7 ms·
An Illustrated Theory of Numbers (2017)
- earthicus 8y agoI'm submitting this beautiful book right now because the American Mathematical Society (AMS) is having a large sale, it's 40% off until the 17th. (You have to make an AMS account). Table of contents (pdf): https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-toc.pdf https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-... Sample Chapter (pdf): https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-prev.pdf https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-...
- xvilka 8y agoBut it has an only paper version, right?
- JoeDaDude 8y agoI presume you need to be a AMS member to get the discounted price? Creating an account with the bookstore doesn't seem to get you the sale price.
- jonsen 8y agoIt did for me.
- dgquintas 8y agoIt did for me. Just click "Register" at the top of the checkout page.
- larryfreeman 8y agoIt didn't appear to work for me until I hit Next and went to Checkout. Right before I entered my credit card, it had the discounted price.
- siliconunit 8y agoWife junkware counter rage-spending :D
- techvella 8y agohttps://techvella.com/elgato-stream-deck/ https://techvella.com/elgato-stream-deck/
- hopler 8y agoAre there sample pages available?
- earthicus 8y agoSample Chapter (pdf): https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-prev.pdf https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-...
- jessaustin 8y agoIn this text, we declare: 0 is a natural number It's nice that they got that right, on the first page!
- throwawaymath 8y agoEh, I think it's fair to consider the natural numbers as either the non-negative, nonzero integers or the non-negative integers. As long as an author declared which use they intend front and center, I don't think one or the other is more "right." Very established texts and papers alternate freely between including and not including 0.
- jessaustin 8y agoAs the author says, it's a matter of taste. The author's good taste is "right" in the same sense that e.g. 0-indexed arrays are "right": it avoids problems that not including zero causes. How many elements are in the empty set? Why shouldn't the natural numbers be able to answer that question?
- hopler 8y agoWhat is 0 minus 1? Why isn't that a natural number? Why shouldn't the nth natural number be N? The author's own book discusses the 1st prime, in chapter 0, which begins on page 1. How is this natural? Problem 0.4 Add the odd numbers between 1 and 30." Why would you say 1 and 30 instead of 0 and 30, since 0 is natural? Getting hung up on notation and arguing over conventions will hold you back from learning math. Offsets (0) and ordinals (1) aree both useful in arrays. The only thing wrong* is not saying which you mean. http://exple.tive.org/blarg/2013/10/22/citation-needed/ http://exple.tive.org/blarg/2013/10/22/citation-needed/
- posterboy 8y ago> In some time past (long before 3000bce), a shepherd paired sheep and pebbles: as the first sheep walked by, he placed down the first pebble; the second sheep walked by and down went the second pebble. At the end of the day, the number of pebbles placed down equaled the number of sheep that walked past. Whether sheep and pebbles, or red dots and blue dots, equality of numbers is defined by pairing off. Good one.
- throwawaymath 8y agoMore concisely: sets of numbers are equivalent if there exists a bijection between them. EDIT: Oh, the sample chapter actually mentions this exact point in a footnote. I guess I can still be clever by saying, "Sets of numbers are equivalent if they're isomorphic." :)
- bigblind 8y agoIs there a full ebook available somewhere?
- thrwthrw93223 8y agoThis looks great, but are solutions provided? Books like this are almost worthless for me to self-study since I don’t have access to a classroom or professors and no way to check my solutions.
- throwawaymath 8y agoIt's a nice book, but I wouldn't use it for study or as a textbook. And solutions are not provided as far as I can tell. I'm afraid you're going to have a difficult time finding books which contain solutions to their problems.
- thrwthrw93223 8y agoThanks. I won’t bother buying it then. Do you have any recommendations on good math books to work through on my own that have solutions floating online, so I can check my work? I’m looking for a theoretical math book to work through. Primarily looking for intro to proofs or algebra related books. But anything will do. I just want something proof-y aimed at beginners.
- HuShifang 8y agoI think Velleman's "How To Prove It" might be useful.
- thrwthrw93223 8y agoThis looks great. Thanks.
- earthicus 8y agoPolya & Velleman are classics. They're about problem solving & proof writing techniques, but won't teach you any abstract math. I've only ever heard good things but i've actually never read them myself! Some other suggestions: Niven - The Theory of Numbers. Contains hints for some of the proof based exercises, and answers for many of the computational exercises. I used it for my undergrad course, I remember it being reasonably beginner friendly. Pressley - Elementary Differential Geometry. Has terse answers to every exercise! The subject is a nice mixture of concrete and abstract, calculation and proofs, and there's some interesting work using differential geometry in CS via computational geometry. Also i think it's used in robotics and a few other things? This book is very beginner friendly, it will get you about 1/2 way to General Relativity.
- martyweissman 8y agoI hope you enjoy the book -- the AMS sale does give a great price! Part of the reason I went with the AMS was that they're a nonprofit and their prices are reasonable for a hardcover book printed (offset, not digital on-demand) in color. As the author, I'll add a few remarks and answer some questions about the book. 1. I made a book webpage at illustratedtheoryofnumbers.com. The errata are there. Also you can find a series of programming tutorials, if you wish to learn number theory with Python. I go from programming basics to primality-testing, RSA, etc. 2. I didn't provide solutions in the book. :( But there's always online discussion boards. Someday I'll write many more exercises and provide some solutions. 3. It's been used as a textbook for undergraduate number theory, e.g. at Rice, UC San Diego, next semester at Georgia Tech I think, etc. 4. No full e-book version is planned. It's all very old-fashioned, but I spent a lot of time on page layout, optimizing for print, etc. 5. I took a stronger stance on zero being a natural number in an early draft. Now I just try to make it clear that it's the convention I choose. If it's good for Bourbaki, it's good for me. Feel free to drop a note if you have more questions about the book. My email is not hard to find. Happy holidays! Marty Weissman
- xvilka 8y agoSeems like a great book, thank you! > 4. No full e-book version is planned. It's all very old-fashioned, but I spent a lot of time on page layout, optimizing for print, etc. It is very strange choice for a book written in 2017.
- thrwthrw93223 8y agoI’m apprecticative of the amount of work and effort you put into the book. Please consider the self-learner and those that don’t have access to solutions, a classmate, a TA, or a professor. I know you probably don’t want to expose solutions to the exercises so they can be used in a classroom, but for people like me, I don’t want to create an online discussion to every problem I attempt just to check my work. I prefer to read textbooks that have solutions, so I can know for sure my answers are correct. I don’t really buy the “you know when your solutions are correct”. The beginner can easily fool themself into thinking their solutions are correct, when they aren’t. Due to that, I won’t be buying your book.
- KennyCason 8y agoLooks interesting. On the page I noticed a sale price of ~$41 in red text but upon checkout it is $69. I don’t mind paying $69, but just want to confirm I’m not missing some opening sale.
- dgquintas 8y agoCreate an account by clicking "Register" at the top of the checkout page. You should then see the discounted price, at least until tomorrow (it seems the sale runs until then).
- KennyCason 8y agoThanks!
- alok-g 8y agoDoes the book discuss foundations of numbers? Peano's axioms, etc. It does not look like from the contents or the sample chapter.
- martyweissman 8y agoNope -- I didn't take an axiomatic approach, or give a set-theoretic construction of different sets of numbers. Instead, I take basic arithmetic and algebra and properties of real numbers as a starting point. I do dwell on things like division with remainder and prime decomposition.