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Everything you always wanted to know about mathematics (2013) [pdf]
- Alifatisk 3y agoI love the style, I'll download it when I get home. Is there anything similar but for statistics?
- rubergly 3y agoCame here to ask the same question. Really hope there are some good recommendations!
- cubefox 3y agoIf you search this post for "statistics", you find several recommendations (over similar books): https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-best-textbooks-on-every-subject https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-best-t...
- tr33house 3y agois there a service that can print, bind and mail PDFs with as many pages as this? It'll be useful for some of the manuals I have to read too
- Frummy 3y agoPerhaps use the pdf split function to order 4 quarters of the pdf in separate binds
- tesin 3y agoA quick google turned up this service - https://www.printme1.com/ https://www.printme1.com/
- ohwellhere 3y ago$47 for this work via that service
- mindcrime 3y agoIn another recent thread, somebody mentioned using some Amazon feature for doing this. I might be wrong, but I think you sign up as an author, upload the PDF like it's your book, then buy one copy (or request a proof) for yourself, and then delete it. Maybe somebody who has used this facility can chime in with more (or better) details...
- emacdona 3y agohttps://www.lulu.com/ https://www.lulu.com/ I used lulu.com to print a copy of OnLisp [1] What I got was one of the best bound paperback books I've ever held. <rant> I wish all publishers would just sell eBooks (and publish settings like "optimal paper size") so that I could print my own copy using a service like lulu. One of my biggest gripes with hardcopy books nowadays is that the paper stock they use is so thin that the ink on the other side of the page shows through. Lulu let's you choose the paper stock. I really can't say enough about how happy I was with the quality of the printed book lulu sent me. </rant> [1] https://www.lurklurk.org/onlisp/onlisp.html https://www.lurklurk.org/onlisp/onlisp.html
- waynesonfire 3y agoI've used lulu few times as well. Really like it. Whats your process for preparing a pdf for it?
- BeetleB 3y agoThere are a lot of variables. I print them myself and take them to FedEx to do the binding. Letter size/A4, though, result in big books and a lot of paper. So I wrote a script that produces a new PDF and reorders the pages. In the new PDF, you have two pages per side of paper (4 pages per sheet). The reordering is done so that FedEx can cut the sheet right in the middle, and put the left half on top of the right half to get the usual ordering. Then they just bind it. Not counting the cost of my paper, they charge about $11 (probably can get it a bit cheaper but I add some extras in the service when I bind them).
- vishnugupta 3y agoI use this site [1] and can recommend them. Though I don't know if they are available outside of India. [1] https://www.printonweb.in https://www.printonweb.in
- phkx 3y agoThere might be a print shop in your area which offers similar services. Or services which explicitly offer to print thesis, but they typically require a minimum number of prints.
- 01100011 3y agoI used Barnes and Noble Press a couple years ago to print a book. Cost $25 or so and was impressed with the results.
- optbuild 3y agoA finely written book for beginners. I like how it slowly explains stuff rather than doing in Theorem Proof style short books.
- layer8 3y agoI wish there were such books for more advanced math topics.
- SleekEagle 3y agoI wish math had its version of Griffiths
- billfruit 3y agoDoes it cover geometry?
- fn-mote 3y agoNo, as a quick perusal of the table of contents would tell you. For geometry, get a book like Art of Problem Solving's Introduction to Geometry. That will cover many beautiful topics in a question and answer style. [1] https://artofproblemsolving.com/store/book/intro-geometry https://artofproblemsolving.com/store/book/intro-geometry
- uldo 3y agoBeautifull! Is there similar book on physics?
- abhayhegde 3y agoI'd say the Feynman Lectures of Physics [1] volumes cover a broad base with some topics in great detail as well. [1]: https://www.feynmanlectures.caltech.edu/ https://www.feynmanlectures.caltech.edu/
- rg111 3y agoNo. Feynman Lectures, to be properly understood requires one to be at least an advanced undergrad. Most people just use it as home decor and many use it like a novel. To properly appreciate the material, you need training in Physics. Otherwise you will be getting much less.
