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An Illustrated Theory of Numbers
- ISBN-101470434938
- ISBN-13978-1470434939
- PublisherAmerican Mathematical Society
- Publication dateAugust 8, 2017
- LanguageEnglish
- Dimensions8.5 x 1 x 11 inches
- Print length323 pages
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Editorial Reviews
Review
This is a meticulously written and stunningly laid-out book influenced not only by the classical masters of number theory like Fermat, Euler, and Gauss, but also by the work of Edward Tufte on data visualization. Assuming little beyond basic high school mathematics, the author covers a tremendous amount of territory, including topics like Ford circles, Conway's topographs, and Zolotarev's lemma which are rarely seen in introductory courses. All of this is done with a visual and literary flair which very few math books even strive for, let alone accomplish.
-- Matthew Baker, Georgia Institute of Technology
“An Illustrated Theory of Numbers” is a textbook like none other I know; and not just a textbook, but a work of practical art. This book would be a delight to use in the undergraduate classroom, to give to a high school student in search of enlightenment, or to have on your coffee table, to give guests from the world outside mathematics a visceral and visual sense of the beauty of our subject.
-- Jordan Ellenberg, University of Wisconsin-Madison, author of “How Not to Be Wrong: the Power of Mathematical Thinking”
Weissman's book represents a totally fresh approach to a venerable subject. Its choice of topics, superb exposition and beautiful layout will appeal to professional mathematicians as well as to students at all levels.
-- Kenneth A. Ribet, University of California, Berkeley
About the Author
Product details
- Publisher : American Mathematical Society (August 8, 2017)
- Language : English
- Hardcover : 323 pages
- ISBN-10 : 1470434938
- ISBN-13 : 978-1470434939
- Item Weight : 2.65 pounds
- Dimensions : 8.5 x 1 x 11 inches
- Best Sellers Rank: #862,188 in Books (See Top 100 in Books)
- #2,520 in Mathematics (Books)
- Customer Reviews:
About the author

Martin Weissman (1976-) grew up in St. Louis, Missouri. He studied mathematics at Princeton University (A.B.) and Harvard University (PhD), before moving west for a postdoc at UC Berkeley. From there, he moved down the coast to join the faculty at UC Santa Cruz. A researcher in number theory and representation theory, he has taught elementary number theory for undergraduates and graduate students, K-12 teachers, and high-school students.
More information and papers can be found at martyweissman.com . Supplementary material for An Illustrated Theory of Numbers can be found at illustratedtheoryofnumbers.com. Check out that page for errata, an introduction to Python programming for number theory, art prints and more!
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Top reviews from the United States
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It is *also* brilliantly laid out and complemented by illustrations that enhance both the pleasure and insight of the reader. And which, in many cases, provide concise ways of summarizing what was learned or useful references while working through a proof.
It is NOT a text designed to mollify math-phobes with pretty pictures. It is a theorem-proof-corrallary text. It also happens to be brilliantly laid out and ilustrated and complemented by lovely historical overviews and scholarly reference.
This is NOT similar to Visual Group Theory, if you have seen that text. Though superficially similar, VGT attempts to shield readers from math as long and as much at possible. IToN instead embraces its subject and uses layout and illustration to offer *additional* insight into the content.
Number theory is a fun/playful area and also a deeply meaningful one. A strong understanding of modular dynamics and analogues of prime decomposition will help a great deal with abstract algebra in particular.
This text, as stated, is also incredibly accessible for anyone motivated to work through the proofs. If you can do middle school math the entire contents will be accessible to you. And yet the fruits of your labor are those of a proper college course on number theory.
Highly recommended. The only other text that used illustration close to as well is Needham’s Visual Complex Analysis (a must read text to anyone working with complex domains, incidentally). But the approach to layout and presentation in this book is hands down the best in any math text I’ve seen. I only hope others seek to emulate it.
It's very similar to Byrne's Euclid book and I'd recommend it as a coffee book but also a serious first introduction to number theory. I'm willing to bet that many full time number theorists don't have the same deep intuition that this author has.
Top reviews from other countries
A word as to the quality of the book: this work provides sheer pleasure by being taken up, kept in the hand, opened and leafed through. Printing and binding are of the utmost quality, which in our days is rare for academic mathematical texts.The book has been paged in such a way that, when presented with a problem, readers are encouraged not to immediately turn the page to see either solution or its proof, but to try their hand first. The illustrative material, up to a splendid picture of an 8th CE century copy of Euclid's "Elements", is all to-the-point and thought-provoking. Bibliographic references are often given in the margin, which is encouraging to readers not familiar with academic quoting and referencing habits. As I am a practicing Chief Engineer who frequently needs to explain math and math-related topics to junior engineers, this book made me stop in my tracks and think on how to improve my own practice in this.
The book doesn't stop, however, at being a pedagogical success (although such is the result of Weissman's efforts). It is a great primer into research topics in number theory as well, encouraging students to delve deeper into topics that may have sparked their interest.
Weissman has delivered a masterpiece, for which I fall short of praise and which I am proud and happy to have in my library.
The pace seems uneven in comparison to more well established textbooks like Silverman's Friendly Introduction to Number Theory. The author's habit of putting details of proofs in the margin became irritating. also the reluctance to cross reference where a result was being used a few chapters later was an annoyance.
There are two nice features that I should mention: the treatment of quadratic reciprocity is very good and very clear and the discussion of quadratic forms is excellent.
However, I couldn't recommend it as a first introduction to number theory for that I'd go with Silverman's text.
Highly recommend for anybody intrested in elementary number theory or just in mathematics and graphical representation in general.





