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Ask HN: Math books that made you significantly better at math?

• theusus 4y ago
  > Discrete Mathematics with Applications by Susanna S. Epp Fantastic book for Discrete Mathematics with lucid explanation and good exercises. The other one would be concrete mathematics.
  • mindcrime 4y ago
    Epp's book is my favorite Discrete Math book by far. Her writing style is very clear and easy to follow. And as you say, there are good exercises. And if you buy an older edition, used copies can be had for a (relatively) reasonable price.
  • adamddev1 4y ago
    I'm working through this right now and really enjoying it.
    • LAC-Tech 4y ago
      what a coincidence, so am I. Though I realise I've spent over a week on section 2.2 so "working through it" may be a bit of a generous term.
• pyuser583 4y ago
  “The Bones”, technically by Euclid. An amazing translation of Euclid’s elements that contains diagrams and commentary that actually make it clear what he’s talking about.
• jspx 4y ago
  A book of abstract algebra - Charles C. Pinter. Each chapter is a few pages of explanation, and the rest you solve yourself by doing exercises that introduce aspects of the theory step by step.
• guhsnamih 4y ago
  Statistics by Freedman, Pisani and Purves. Don't know if I got better but loved the real world examples and cartoons. Does not have too many pre-requisites. Each section presents a tiny concept which is followed by plenty of exercises that have answers at the end. The furthest I got in a book in recent days, Math or not.
  • madcaptenor 4y ago
    I taught from this book (it wasn't my choice, it was the standard book where I was teaching). It's really good for intuition, but because it doesn't use standard notation I think it might have done a disservice to students who were going to go on to learn more.
    • jldugger 4y ago
      My pandemic project in 2020 was to finally read through the used copy I bought a decade ago. I agree it was really useful at building foundational intuitions. And that it doesn't use professional jargon which sometimes makes Stats Wikipedia's "death by integrals" approach a dense barrier to entry. For example, the book uses "the box model" all over the book but is not used anywhere else, and every else uses the phrase "i.i.d" which is not used in the book. Still, it's been really useful at my job in reasoning about timeseries data from Prometheus, especially in canary analysis. Far more useful than the whirlwind tour of distributions my 1 semester "Statistics for Engineers" course in college undertook.
      • guhsnamih 4y ago
        Yes, the intuition was key for me. So many of the problems could be solved with the simple box model.
    • dysoco 4y ago
      Any suggestions for more conventional Statistics books? (Math-oriented, with proofs if possible). I'm reading Devore's one for Engineering and the Sciences and it's pretty good but I'm having a bit of hard time with p-values, hypothesis tests, etc. and wanted a second book as reference for those topics.
• okaleniuk 4y ago
  Calculus on Manifolds by Spivak. Brilliant. And relatively thin too.
• curious16 4y ago
  Not a book. But a course by Prof Keith Devlin on Coursera called Introduction to Mathematical Thinking.
  • wannabebarista 4y ago
    I jumped into the first analysis class (using baby Rudin) completely unprepared and this course saved me!
  • AlanYx 4y ago
    [dead]
• keiferski 4y ago
  I would not call myself great at math – I struggled with it in school, in fact – but in recent years I’ve begun “correcting” my lack of mathematical knowledge. The single best decision I’ve made is to first start with the philosophy of mathematics. Maybe it’s because my background is in philosophy, but I also think that for certain people like myself, understanding what math is makes me far more interested in understanding how it works, rather than just doing context-less calculations using formulas I don’t know the history or deeper purpose of. When I learned math in school, it was entirely cut off from any of these deeper questions. Here’s a good starting point for philosophy of mathematics : https://plato.stanford.edu/entries/philosophy-mathematics/ https://plato.stanford.edu/entries/philosophy-mathematics/
  • bombcar 4y ago
    Reading Euclid's Elements and Newton's Principia really helped me get an intuitive feel for geometry and calculus. They may not be entirely easy (at least the second) without some commentary, but well worth the study.
    • macrolocal 4y ago
      Ditto for Euclid. Doing this early in life pays huge dividends.
    • pen2l 4y ago
      While it's laudable that you sought those texts and profited from them, I worry about what others might take away from this. When I was young I knew some geniuses who highly spoke of Principia and how it gave them great insights. And the teenager me said, okay cool, I'll have a go! The problem is that it's in Latin and quite impenetrable. We have some geniuses here and they would no doubt be able to take away a lot from these texts, but for you normals out there: don't optimize too much, you're quite alright in taking the normal approach of just taking a class at a community college, doing the exercises the teacher assigns, etc.
      • troupe 4y ago
• okaleniuk 4y ago
  Also, Geometry for Programmers but only because I wrote it. I had to update my skills significantly while gathering material and doing all the experiments. Not sure if reading the book would have the same effect :-)
• wannabebarista 4y ago
  Measure and Category by John Oxtoby. This book studies duality results between different notions of "small" sets in measure theory and topology. It's the first (and to some extent the only) math book where things just clicked and I didn't feel like I was drowning in a sea of notation and ideas. Here are some more thoughts on it: https://bcmullins.github.io/Top-Books-2019 https://bcmullins.github.io/Top-Books-2019.
  • enriquto 4y ago
    I'm so happy to hear that! I've always loved this little book (even if it's completely independent of the math needed for my work). In a similar spirit, but with a much more geometrical flavor, there is Evans-Gariepy.
• mohamez 4y ago
  Any good book about the history of mathematics that will teach you a natural historical development of concepts to reach more generalizations. History of mathematics will give you a very subtle entry into the minds of mathematicians and the motivation behind their theorems. This will surely make you more appreciative of subjects and concepts you are learning.
  • mrazomor 4y ago
    The Mathematical Experience -- https://www.goodreads.com/book/show/1113522.The_Mathematical_Experience https://www.goodreads.com/book/show/1113522.The_Mathematical... It's touching many areas. For some it explains how they were developed or the controversy around them (e.g. the definition and use of infinity).
  • mharig 4y ago
    Foundations and Fundamental Concepts of Mathematics, by Howard Eves
• scruple 4y ago
  Calculus Made Easy and Probability Through Problems. I'm not sure that I'd have gotten through either my university Calculus courses or Probability and Statistics without these two books. I used them as supplementary material to the course textbooks and homework. They both have a style that is approachable and helped me build an intuition for the material unlike anything else I found.
  • tylerstorm 4y ago
    I second this suggestion for Calculus Made Easy by Thompson. It's become a bit of a classic...was published in like 1915. Super unique approach to teaching calculus. It's an excellent supplement...lots of good insights. It may be particularly good for people who believe they're bad at math. His style may convince people otherwise. Also, Vibrations and Waves, by AP French. Granted, this is a physics book, but I appreciate his style so much. He makes use of a lot of geometric methods to solving problems. It definitly expanded my math horizons! His other books are good too.
  • apohn 4y ago
    >Probability Through Problems First time I'm hearing about this one, thanks for the recommendation. Unlike Calculus or even a typical one semester Statistics course, probability is one of those topics where you need to see a lot of problems to really grok anything. The only way is to see a lot of solved problems and think about why that's the right answer. Even highly recommended books (e.g. by Blitzstein) don't have enough solved problems, so it's nice to there's a problem focused book out there.
• Bootvis 4y ago
  Meta comment: might be good to add the level of mathematical maturity needed to enjoy the book.