- abhayhegde 3y agoFair enough -- to appreciate it really, one needs a motivated undergrad. But, it's similar in pedagogical style. It's not run of the mill concepts, but rather like a conversation that builds up with strong hints to form intuition.
- Koshkin 3y agoSusskind's series does a pretty decent job walking the reader through topics in (theoretical) physics. At a somewhat more advanced level, you can try Schwichtenberg's No-Nonsense books. I also enjoyed Stevens' The Six Core Theories of Modern Physics.
- ivansavz 3y agoDo you mean basic physics like mechanics (PHYS 101) ? If this is what you're interested, check out my MATH & PHYS book. Posted link to it in another comment this thread.
- quickthrower2 3y agoInteresting! No touch on probability/stats though? Or calculus?
- mbork_pl 3y agoWell, there's too much of (modern) mathematics to touch everything - even everything important... One of the most important notions is that of compact sets, and it's not even mentioned. Neither are groups (well, they are mentioned, but not much else), etc. From a quick skim of the ToC this looks very well thought-out. Looks like an excellent book!
- billfruit 3y agoDoes it touch geometry?
- fn-mote 3y agoThis is a book about writing proofs. It is intended to develop that skill, not introduce you to a breadth of topics.
- lmwnshn 3y agoJudging by the URL, this book was used for CMU's 15-151 / 21-128, which is a first-semester course for CS and math undergrads. Nowadays, the course uses [0]. [0] https://infinitedescent.xyz/ https://infinitedescent.xyz/
- roter 3y agoThanks for this resource. It also serves as a LaTeX math example --- the source for the book is provided.
- rickstanley 3y agoDoes this replace the OP? Or is "An Infinite Descent into Pure Mathematics" a complementary book?
- lmwnshn 3y agoMy link replaces; we did not use OP's book when I took the course. That said, OP's book looks more conversational in tone, which I personally have a slight preference for.
- mjvmroz 3y agoGreat insight, thanks. I was tossing up on which one to take a stab at first, but I have a pretty strong preference for conversational tone.
- lying4fun 3y agoEvery chapter of the OP book has an introduction which has the following subchapters: Objectives, Segue from previous chapter, Motivation, Goals and Warnings for the Reader. Which I really appreciate and I think its a great way to teach stuff, especially mathematics, since all those chapters contextualize the coming topic in various ways. (E.g. I imagine ‘Motivation’ does this with respect to the history and origins of the idea and ‘Segue from previous chapters’ contextualizes it with reference to the stuff reader has learnt so far. I didn’t read anything yet but it looks promising
- 3y ago
- ConnorMooneyhan 3y agoAs someone with a B.S. in Pure Mathematics who is now a programmer, it makes my heart happy to see my true love at the top of HN.
- deleted 3y ago[deleted]
- ggr2342 3y agoDid you use it at CMU?
- ConnorMooneyhan 3y agoNo, I actually didn't use this book. By "true love" I meant mathematics ;)
- kovac 3y agoSame here! May I ask which field of programming you went into? And how you feel about being a programmer? I often wonder how it might have been if I just had stayed with math. Especially, after years of doing regular programming for the Web, recently I had to develop a computational geometry library. It had been years since I graduated but really made me feel nostalgic. I think I lost something when I left the field, but then again life is a lot easier now...
- slopbop 3y agoIf I remember correctly, Brendan Sullivan had a reputation as a TA for Concepts of Mathematics at CMU as "Math Jesus", not sure if that was a testament to his pedagogical skills or just due to the long hair and beard...
- ggr2342 3y agoWhere is he now? Why doesn't he write more books like this? I mean in this lucid explanatory style.
- witchesindublin 3y agoI like how the book is written in a teaching style rather than a textbook style.
- istjohn 3y agoThis looks great! Does anyone know of any solution sets for the exercises or other resources with similar problem sets with solutions?
