non-specialists.

Physical Description: This is the sore spot. I bought the new 4th edition. It has inferior paper and inferior printing to the third edition, which was practically a work of art. The really puzzling thing is that the authors seem to have reverted to some klunky-looking pre-TeX mathematical typesetting system. Did Donald Knuth run over their dog? Did they unintentionally agree to promote some low talker's inferior mathematical fonts (instead of a puffy shirt)? It looks worse than my Masters Thesis that was done three decades ago using an ancient copy of Microsoft Word. I guess if you're an expert you need to have the latest edition, so you have access to the incremental improvements. For everyone else: Buy a used copy of the 3rd edition. You'll be glad you did.

Fev 22, 2017, 1:12 pm

Title: Group Theory in a Nutshell for Physicists
Author: A. Zee
Publisher: Princeton University Press
Publication Date: 2016
Content: Part of the big Princeton series "<Some Area of Physics> in a Nutshell", although this is really a math book. Zee would strongly emphasize that this book is written for (prospective) physicists, not (prospective) mathematicians. His preface and footnotes are fun, and so far there haven't been any physical arguments that have baffled me the way some of them did in his "Einstein Gravity" book. And as I said in #3, I do find some controversies to be entertaining.

Physical Condition: Big hardback book. Sewn binding. Typical Princeton quality. (Good.) Sharp printing using the Scala LF fonts (that I think sacrifice some readability to look artsy).

Fev 22, 2017, 1:41 pm

Title: Symmetry and the monster : one of the greatest quests of mathematics
Author: Mark Ronan
Publisher: Oxford University Press
Publication Date: 2007.
Content: "Prologue", "1. Theaetetus's Icosahedron", "2. Galois: Death of a Genius", "3. Irrational Solutions", "4. Groups", "5. Sophus Lie", "6. Lie Groups and Physics", "7. Going Finite", "8. After the War", "9. The Man from Uccle", "10. The Big Theorem", "11. Pandora's Box", "12. The Leech Lattice", "13. Fischer's Monster", "14. The Atlas", "15. A Monstrous Mystery", "16. Construction", "17. Moonshine", "Notes", "Appendix 1: The Golden Section", "Appendix 2: The Witt Design", "Appendix 3: The Leech Lattice", "Appendix 4: The 26 Exceptions", "Glossary", "Index".

About the classification of finite groups. And quite a bit about Conway and the way math is done in the fast lane.

Fev 23, 2017, 10:26 am

Title: Rigor & Structure
Author: John P. Burgess
Publisher: Oxford University Press
Publication Date: 2015
Content: I think most mathematicians can't "connect" with most books on the philosophy of mathematics. The books are too technical for mathematicians to appreciate, or uninteresting to them, or insufficiently related to what they care about. I myself have been working through The Oxford Handbook of Philosophy of Mathematics and Logic for eons; I see it sitting on the shelf, read a couple of pages, wonder what it meant, and put it back on the shelf for another couple of months. Rigor & Structure is not at all like that. The whole book is very interesting and closely related to a mathematician's work. At the same time, it is taken seriously enough by the philosophy community to have triggered lots of lengthy reviews.

Physical Condition: Cloth cover, glued binding. No complaints.

Fev 23, 2017, 12:17 pm

>4 Lyndatrue: >7 cpg:

Agree, great thread. Not sure when I'll get around to posting the few books that qualify for the thread, but I'm liking what I see here already. The Shannon text in >5 Lyndatrue: looks really promising, as I'm keen on cybernetics. But Burgess's Rigor & Structure is up my alley, as well. I'm going to have to be on guard when I enter this room, I can see that now.

Jan 4, 2018, 10:13 am

Title: I Want to be a Mathematician: An Automathography
Author: Paul R. Halmos
Publisher: Springer Verlag
Publication Date: 2010

This book was released in 1985, but my copy is a crummy print-on-demand 2010 reprint with low-resolution text, muddy photographs, and an instantly-broken glued binding. Despite its physical defects, I'm glad I acquired my copy, because this is a fantastically good read. Halmos was one of those famous Hungarian mathematicians, but he immigrated to the USA as a young teenager in 1929, so he missed out on most of the drama of Hitler and WWII, and he was thoroughly an American at heart. This autobiography is jam-packed with math gossip and strong opinions and encounters with scores of the 20th century's top mathematicians. It will make more sense to professional mathematicians than amateurs, but even the latter have a good chance of finding it enjoyable.

Ten years after Halmos died, 7 logicians published a curious article in an ostensible research journal criticizing Halmos for being insufficiently respectful of logicians, so apparently not everybody is a Halmos fan.

Set 4, 2018, 7:58 am

Title: Budget of Paradoxes
Author: Augustus De Morgan
Publisher: Open Court (a reprint)

I chanced across this in a used bookstore; its based on an ongoing column De Morgan wrote for The Athenaeum, a weekly review journal, in the 1860's. Do Morgan earlier produced one of the first bibliographies of mathematics books ( Arithmetical Books, 1847 ), and Budget of Paradoxes is a kind of bibliography, of mostly misguided books in mathematics, astronomy, natural philosophy and so on. De Morgan was an entertaining writer and this book was a lot of fun to read. A few of the books covered are for authors who were way ahead of their time (rather than misguided) but mostly there are the type that believes they have discovered something that the established authorities in their field have missed - pi is a rational, the moon has nothing to do with tides, and so on.

Its also pretty impressive that a weekly magazine published a column of this type for a general audience.