  • 082349872349872 4y ago
    Skimming over the replies, they range from arithmetic to algebraic geometry and measure theory! Along the lines of fascicules de résultats, I find talks are a good way to get a coup d'oeil for a field: people giving a talk tend to take a direct approach to what they want to introduce, hitting only the salient points. But that yields enough keywords to then consult any relevant texts.
• awelxtr 4y ago
  Significantly better I don't know but when I was a child I was given Der Zahlenteufel. Ein Kopfkissenbuch für alle, die Angst vor der Mathematik haben (The Number Devil) and I liked it very much
• Mimmy 4y ago
  Linear Algebra Done Right by Sheldon Axler for the following reasons: - I was revisiting a topic in greater depth, which is a common theme in university-level math courses. - It is a rigorous book, written in the style of definition, proposition, theorem, etc. - It was the first math book where the exercises don't just reinforce what you learned in the chapter, but teach you new material (another common theme in advanced math textbooks). - Linear Algebra is arguably the most important math subject these days.
  • mohamez 4y ago
    Linear Algebra Done Right by Sheldon Axler is indeed a good book if you are looking for a rigorous proof based book to learn linear algebra. Here [1] you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel! How wonderful is that! Here [2] you can find the solutions to the exercises in the book. This [3] Lectures might help as well, among the books this course follow is Algebra Done Right. Good luck learning the subject of Linear Algebra you'll have fun doing so. [1] https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS... [2] http://linearalgebras.com/ http://linearalgebras.com/ [3] http://nptel.ac.in/courses/111106051/ http://nptel.ac.in/courses/111106051/
  • sgdpk 4y ago
    I have to second this. It's very well written and presents a clear view of what Linear Algebra is. Although it might be best used as a second book in Linear Algebra (depending on your preparation).
• troupe 4y ago
  From Mathematics to Generic Programming - Stepanov & Rose Gödel, Escher, Bach: an Eternal Golden Braid - Hofstadter Euclid's Elements
• dfan 4y ago
  This is different from the other answers, but it does answer your question: When I was a kid I had tons of math and logic puzzle books. Two I remember specifically are "Aha! Insight" and "Aha! Gotcha" by Martin Gardner. Decades later, when a math problem comes up in my work, I have an apparently unusual ability to cut to the heart of it ("by symmetry, we must have X" or "looking at this extreme case, we must have Y" or "this looks like a special case of Z" sort of things) instead of starting by soldiering through equations, and I credit a lot of that to all the puzzle-solving I did as a kid.
  • wannabebarista 4y ago
    I had a similar experience with Raymond Smullyan's books, particularly The Gödelian Puzzle Book: https://www.raymondsmullyan.com/books/the-godelian-puzzle-book/ https://www.raymondsmullyan.com/books/the-godelian-puzzle-bo.... Recreational math is quite underrated.
  • macrolocal 4y ago
    A Mathematical Mosaic is a little-known gem here.
• cccybernetic 4y ago
  The best resource I've found is this random, somewhat obscure website (though I've learned that it has grown in popularity) called Paul's Online Notes. The professor has a real knack of pedagogy, and the problems are perfectly structured in terms of their difficulty. His explanations are clear and without jargon, and it goes from algebra to diff eq. A note: this isn't a resource for higher-level, proof based maths. It will give you a solid foundation and a pragmatic understanding to build upon. Very useful for STEM. Link: https://tutorial.math.lamar.edu https://tutorial.math.lamar.edu
  • agucova 4y ago
    This page got me through my engineering calculus I, II and III, linear algebra and ODEs courses. I'm eternally grateful ;)
  • ask_b123 4y ago
    I used this a lot while in school, very useful!
  • downboots 4y ago
    Seconded.
• yodsanklai 4y ago
  I wonder how good you can get at maths just by casually reading books. You need to work on problems for hours and hours to get a grasp on the theories. Programming is different in the sense that it's something people routinely do as a hobby because it's quite fun and addictive. But maths? maybe if you have already strong foundations you can pick up a new topic and develop your culture. But I doubt one can get these foundations without actually graduating in maths as it's an extremely strong commitment.
  • ag315 4y ago
    I don't think you can get good at doing calculations without practicing the calculations, but reading books that discuss the higher-level aspects of math and the philosophical underpinnings can help you look at it in a different way that may inspire more interest as well as an easier time grasping the difficult parts.
  • posed 4y ago
    I second this strongly, you can’t get better at math just by reading books. You need to hone your problem solving skills, you need to fight with the problems, have the mindset of a warrior, a conqueror, only then you’ll get the juice out of it and have a clear understanding of the subject. I’ll suggest starting with Concrete Mathematics by Donald Knuth, it’s a beautiful book that catches the essence of mathematics. Art of problem solving(https://www.amazon.in/Art-Problem-Solving-Basics/dp/0977304566 https://www.amazon.in/Art-Problem-Solving-Basics/dp/09773045...) is also a great start, especially if you don’t have much experience.
  • mindcrime 4y ago
    I wonder how good you can get at maths just by casually reading books. You need to work on problems for hours and hours to get a grasp on the theories. Maybe I'm unique in this regard, but I always took it as sort of implied that "reading a math book" entails "reading the book and working (at least some of) the exercises". The tricky part is once you get to math where you can't trivially check your answer by "substituting back in" or "using a calculator" or whatever. Doing proofs, for example. Without a teacher, how do you know if your proof is correct? So far the only thing I've really found to do for that is to post on MathOverflow or one of the "learn math" related sub-reddits. I've often wondered if learning to use an automated theorem prover / proof assistant of some sort would be helpful, but that's such a huge undertaking in its own right...
• ABeeSea 4y ago
  The classic, How to Solve It by Polya. A lot of the advice seems obvious in retrospect but being systematic about a problem solving framework is enormously helpful.
• zrkrlc 4y ago
  Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach It's a rigorous but chatty textbook in the style of Spivak but written by someone who is sensitive to applied maths. I would not have survived my astrophysics classes without it. (Not to mention it's where I first saw this really intuitive way of doing matrix multiplication: https://blogs.ams.org/mathgradblog/2015/10/19/matrix-multiplication-easy/ https://blogs.ams.org/mathgradblog/2015/10/19/matrix-multipl...)