- hgsgm 3y agoArt of Problem Solving website and books.
- foobarbecue 3y ago"This work is submitted in partial fulfillment of the requirements for the degree of Doctor of Arts in Mathematical Sciences." So does that mean this is his PhD thesis? What's a Doctor of Arts?
- shwestrick 3y agoIt's a doctoral degree with a heavy emphasis on pedagogy and teaching. From https://www.cmu.edu/math/grad/phd/index.html https://www.cmu.edu/math/grad/phd/index.html: > The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.
- hapidjus 3y agohttps://en.wikipedia.org/wiki/Doctor_of_Arts https://en.wikipedia.org/wiki/Doctor_of_Arts
- zhte415 3y agoTo echo others on writing style, it's very lucid. This would be a fantastic coffee table book; not for everyone, but for a countable number of people.
- anthk 3y agoIt looks a lot like Gentle Introduction to the Art of Mathematics.
- bannedbybros 3y ago[dead]
- _aaed 3y agohttps://pimbook.org/ https://pimbook.org/ Read this instead
- Koshkin 3y agoRead both.
- fn-mote 3y agoThat book has a completely different focus... breadth instead of understanding argumentation. I agree that the Programmer's Introduction to Mathematics is more likely to contain useful content (instead of being about how to develop the ability to reason carefully). It also has a LOT more breadth than the OP. The free part of Chapter 3 "On Pace and Patience" is a key very important attitude toward learning from this book (especially on your own). If you are thinking about studying from this book, make sure you philosophically agree. I tried to copy and paste a paragraph here, but it looks like it has been ROT-13 encoded in the PDF (or something)! > [...] mathematical culture requires being comfortable being almost continuously in a state of little to no understanding It's a humble life [...]
- zdms 3y agoIts using ROT25 ¯\_(ツ)_/¯
- no_wizard 3y agoDoes anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.
- engineer_22 3y agoCheck out Kahn Academy, they have a gamified course to guide you through the equivalent of a high school and early college math curriculum. AFAIK it's free?
- engineer_22 3y agohttps://www.khanacademy.org/math https://www.khanacademy.org/math
- culi 3y agoKhan Academy is great. When I was taking AP calculus in highschool I failed to complete any homework and barely passed the class. But when it came time for the AP test I binged Khan Academy videos for 3 days beforehand and ended up getting a 5 (the max score). Great resource and even bingeable
- alphameese 3y agoSpecifically these three courses [0][1][2] will take you from basic algebra to precalc. They're very thorough and I've found them extremely useful in upgrading my high school level math skills. I have heard that their calculus courses aren't sufficient though, and that it should be learned from somewhere else. [0]https://www.khanacademy.org/math/math1 https://www.khanacademy.org/math/math1 [1]https://www.khanacademy.org/math/math2 https://www.khanacademy.org/math/math2 [2]https://www.khanacademy.org/math/math3 https://www.khanacademy.org/math/math3
- bloemheuvel1 3y ago
- evanmoran 3y agoAs a CS major who went to CMU years ago, my favorite book from all of my professors was for my 15-213 class called Computer Systems: A Programmers Perspective I remember at the time the book was in loose leaf paper so it warms my heart to see the book has a 3rd edition. It was used as a core part of teaching assembly, memory representations, and getting students ready for the operating systems class. When I help people learn to program, it's the only book I think is a must have: https://www.amazon.com/Computer-Systems-Programmers-Perspective-Edition/dp/013409266X https://www.amazon.com/Computer-Systems-Programmers-Perspect...
- GitPushOrigin 3y agoIs there a book or resource you'd recommend for operating systems? I recently finished CS:APP and really enjoyed it. Though I've been programming for ~7 years and felt that made it easier to digest.
- wbrd 3y agoGoing through this now and it's great
- donkey-hotei 3y ago+1. This book changed my life. Wouldn't be doing what I'm doing today without it!
- abtinf 3y agoCould you expand on how it changed your life?