• thehappypm 4y ago
  The Art of Approximation gave me far more intuition than any class
• steppi 4y ago
  Some favorites below. Books 0-3 are accessible. The remaining books are more difficult but I'd highly recommend them to math students. 0. Jan Gullberg, Mathematics, From the Birth of Numbers. A highly accessible popular survey on different branches of higher mathematics. I read this over the Summer between high school and starting my undergraduate degree. It's what made me want to study math. Previously I'd wanted to be a guitar player, but had to find a new ambition after an injury left me unable to play. 1. The high school mathematics series by Israel Gelfand. Algebra, Trigonometry, The Method of Coordinates, and Functions and Graphs. I didn't have much mathematics background in high school, but working through these really solidified my grasp on the basics. 2. George Polya. How to Solve it. A short book giving excellent high level advice on mathematical problem solving. 3. George E. Andrews, Number Theory. I worked through this freshman year contemporaneously with my first proof based class on simple logic and set theory. A very beautiful and accessible introduction to basic number theory. The combinatorial/geometric proofs of Fermat's Little Theorem and Wilson's Theorem are lovely. It also includes a very nice proof of Chebyshev's theorem on the asymptotic density of primes and even the Rogers-Ramanujan identities for integer partitions. 4. Vladimir Arnold, Ordinary Differential Equations: Undergrad ODE classes are often taught in a cookbook fashion and if so, don't offer much enlightenment. This book explains what's going on at geometrical level. I didn't appreciate ODEs until I read this. See https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html for Arnold's views on teaching mathematics. 5. E.C. Titchmarsh The Theory of Functions: Recommended by my undergraduate advisor because he noticed that I liked reading older books. It contains sections on complex analysis and real analysis with measure theory, but I've only read the complex analysis sections. It's not for everyone, if I recall correctly, there is not a single picture, but it is very lively and has a lot of material you won't find in a standard complex analysis book, including Dirichlet series. Excellent as a supplement to a standard complex analysis book. 6. George Polya. Mathematics and Plausible Reasoning. An excellent expansion on Polya's ideas on How to Solve it. While the goal is to seek rigorous proofs, to get there it's powerful to be able to think based on intuition, heuristics, and plausible reasoning. A lot of math exposition is theorem/proof based and doesn't help develop these skills. In a similar vein, see also Terence Tao's classic post There's more to mathematics than rigour and proofs https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-.... 7. H.S.M Coxeter, An Introduction to Geometry. A book of very beautiful classical geometry. Something typically not touched on at all in a typical mathematics curriculum.
• fsloth 4y ago
  ”Road to reality” by Roger Penrose is an interesting book as a refresher and review if the content is otherwise within familiar territory.
• Penyngton 4y ago
  Since I haven't seen many discrete maths books, he's my list: Beginner: NL Biggs, Discrete Mathematics, Oxford University Press Intermediate: PJ Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press Advanced: JH van Lint & RM Wilson, A Course in Combinatorics, Cambridge University Press
• nopeopenope 4y ago
  Shankar Basic Training in Mathematics
• pncnmnp 4y ago
  During my undergraduate studies, I loved "Discrete Mathematics and Applications" by Kenneth Rosen. I really enjoyed reading through the various examples and biographies of famous mathematicians included in each chapter. For those looking to delve into discrete mathematics, I highly recommend the lecture notes from L. Lovasz and K. Vesztergombi (Yale University, Spring 1999) and from Eric Lehman, Tom Leighton, and Albert Meyer (MIT, 2010).
  • jytug123 4y ago
    On a similar subject I recall Concrete Mathematics by Donald Knuth being my favourite book from school.
• Kaizeras 4y ago
  Mathematik für Ingenieure und Wissenschaftler I, II and III from Lothar Papula (in German). The solutions are detailed, making it perfect for self-studying. Book of Proof by Richard Hammack. A great introduction to proofs in mathematics. The book is available free online [0], but also I bought the physical version because I really enjoyed it. [0]https://jdhsmith.math.iastate.edu/class/BookOfProof.pdf https://jdhsmith.math.iastate.edu/class/BookOfProof.pdf
  • oogway8020 4y ago
    I just started reading Book of Proof by Richard Hammack and I agree it's an amazing book
• annowiki 4y ago
  A Programmer's Introduction to Mathematics https://pimbook.org/ https://pimbook.org/ It introduces math from a mathematician's point of view (complete with proofs, etc.) rather than rote memorization and exercises, but it does so from the perspective of a programmer.
• adamsmith143 4y ago
  A lot of comments about textbooks that helped in specific topics but I don't think that answers the spirit of OP's question. Sure working through ANY Linear Algebra textbook is going to improve your Linear Algebra skills. In the spirit of OP's question: How to Solve it by G. Polya Solving Mathematical Problems by Terrence Tao Introduction to Mathematical Thinking by Keith Devlin Are all amazing, How to Solve it in particular is an all time classic.
  • fghorow 4y ago
    For my tastes, Strang's Linear Algebra book is a winner! I'm somewhat surprised the nobody has mentioned it yet...
• binarymax 4y ago
  “Mathematical Notation: A Guide for Engineers and Scientists”[0] really changed my abilities with being able to read papers and decipher what was going on. I had university math experience but it was a long time ago. When I started reading papers for algorithms later in my career I couldn’t get past the notation. Once the symbols are explained, as a programmer, I was able to grok so much more. This should be on everyone’s shelf. [0] https://a.co/d/gQmDIo7 https://a.co/d/gQmDIo7
  • slicktux 4y ago
    Plus one for this! I bought two copies of the referenced book…and for the exact same reasons; I’m a programmer and being able to explain my algorithms using mathematical notation helps validate a program as well as troubleshoot a program… An oldie but goodie is “Mathematics for the million”
  • fouronnes3 4y ago
    As a programmer I really wish math notation was more rigorous: less ambiguity, more explicit typing, no implicit variables, etc. So much of it would never pass code review. We programmers figured out that code should be optimized for readability, not writtability ; I wish mathematicians did too.
    • User23 4y ago
      It can be made to be. Dijkstra came up with a nice and rigorous notation he used for his own proofs[1]. That page also includes some slightly spicy takes on why things are as they are. I agree that this is an area where the broader mathematical field has much to learn from computing science. The unforgiving nature of computing automata really drove that innovation. Meanwhile one can afford to be sloppy when one is trying to convince some other mathematician with a sky high IQ. [1] https://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/EWD1300.html https://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/E...
      • blevin 4y ago
        I did not expect that to read so similarly to a good doc on coding conventions as it did.
• belter 4y ago
  If you have a Love of Books and Math Books in particular, you can't miss this playlist by The Math Sorcerer: https://www.youtube.com/playlist?list=PLO1y6V1SXjjM-1azbCNYq2-A1_7KaioNr https://www.youtube.com/playlist?list=PLO1y6V1SXjjM-1azbCNYq...
  • sthu11182 4y ago
    I've really enjoyed the Math Sorcerer's overview of various math books. Such a breath of topics and levels.
• homerowilson 4y ago
  I'm coming from an applied math perspective. A few of my favorites (and ones I find myself regularly referring to) are: Matrix Analysis by Horn and Johnson (perhaps the best end-of-chapter problem sets of any math book I've encountered!) Matrix Computations by Golub and Van Loan Elements of Statistical Learning by Hastie, Friedman, Tibshirani Functional Analysis by Reed and Simon
• miguelmurca 4y ago
  Knuth's "Concrete Mathematics" is fantastic, precisely because it's very applicable.
• mohamez 4y ago
  I think you guys might find this list I found long ago very useful when deciding on a mathematics book you want to read. This is an introduction written by the original author of the list: "Somehow I became the canonical undergraduate source for bibliographical references, so I thought I would leave a list behind before I graduated. I list the books I have found useful in my wanderings through mathematics (in a few cases, those I found especially unuseful), and give short descriptions and comparisons within each category. I hope that this list may serve as a useful “road map” to other undergraduates picking their way through Eckhart Library. In the end, of course, you must explore on your own; but the list may save you a few days wasted reading books at the wrong level or with the wrong emphasis. The list is biased in two senses. One, it is light on foundations and applied areas, and heavy (especially in the advanced section) on geometry and topology; this is a consequence of my interests. I welcome additions from people interested in other fields. Two, and more seriously, I am an honors-track student and the list reflects that. I don't list any “regular” analysis or algebra texts, for instance, because I really dislike the ones I've seen. If you are a 203 student looking for an alternative to the awful pink book (Marsden/Hoffman), you will find a few here; they are all much clearer, better books, but none are nearly as gentle. I know that banging one's head against a more difficult text is not a realistic option for most students in this position. On the other hand, reading mathematics can't be taught, and it has to be learned sometime. Maybe it's better to get used to frustration as a way of life sooner, rather than later. I don't know." - by original author. [List] https://www.ocf.berkeley.edu/~abhishek/chicmath.htm https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
• hackerbrother 4y ago
  Rudin's Principles of Mathematical Analysis has a really special place in my heart. Chapter 3 is great- it's a great reference for derivations of a lot of fundamental identities about limits used in undergrad calculus. Chapter 4 is a great place to learn about topology for the first time. In general, it kicks up the mathematical rigor you're used to a notch. Seeing ">" defined as "not <" really blew my mind when I first read it! "<" is just something that satisfies some axioms, like anything else in math.