- deleted 3y ago[deleted]
- nailer 3y agoSlightly off topic - does anyone know a 'reader mode' for PDFs? I frequently look at PDFs online and am looking for a tool that reformats the PDF into a single column, so I can just scroll, absorbing the content.
- cubefox 3y agoNote that these are 700 pages which could take multiple years (if you're doing it in your spare time) to go through. I'm not sure who would have the motivation and discipline for this.
- l33t233372 3y agoIt might, but it shouldn’t. There are 8 chapters and most of the content in the first 7 shows up in any run of the mill “Introduction to Higher Mathematics” or whatever that university decides to call their first actual math class, although occasionally combinatorics will replace number theory content.
- abhayhegde 3y agoMost of the books are meant to be consumed in parts. This book explicitly mentions "Segue from previous chapter" for most chapters indicating what key concepts are continued in exploring/building new ones. Also, I believe any reader on HN can make sense quickly of the basic definitions needed to understand a concept in isolation. However, mathematics is especially known to require continuous dedication for years to attain any sort of mastery.
- eimrine 3y agoKids, cherry-picking students of other disciplines, those who really understand what is a good read.
- Koshkin 3y ago> Everything you... wanted Far from being "everything" anyone would want or need, it's rather "some (fundamental) things" you must know. A couple of pages a day, on average, would get you there within one year.
- cubefox 3y agoStill, I'm in doubt that a significant proportion of us would have the discipline for this. One reason why some things are pretty much only learned in university is that they provide the necessary motivation.
- dexter89_kp3 3y agothis is awesome
- RedPanda250 3y agoCan someone share how this compares to Math for Computer Science by Lehman, Leighton, and Meyer ? https://courses.csail.mit.edu/6.042/spring17/mcs.pdf https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
- pmoriarty 3y agoOne thing I've always wanted is a comprehensive guide to mathematical notation, which tells you what symbols mean or at least what field of mathematics they come from. I frequently come across all sorts of weird mathematical symbols in papers, and of course these symbols are virtually never explained, so I have no idea what they mean. Even better would be if there was some way an LLM could read through a paper itself and then explain the equations.
- sorokod 3y agoI doubt that having a "dictionary" attached to a math paper, something like 1. ∇ = nabla see https://mathworld.wolfram.com/Nabla.html https://mathworld.wolfram.com/Nabla.html 2. ... 3. ... would improve your understanding. Notation encodes ideas, it is the understanding of the ideas that is tricky, not the encoding.
- pmoriarty 3y agoIt would actually help. I'd know what fields I need to study to more fully understand the papers I'm interested in. It would also help me figure out what to ask LLMs (or people) to explain to me.
- cubefox 3y agoGPT-4 can probably explain LaTeX formulas pretty well, but when they are compiled PDFs, the encoded PDF plain text is often garbage, so GPT-4 probably couldn't understand much.
- SleekEagle 3y agomany books will have a page in the preface that lays out the notation, even for very common objects. it's hard to make a cheat sheet for something like this because many symbols are used in different fields, and even if different subfields of the same field.
- cubefox 3y ago
- dwheeler 3y agoIf you want to go deeply into formalized mathematics, take a look at the Metamath Proof Explorer <https://us.metamath.org/mpeuni/mmset.html https://us.metamath.org/mpeuni/mmset.html>. It defines a set of axioms, and formally verifies every proof showing every step (hiding nothing).
- adamgordonbell 3y agoAt some point I was interested in learning to read and write proofs. I did the "Introduction to Mathematical Thinking" MOOC from Keith Devlin. The curriculum is available as a book as well. The class is basically how to write and read proofs for non-math majors. It starts pretty slow, but gets harder at some point. The number theory proofs were fun. You 'got to' grade others proofs online, and they graded yours which was an interesting way to get familiar with reading and writing proofs. I recommend it because instead of an area of math it focuses on what it means to prove something. And the teacher is pretty entertaining. https://www.amazon.ca/Introduction-Mathematical-Thinking-Keith-Devlin/dp/0615653634 https://www.amazon.ca/Introduction-Mathematical-Thinking-Kei... https://www.coursera.org/learn/mathematical-thinking https://www.coursera.org/learn/mathematical-thinking
- actinium226 3y agoIf I could read, and understand, a textbook like this in a day, I would be so happy. Alas, I must only look with longing at the links provided by HN, thinking wistfully 'someday...'