  • r-zip 4y ago
    Wouldn't ">=" be "not <"?
    • hackerbrother 4y ago
      Yup.
• enriquto 4y ago
  The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * Solid Shape by Koenderink * Analyse fonctionnelle by Brézis * Tristan Needhams "visual" books about complex analysis and differential forms * Information theory, inference, and learning algorithms by MacKay (great book about probability, plus you can download the .tex source and read the funny comments of the author) And finally, a very old website which is full of mathematical jewels with an incredibly fresh and clear treatment: https://mathpages.com/ https://mathpages.com/ ...I'm in love with the tone of these articles, serious and playful at the same time.
  • salusinarduis 4y ago
    I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?
    • tomca32 4y ago
      I think Khan Academy is pretty much made for this.
    • friedman23 4y ago
      I'm doing this and am starting with Linear Algebra on MIT OCW (taught by Gilbert Strang). My current plan is to relearn Linear Algebra, Calculus, Probability, and Statistics and actually focus on retaining the knowledge in my memory using something like SRS learning. I think planning past that is pointless since by the time I'm done I will have a better ability to plan my future coursework.
      • _fullpint 4y ago
        Going back through Discrete would probably be a good idea as well.
• samuel2 4y ago
  If you are into numerical optimization, a nice source of intersting problems and examples (that e.g. contradict the intuition) can be found in Mathematical Tapas: Volume 1 and Vol. 2.
• samuel2 4y ago
  Probably the most elegant math book I have ever seen is Probabilty theory a graduate course by Achim Klenke. A very nice exposition into the abstract, measure theoretic prob. thoery (but it assumes some prior knowledge).
• kxyvr 4y ago
  1. Principles of Mathematical Analysis by Walter Rudin (baby Rudin) - I'd studied real analysis in the past, but this book is direct and rigorous and provided a good framework to move forward into things like functional analysis in a way that I was not prepared for with other books. 2. Differential Equations and Dynamical Systems by Lawrence Perko - Solidified for me how dynamic systems behaved and were solved. Very much helped my understanding of control theory as well. 3. A Concise Introduction to the Theory of Integration by Daniel Stroock - Helped solidify concepts related to Lebesgue integration and a rigorous formulation of the divergence theorem in high dimensions. 4. Convex Functional Analysis by Kurdilla and Zabarankin - Filled in a lot of random holes missing in my functional analysis knowledge. Provides a rigorous formulation of when an optimization formulation contains an infimum and whether it can be attained. Prior to this point, I often conflated the two.
• codr7 4y ago
  If I could pick one, that would be How to Solve it by George Polya.
• krmboya 4y ago
  I have not yet become significantly better, and not a math book, but I recently read A mathematicians Lament by Paul Lockhart and it resonated so much with me that I plan to take another stab at math different from how it is taught in school. Waiting to get my hands on his book 'Measurement' and approach it more like art. If what he says is true, perhaps many who would have turned out great at math are locked out by how it's taught in school. For now, I have a test subject of one :)
  • leephillips 4y ago
    What he says is true. If you teach math, you should read it. If you’re like all the other people I know who teach math, you will ignore it.
• aquafox 4y ago
  I can recommend Teschls book on ODEs, and it's completely free: https://www.mat.univie.ac.at/~gerald/ftp/book-ode/index.html https://www.mat.univie.ac.at/~gerald/ftp/book-ode/index.html And if you like something very applied: Modern Statistics for Modern Biology https://www.huber.embl.de/msmb/ https://www.huber.embl.de/msmb/
• vippy 4y ago
  Velleman's How to Prove It greatly helped my ability to construct set theoretic proofs, which better prepared me for Spivak's calculus and Baby Rudin. Hamkins' Proof and the Art of Mathematics is designed as a a good, less set-theory heavy, introduction to proof writing that leads more naturally to analysis. OpenStax books are FREE.
  • JoelMcCracken 4y ago
    I have been going through Velleman, and it has been significantly helping me understand various CS papers and books, for example, I struggled understanding through proof outlines in PFPL, but working through just part of this book has helped. I have had life things interfere with my learning now for the past month or so, but I hope to get back to it soon.
  • strls 4y ago
    Surprised to see Velleman's book so far down. It taught me that proofs are fun and do not in general require clever tricks. As a bonus, it provided plenty of practice with foundational objects such as sets, relations and functions. All this made me much better at doing mathematics and prepared to texts in real analysis, CS, algebra.
• deleted 4y ago
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• kdavis 4y ago
  * 4-Manifolds and Kirby Calculus by Andras I. Stipsicz and Robert E. Gompf * Differential Manifolds by Antoni A. Kosinski * Introduction to Smooth Manifolds by John M. Lee
• angvp 4y ago
  Baldor's series of books (Spanish)
• kache_ 4y ago
  linear algebra done right - sheldon axler
• nhatcher 4y ago
  Lot's of good books already here! In the same spirit as Polya's book "Thinking mathematically" by J. Mason, L. Burton and K. Stacey I learned a lot in the early days with Demidovich book on 5000 problems on mathematical analysis. Tom Apostol books on calculus, but for me his book on analytical number theory. Alongside alan baker's thin book on number theory. Gilbert Strang book(s) on linear algebra. Rudin book on functional analysis. Oh Hardy's book on divergent series! Ian Steward books on transcendental numbers and Galois theory. Elements of algebraic topology by Munkres is a fantastic book. So many books are invaluable to me in teaching not only math but mathematical thinking. I guess if you want to learn thinking but not necessarily math "thinking mathematically" above mentioned is your friend.
  • matthewmorgan 4y ago
    Came here to recommend Thinking Mathematically (text only) by J. Mason. If only every high school maths teacher had this book, the world would be a better place
    • mlpinit 4y ago
      This is a great book. Unlike any other book I've read. It helps with defining a process that I think every person working in a technical field uses one way or another. It helps you develop a way of thinking that reduces anxiety when you are stuck and helps develop paths to get unstuck. This book made me love math and I wish more people knew about it. It's also never too early or too late to pick it up.
• javier123454321 4y ago
  Not a direct answer, but I once read that the best book about a technical topic is the third book you read on it. Often you'll see things in comments sections like: "I have heard this explained so many times by others, but this explanation finally clicked!". The assumption is that that's the case because the explanation is better, rather than assuming it's the case because you've struggled with the material before and you're still going at it.
• mannerheim 4y ago
  Baby Rudin for analysis. Dummit and Foote for algebra.
  • wannabebarista 4y ago
    As far as the canonical texts of math goes, Dummit and Foote is excellent. I'm also fond of the first half of Munkres' Topology.