- rg111 3y agoThe key to learning Math in adult life, as I have found- setting aside 40-180 mintues every day to learn regularly. It would be golden if you can create a study group that meets weekly. Just start a discord/Element room/Zulip/IRC chat and go from there. I am learning Topology as an adult and learned Category Theory this way. This truly works. Setting aside time 4-5 days a week works. Make it a habit.
- mmmmpancakes 3y agofancy name for what seems like a fairly standard "intro to proofs" textbook, at least based on the ToC.
- sanderjd 3y agoHow do people here like to read pdfs? It doesn't work on my ebook reader and I never actually read anything long-form on a computer screen, even when I think I will. Someone below mentioned using a service to print and bind into a book. Anyone have a better workflow for this kind of thing?
- 70rd 3y agoSome software has PDF reflow, like koreader.
- adnauseum 3y agoI purchased a Supernote for this very reason. Not cheap, but I (unfortunately) read a lot of PDFs.
- sanderjd 3y agoAnd it works well for it? I have a Remarkable, but never felt like it worked that well with pdfs.
- JenrHywy 3y agoI bought an iPad specifically for reading PDFs. It does get used for other things too, but the primary driver was PDFs. Most tablets seem to be optimised for horizontal video content, which makes then too narrow for A4 PDF, whereas the 4:3 of the iPad is perfect.
- DantesKite 3y agoTempted to train a small language model on this text and see what happens lol.
- deleted 3y ago[deleted]
- whatscooking 3y agoMore like everything you should already know about mathematics
- m00n 3y agoWith that title and reception I can imagine people bookmarking this for „later“ and feeling good about it. But who reads that stuff really? To each their own, but 700+ pages for material that is done in my experience in the first 2-3 weeks of undergraduate math is more disheartening than empowering for a student, in my opinion. If you can open a math book anywhere in the last 20% of pages and just start reading, you are looking at pop science and not lecture notes.
- PestoDiRucola 3y ago> With that title and reception I can imagine people bookmarking this for „later“ and feeling good about it. I'm in this comment and I don't like it. > If you can open a math book anywhere in the last 20% of pages and just start reading, you are looking at pop science and not lecture notes. What do you mean?
- ravish0007 3y agoIs there a similar book on CS?
- gradschool 3y agoFWIW, Barr and Wells in a well respected reference on category theory [1] use a different definition of a function than the one in this book. Essentially they avoid insisting on the concrete model of a function as a set of ordered pairs (which they call its graph), and would regard two functions having identical graphs as being nevertheless distinct if they have different co-domains (section 1.2). IMO their definition is better thought out and ultimately less troublesome when it comes to reasoning about functions. The definition of a function is always the first thing I check in any book about math for a rough assessment of whether reading the rest of it might make me dumber or smarter. [1] https://abstractmath.org/CTCS/CTCS.pdf https://abstractmath.org/CTCS/CTCS.pdf
- red_admiral 3y agoIndeed. The question "given a function as a set of ordered pairs, write code to decide if it is injective" has an answer, but replace that with "surjective" and suddenly you need to drag the codomain along as an extra parameter or the question makes no sense. This asymmetry bothers me. EDIT: to be clear, "code" only works if your set is finite, but the principle of "does this question even have an answer" remains "yes" for injective and "no" for surjective without the codomain being named explicitly.
- EmilioMartinez 3y agoIs there a version of this but for advanced topics? (presented without proof of course, like short expositions on the topics)
- deleted 3y ago[deleted]
- ladreamteam 3y agoIs there a printed copy of this book that we can buy?