• michaericalribo 4y ago
  In my experience, the best way to get better at math is to do a lot of it. Find some book that's "good enough" for some topic you're interested, and work many many problems from the book. You'll learn about the topic, but more importantly you'll learn problem solving skills. I recommend working the problem until you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct. For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces. Again, I recommend working nearly every problem. [1] https://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383 https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat...
• lamontcg 4y ago
  Div Grad Curl and All That https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161 https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161
• hyperific 4y ago
  Calculus Made Easy (1910) simply for the quote at the beginning: "What one fool can do, another can." I did horribly in math because I figured it was hard and just accepted I'd never be good at it. That quote somehow managed to dissolve my mental block.
  • djrockstar1 4y ago
    Had to do a Calculus course in uni despite not having taken any calc or pre-calc in high school. "Precalculus Mathematics in a Nutshell" and "Calculus Made Easy" were complete lifesavers.
• Llamamoe 4y ago
  A better question: What books made you significantly better at math that are also genuinely FUN to learn from? I find that my biggest barrier to learning math has always been how unengaging, excessively contrived, and unfun the learning material has been.
  • ABeeSea 4y ago
    David Bressoud’s 4 books on calculus/analysis are the most engaging math books I’ve ever read. He uses the history of mathematics to drive the narrative and it’s an enlightening approach. However, this means certain theorems often taught in undergrad analysis are delayed until his “graduate” book and his graduate book would not be sufficient for passing many universities analysis quals. But the context and history he gives is fantastic.
    • wannabebarista 4y ago
      I always recommend Bressoud's measure theory/integration text as a supplement the first graduate course in analysis. His discussion of weird and pathological sets of reals such as fat Cantor sets are really helpful for building intuition.
• ummonk 4y ago
  It's unclear what kind of mathematical thinking and skills you want. "How to solve it," by Polya perhaps?
• legends2k 4y ago
  Not strictly math books but these three books turned me to live mathematics and appreciate for what it is: [1]: 3D Math Prime for Games for Graphics and Game Development; https://www.gamemath.com/ https://www.gamemath.com/ (free to read online) [2]: Essential Mathematics for Games and Interactive Applications; https://www.essentialmath.com/book.htm https://www.essentialmath.com/book.htm [3]: Mathematics for 3D Game Programming and Computer Graphics; https://www.mathfor3dgameprogramming.com/ https://www.mathfor3dgameprogramming.com/
• lower 4y ago
  There exist only two kinds of modern mathematics books: ones which you cannot read beyond the first page and ones which you cannot read beyond the first sentence. -- Chen Ning Yang
• haskellandchill 4y ago
  I love math books with great exercises, I just wish I could code them up in a theorem prover and solve and store my proofs that way. I've tried a bunch of tools but haven't found a language or workflow that really meets the needs for computer assisted study of mathematics.
• super256 4y ago
  For the German speakers: Something that really helped me with my mathematic modules at university: Lothar Papula's "Mathematik für Ingenieure und Naturwissenschaftler" [1]. If you get the stuff in this book right, you're set for life. [1] https://www.amazon.com/Mathematik-f%C3%BCr-Ingenieure-Naturwissenschaftler-Band/dp/3658056193/ref=sr_1_4?qid=1674146108&refinements=p_27%3ALothar+Papula&s=books&sr=1-4 https://www.amazon.com/Mathematik-f%C3%BCr-Ingenieure-Naturw...
  • amai 4y ago
    I recommend Lang: Mathematische Methoden der Physik https://link.springer.com/book/10.1007/978-3-662-49313-7 https://link.springer.com/book/10.1007/978-3-662-49313-7
• mindcrime 4y ago
  Maybe not "made me better at math" per-se, but definitely "made me more enthusiastic about math": The Universe Speaks in Numbers[1] by Graham Farmelo I found this very motivating and insightful, in terms of developing even more of an appreciation for how much math underpins other branches of science. Not that that is a novel insight by any means... but the details of the incidents where breakthroughs in mathematics allowed further advances in physics, etc. and looking at the "back and forth" between the domains, that was wildly interesting to me. Reading this book definitely helped motivate me to get serious about committing more time / focus to studying mathematics. I also enjoyed the "counterpoint" book by Sabine Hosenfelder, Lost in Math[2]. I think these two books complement each other nicely. Then the handful of additional (no pun intended) books that jump to mind would be: - How Mathematicians Think by William Byers[3] - How to Think Like a Mathematician by Kevin Houston[4] - Discrete Mathematics with Applications[5] by Susanna Epp - How Not To Be Wrong[6] by Jordan Ellenberg - Introduction to Mathematical Thinking[7] by Keith Devlin - How to Measure Anything[8] by Douglas Hubbard [1]: https://www.amazon.com/Universe-Speaks-Numbers-Reveals-Natures/dp/0465056652 https://www.amazon.com/Universe-Speaks-Numbers-Reveals-Natur... [2]: https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/1541646762/ https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/15... [3]: https://www.amazon.com/How-Mathematicians-Think-Contradiction-Mathematics/dp/0691145997/ https://www.amazon.com/How-Mathematicians-Think-Contradictio... [4]: https://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X/ https://www.amazon.com/How-Think-Like-Mathematician-Undergra... [5]: https://www.amazon.com/Susanna-S-Epp-Mathematics-Applications/dp/B008UB79NW/ https://www.amazon.com/Susanna-S-Epp-Mathematics-Application... [6]: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535/ https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143... [7]: https://www.amazon.com/Introduction-Mathematical-Thinking-Keith-Devlin/dp/0615653634 https://www.amazon.com/Introduction-Mathematical-Thinking-Ke... [8]: https://www.amazon.com/How-Measure-Anything-Intangibles-Business/dp/1118539273 https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...
• racl101 4y ago
  I had a print of Euclid's Elements as a kid. My mom was really into mathematical proofs and I being a huge loser kid with no friends naturally took to this book as well.
• sfpotter 4y ago
  Honestly, unless you're very gifted, a book on its own is not going to be enough to really develop your skills. You need to work interactively with a teacher. Getting a degree in math is a good start, but even then it will be limited if you don't work with other people, go to office hours, form relationships with professors---embed yourself in the culture, so to speak. I think getting engaged with an online community like MathOverflow or similar could be a substitute for this. IMO, programming is "easier" to learn on your own for a few major reasons: 1) The sorts of things most people are interested in building just aren't unforgiving intellectually in the same way that math is. 2) You have a compiler to check if you're right, and your code will often still work even if it's "wrong" (not as efficient as it could be, has unwanted side effects, etc.). In some sense the compiler is a bit like a teacher this way. 3) With programming, you can upload and make it available for free, and whether it's legit or not is largely disconnected from your pedigree or how "correct" it is. This makes programming far more accessible. This makes sense considering that programming is primarily a practical tool. On the other hand, mathematics is primarily a field of scientific inquiry and is judged by different standards. If you learn a bit of math, try to write a paper, submit it to the arXiv... well, people will probably think you're a crank. On the other hand, if you're just interested in math for the love of the game... you can certainly pick up a book and read it, maybe work some problems, but I think at this point it's quite easy to fool yourself into thinking you understand more than you actually do. I guess there's no real harm in being a charlatan, but probably the average person is interested in having some kind of real relationship with mathematics that they can be confident has a firm foundation. I'm very skeptical most people can truly pull this off by just reading books and not actually going to school. --- As an aside, I think the fetishization of math in programming communities is very interesting...
  • mindcrime 4y ago
    Honestly, unless you're very gifted, a book on its own is not going to be enough to really develop your skills. You need to work interactively with a teacher. Wouldn't that depend on what level of skill we're talking about? I believe that most people who need to learn just, say, high-school algebra/geometry/trigonometry/etc. can probably do so with "just books" if they are motivated. Heck, I'd even venture that most anybody who is motivated enough can learn at least through Calc III on their own using online resources. I'm going through Calc III right now actually, using a combination of books and online videos, and there hasn't been anything that has struck me as particularly challenging so far. This after only making it to Calc I before I dropped out of school "back in the day". Getting a degree in math is a good start, but even then it will be limited if you don't work with other people, go to office hours, form relationships with professors---embed yourself in the culture, so to speak. I think these things would be critical if one wants to become a mathematician. But for somebody who just wants to learn more math for the purpose of reading (non math) research papers (maybe in machine learning to pick an obvious, if possibly trite, example), solving problems in everyday life or at work, or possibly even for doing research in another (non math) field and then writing up their research, I would think of all of those things as being "nice, sure, if you have access, time, money etc. But not even close to absolutely essential". Unfortunately the OP didn't really say what their goal is, so it's hard to say what advice makes the most sense for them. Also unfortunate is that for probably most people who are working career professionals, there likely isn't enough free time available to go back and do an actual math degree in school. So learning on ones own from books, videos, etc. is probably the only viable choice.
• ericmay 4y ago
  I'm going to cheat and combine a couple of books into "one book". The Manhattan Prep GMAT test prep math books were really good for me for everyday life. I learned a lot of shortcuts and quick heuristics to use and got better at estimating after going through those books. It doesn't help me "get better" in an academic sense, but those books pay dividends every day for me.
• phonebucket 4y ago
  A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics (Wasserman) There are some authors I trust and am happy to buy so long as the topic vaguely interests me: VI Arnold, Tristan Needham and John Stillwell. I really like the list put out by @enriquto in a separate comment, but I've avoided duplicating those recommendations in the list above.
  • wannabebarista 4y ago
    Great list! I want to call out John Stillwell's Reverse Mathematics as a fun and accessible introduction to the field.
• jjgreen 4y ago
  Analysis Now, Gert Pedersen https://link.springer.com/book/10.1007/978-1-4612-1007-8 https://link.springer.com/book/10.1007/978-1-4612-1007-8
• sambapa 4y ago
  Not one book, but this: https://github.com/TalalAlrawajfeh/mathematics-roadmap https://github.com/TalalAlrawajfeh/mathematics-roadmap
• lcuff 4y ago
  Several people who have mentioned "How to Solve It" by George Polya. It's been decades since I've looked at it, but a favorite Polya quote of mine is " "The open secret of real success is to throw your whole personality into your problem." I can't remember if the book addresses this, but for myself my inability to tolerate frustration really impeded my ability to work on any mathematical challenge for decades.
• bmitc 4y ago
  While I have a ton of favorite math books, the two books that I felt really helped me the relevant subject are: * An Introduction to Manifolds by Loring Tu * The Elements of Integration and Lebesgue Measure by Robert G. Bartle. These two books were instrumental to my studying for my qualifying exams.
• college_physics 4y ago
  Math always seemed a bit arbitrary to me. Why and how did all those fields and branches develop, why are some so much more intuitive than others etc. What helped me cope with that challenge (and ultimately be a better learner / user of mathematics) was digging into the history of mathematics. Many great books in that genre but a very influential one for me was the Concise History of Mathematics by Dirk Jan Struik
  • javajosh 4y ago
    >Math always seemed a bit arbitrary to me. That's because math is fundamentally arbitrary. This realization came to me late in life. Math was always presented as some aspect objective reality. However over time I've come to understand it as software for human brain. Using this math or that to describe something is often simply a matter of taste! Very similar to programming, in fact. Your study of history gives context to the question of utility different maths "packages" for certain problems, but does not invalidate your original impression.
    • ska 4y ago
      I think "arbitrary" gives the wrong flavor here. Math is fundamentally curated. It's easy to create something new, because you get to play with the rules - but unless it is in some sense deep, effective, and usually elegant [1] it won't stick around. [1] this is a bit acculturated.
• mythhouse 4y ago
  spivak calculus
• lvl102 4y ago
  The answer is always Elementary Number Theory by David Burton. I read this book since 7th grade.
• DrNosferatu 4y ago
  The classic "Advanced Engineering Mathematics" by Erwin Kreyszig was absolutely 'good enough'. Maybe even more important - for me: it was one of the easiest books to follow and digest during my undergrad. See it as a solid base for other heavier/purer titles.
• anthomtb 4y ago
  The Art of Problem Solving: https://artofproblemsolving.com/store/book/aops-vol1 https://artofproblemsolving.com/store/book/aops-vol1 Yes, it is targeted towards middle and high school students. Yes, I read it and (more importantly) worked through most of the problems in my mid-30's. It is great if, like me, you coasted/crammed through your early mathematics education and never felt like you dialed in the fundamentals. It is also great if, like me, you needed some pen-on-paper practice and did not know where to start.
• gibrown 4y ago
  Nonlinear Dynamics and Chaos by Strogatz Chaos theory and deterministic systems are a fascinating vantage point for thinking about the dynamics of large computer systems. Thinking of them as stochastic systems is sometimes useful, but most of the systems are actually just operating in unstable periodic processes which are much closer to being a chaotic system rather than a stochastic system. This influences how I think about testing and debugging large distributed systems. I will say, I'm not sure I could have learned it well without a class and a good professor. The author has a number of books though and is a professor at Cornell.
  • dorchadas 4y ago
    Absolutely loved this book. Had a class on it in my applied maths and theoretical physics masters and it was hands-down my favourite.
• time_to_smile 4y ago
  I highly recommend working through Claude Shannon's Mathematical Theory of Communications [0]. It's originally a paper but was later restructured as a book, in either form it works quite well. The reason I recommend it is because it shows mathematical reasoning that is easy to follow and relevant to your daily life. It's real math, but very easy to read through and understand. If your unfamiliar this paper is where the very idea of "bits" comes from. One of the most important things in the paper for non-mathematicians to see is that the definition Information Entropy is derived simply from the mathematical properties Shannon desires it to have. This is important because I find that one of the biggest questions people ask about mathematical formula and idea is "What does this mean? Why is it this way?" without realizing that math is really not engineering nor physics. When deriving his definition of Information, Shannon simply states that information should have the following x,y... properties and then goes on to show that the now standard definition of information meets all these criteria. In mathematics it is very often the case that only after an idea is created to we start realizing the applications. This is quite different than science where a model is only adopted if it correctly describes a physical process. Work through the paper and you will have worked through the mathematical underpinnings of the information age and will likely have understood most of it pretty well. 0. https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf https://people.math.harvard.edu/~ctm/home/text/others/shanno...
• northstart001 4y ago
  What if by Randall Munroe Not rigorous but it changed my perspective that was instilled in me in middle school. Otherwise Feynman Notes changed me academically. Easier to pickup math through physics if you arent looking for deeply pure avenues.
• fnordpiglet 4y ago
  Advanced engineering mathematics by Kreyszig Advanced Engineering Mathematics, 10Ed, Isv https://a.co/d/axcq9nk https://a.co/d/axcq9nk
• MrMan 4y ago
  take math classes, start a level lower than you think you need to, do lots of practice problems
• jsenn 4y ago
  * The Art of Probability by Hamming. An opinionated, slightly quirky text on probability. Unlike the text used in my university course its explanations were clear and rigourous without being pedantic. The exercises were both interesting and enlightening. The only book in this list that taught skills I've actually used in the real world. * Calculus by Spivak. This was used in my intro calculus course in university. It's very much a bottom-up, first-principles construction of calculus. Very proof-based, so you have to be into that. Tons of exercises, including some that sneakily introduce pretty advanced concepts not explicitly covered in the main text. This book, along with the course, rearranged by brain. Not sure how useful it would be for self-study though. * Measurement by Lockhart. I haven't read the whole thing, but have enjoyed working through some of the exercises. A good book for really grokking geometric proofs and understanding "mathematical beauty", rather than just cranking through algebraic proofs step by step. * Naive Set Theory by Halmos. Somewhat spare, but a nice, concise introduction to axiomatic set theory. Brings you from nothing up to the Continuum Hypothesis. I read this somewhere around my first year in university and it was another brain-rearranger.
  • bitforger 4y ago
    Arithmetic by Lockhart is also a gem.
  • nextos 4y ago
    These are good recommendations, but I think beginners tend to burn out due to the lack of a structured program and/or exercise solutions if they are trying to study on their own. The simplest structured program I can think of that satisfies both is: * Basic Mathematics by Lang. Covers basic algebra and geometry at high school level. Then one of these two, depending on your interests, or both: * Vector Calculus, Linear Algebra and Differential Forms by Hubbard and Hubbard. Takes you through linear algebra, single-variable calculus and multiple variable calculus. Analysis is discussed in an appendix. All proofs have a constructive bias, so it's very algorithmic and natural for a CS-minded student. Solutions are in a separate volume. * Program = Proof by Mimram. Discusses logic and computation, and takes you from the basics to depedent type theory and beyond. Uses OCaml and Agda. Freely available at: https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching/INF551/course.pdf https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching...
• boothby 4y ago
  No specific book, but generic advise about how to use a math book. Homework, homework, homework. Read the whole thing, but focus on the exercises. Do every exercise as soon as you can manage: don't wait until you've read the whole chapter -- once you get confused and stumped, the lesson of the chapter becomes urgent and I find that sharpens my attention.
  • wheelinsupial 4y ago
    I would add understanding the reasons for definitions, how they fit together with theorems, lemmas, corollaries, proofs, and some basics of the format of proofs. You can find good explanations through Google. For more applied or computational branches of math, I'd also add how to check your answers by using numerical methods or a computer algebra system if possible.
  • sn9 4y ago
    For a case study in how specifically to do this, see this post about how Cal Newport studied discrete mathematics in college: https://www.calnewport.com/blog/2008/11/25/case-study-how-i-got-the-highest-grade-in-my-discrete-math-class/ https://www.calnewport.com/blog/2008/11/25/case-study-how-i-...
    • dysoco 4y ago
      I usually enjoy Newport but... this was rather underwhelming? It's basically "do a lot of proofs and study consistently not just 48hs before the exam". Most if not all of my math and some comp-sci courses would require this, they were very proof-heavy, specially Algebra, Logic and Graph Theory, and there was no way you could even pass just studying for a week after let alone 48hs before.
      • sn9 4y ago
        I mean it's underwhelming if you've done it before, but for people who are unsure about how to succeed in a proof-heavy course, seeing it laid out like this in concrete steps is helpful. You've outgrown being in the target audience for it, but that doesn't mean the audience wouldn't find it helpful.
• acrodrig 4y ago
  The enjoyment of Math (https://www.barnesandnoble.com/w/enjoyment-of-math-hans-rademacher/1101640979 https://www.barnesandnoble.com/w/enjoyment-of-math-hans-rade...). Best book ever. Made me fall in love with math as a teenager.
• downboots 4y ago
  Algebra Baldor ! College Algebra Heineman Discrete Math Rosen ! Linear algebra D lay Calculus Stewart Nonlinear Dynamics Strogatz + Combinatorics Mazur + Statistics * ESLR +
• readingnews 4y ago
  Books do not make you better at math. Working math problems makes you better at math. Go ahead, down vote all you want. Reading about running does not make you a better runner. You can watch 1000 marathons, sprinters, Olympians. You may get _ideas_ for running, but it will never make you a better runner. To be a better runner you have to do it. To be a better programmer/mathematician/physicist/whatever, you need to go work at it. I suppose I am just taking action against how the question is written, but I see a lot of people seemingly hoping that "if they just found the correct book, tutorial, or video, they would be better". A lof of those people are my students. When I ask how many problems they have worked, I typically always get the same response. Zero, or the bare minimum.
  • mcculley 4y ago
    If I were a student, eager to solve math problems and become better at math, no book would be better than any other book at presenting and guiding me to problems that would improve my understanding?
  • enriquto 4y ago
    > Books do not make you better at math. Working math problems makes you better at math. But math books are often full of exercices that you are supposed to do! Actually reading a math book means that you try to anticipate the proofs before reading them, and you work out all the details and do all the exercices. Reading a math book and working math problems are essentially the same thing.
  • philip-b 4y ago
    Reading math textbooks typically involves solving a lot of problems, so you saying it like it's books OR problem solving doesn't make sense.
  • fumeux_fume 4y ago
    So many great responses recommending all kinds of books and then there's... this. Lol. Such a jaded/cynical teacher thing to say, but sure, nothing is a substitute for what you get out of putting the effort into doing. For me, the biggest hurdle to succeeding at college-level math was a lack of motivation due to the meaninglessness of most of the content.
• d_tr 4y ago
  A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekeres My intro to abstract math... Wide range of topics, very clearly written and very well structured. Sets, groups, vector spaces, tensors, topology, differential geometry, lie groups and more. An Introduction to Category Theory by Harold Simmons Very enjoyable read. You cannot go wrong with this as your first book on the subject.
• rcpt 4y ago
  Apostol's Calculus changed my life when I was 18
• LanceH 4y ago
  The Time/Life book "Mathematics" published 1969. I was in 2nd grade, liked mathematics and saw a book with that name and pictures. It was a high level survey of a lot of mathematical concepts, explaining things in a way I could understand at that age, but also in a way that wouldn't be talking down to me today.
• Ian_Macharia 4y ago
  A Programmer's Introduction to Mathematics by Jeremy Kun
• mindcrime 4y ago
  To add one more thing: the "thing" that has helped me most lately isn't a specific book or video or anything, but rather simply committing to spending 1 hour every day on math. I even set up a Google Calendar task to remind me of this every. single. day. And so far this year I haven't missed a day yet. Now what constitutes that hour can vary. It can be watching math videos, it can be solving problems on paper, and I might even let myself count futzing around with numerical computing stuff or something at some point. In practice so far it's basically always either watching videos, reading books, or doing exercises (from books). I won't claim that everybody must do this, or that you need to commit 1 hour every day. Maybe 30 minutes would be fine. Or maybe some people who can spare the time would be well served to commit 2 hours a day. Who knows? But having some kind of routine strikes me as something that most people would probably find valuable.
  • empyrrhicist 4y ago
    Yeah, I've been doing the same thing, but with the rule that I have to do "a math problem". Right now I'm going through a stochastic processes book a bit at a time that way and really enjoying it.
    • jay3ss 4y ago
      In my experience, nothing beats solving problems. Even if you get help via solution manuals. I went from being a B/A student to top of my classes (engineering) by solving many problems. I would do my homework and then go back before exams and redo the homework twice for a total of solving the problems 3 times. Never failed me. I actually managed to get a perfect score from a professor who wrote notoriously difficult exams where a 50% to 60% was curved to be a B
      • empyrrhicist 4y ago
        Yep, a book with proofs and worked exercises is great for this because you can try to do the proof and then look at the solution to see if you got it reasonably correct. In my case the book covers a lot of stuff that I passively "know", but working problems has helped get be back to an active understanding.
• wallscratch 4y ago
  Going to echo the suggestions for the Art of Problem Solving books, particularly I recommend the contest books (vol 1 or 2). Several very talented people have said to me that these books taught them how to think. Maybe a bit exaggerated, but they’re very good.
• Jimmc414 4y ago
  Some that stand out "Concrete Mathematics: A Foundation for Computer Science" by Knuth, Graham, and Patashnik - solid foundation in mathematical concepts and techniques, and it helped me develop a deeper understanding of mathematical notation and problem-solving. "Introduction to the Theory of Computation" by Michael Sipser - introduced me to the theoretical foundations of computer science, and it helped me develop a strong understanding of formal languages, automata, and complexity theory. "A Course in Combinatorics" by J.H. van Lint and Wilson - provided a comprehensive introduction to combinatorics, and it helped me develop a strong understanding of combinatorial techniques and their applications. "The Art of Problem Solving" by Richard Rusczyk - This book is a comprehensive guide to problem-solving, with a focus on mathematical problem-solving strategies. It helped me develop my problem-solving skills and learn how to think critically about mathematical problems.
  • bick_nyers 4y ago
    +1 for The Art of Problem Solving
  • yownv 4y ago
    +1 for Introduction to The Theory of Computation
• agentultra 4y ago
  How To Solve It by G. Polya https://press.princeton.edu/books/paperback/9780691164076/how-to-solve-it https://press.princeton.edu/books/paperback/9780691164076/ho... A Logical Approach to Discrete Math by David Greis and Fred Schneider, https://link.springer.com/book/10.1007/978-1-4757-3837-7 https://link.springer.com/book/10.1007/978-1-4757-3837-7 I'm self-taught so for me it was learning how to write proofs that gave me a big boost in being able to branch out into different area of interest and not give up. :)
• epistemer 4y ago
  [dead]
• bluenose69 4y ago
  Jeffreys, Harold, and Bertha Swirles Jeffreys. Methods Of Mathematical Physics. Cambridge At The University Press, 1950. http://archive.org/details/methodsofmathema031187mbp http://archive.org/details/methodsofmathema031187mbp.
• WillAdams 4y ago
  A pair which I am most of the way through: _Make: Geometry: Learn by coding, 3D printing and building_ https://www.goodreads.com/en/book/show/58059196 https://www.goodreads.com/en/book/show/58059196 and _Make: Calculus: Build models to learn, visualize, and explore_ https://www.goodreads.com/book/show/61739368-make https://www.goodreads.com/book/show/61739368-make I'd really like to find a similar book on conic sections --- my next major project seems to need them, and when I tried to solve it using trigonometry alone, I wound up 7 or 8 levels deep in triangles and wasn't much more than half-way to where I needed to be.
• amai 4y ago
  Polya: How to solve it https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It
• makr17 4y ago
  Freshman year of undergraduate math required How to Solve it -- Polya The Art of Problem Posing -- Brown and Walter I'm not sure it made me any _better_ at math, but I did always enjoy How to Lie With Statistics -- Huff
• omershapira 4y ago
  Donald Sarason's "Complex Function Theory". There are bigger more complete books on complex analysis. There are even ones that are more appealing, like "Visual Complex Functions" by Elias Wegert. Sarason's book is only 160 pages long, with legible text and clear examples. It covers the length of an undergraduate university class, and explains Holomorphic functions perfectly. The proofs are crystal clear, and so are the motivations. I haven't seen a better introduction.
• stormdennis 4y ago
  K A Stroud Engineering Mathematics is probably the book that helped me most. 31 chapters each composed of about 60 problems. The problems are progressive and contain explanations of the new concepts that they contain. All the answers are at the back.
  • kingkongjaffa 4y ago
    I used this book and the sister book “advanced engineering mathematics” for my bachelors and masters degree in mechanical engineering. It is probably the best pair of books ever written for what I like to call “plug and chug” maths. Strouds books cover the whole of engineering mathematics. I turned to them for calculus in first year, and for Fourier and Laplace in my final year and masters. But it will not teach you how to solve and develop proofs.
• lsandov1 4y ago
  * 'The Joy of X' by Steven Strogatz. I really like this book, on my second read now.
• thrownawaydad 4y ago
  Not a book, but an animated short: https://en.wikipedia.org/wiki/Donald_in_Mathmagic_Land https://en.wikipedia.org/wiki/Donald_in_Mathmagic_Land “If you want to build a ship, don’t drum up the people to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea.” --Antoine de Saint-Exupéry
• sampo 4y ago
  I was reading this book, when the ideas of function spaces, functions as vectors, functions as elements of vector spaces, functional analysis clicked on me. I am not sure if this book is particularly good or better than other books. (Well, it still looks like a very gentle introduction to the topic.) But as per your question, this was the book at the right time for me. "Fourier Series and Orthogonal Functions" by Harry S. Davis. https://www.amazon.com/dp/0486659739/ https://www.amazon.com/dp/0486659739/
• skyde 4y ago
  On a similar note: Does anyone have book they would recommend to teach Algebra or pre-algebra to young kid?
  • rahimnathwani 4y ago
    Not a book, but I recently had my son look at the pre-algebra track brilliant.org, and it looks nice. I'm not sure whether there's a paywall.
  • sn9 4y ago
    AOPS: https://artofproblemsolving.com/store https://artofproblemsolving.com/store
• hintymad 4y ago
  For what level and in which area? Books like _Methods of mathematical physics_ can be both too hard and irrelevant to your needs. For starters, To become a better problem solver with high-school level maths: - Polya's How to Solve It. - Books of your choice about math contests. - Concrete Maths. I understand that this book is taught in college, but it requires very little advanced maths, and its techniques are hugely useful for high school students too. To hone my intuitions. I learned it the hard way that college maths were different from high school math: in high school, my teachers painstakingly drilled intuitions into us with very targeted explanations and tons of well designed exercises. In college, we won't get such luxury. So, it's really up to us to understand mathematical concepts intuitively before diving into technical details. For that matter, the following books helped me a lot: - The visual series. Visual Complex Analysis and Visual Group Theory, for instance - Pinter's A book of Abstract Algebra - Strichartz's The Way of Analysis - Linear Algebra Through Geometry by Wermer. The book offers a comprehensive geometric interpretation to linear algebra concepts. It's especially helpful for me to understand quadratic forms. To understand Analysis better. This area is vast, so I'll skip recommendations of excellent text books: - _Counterexamples in Analysis_. Those counterexamples in Analysis play a huge role in helping me truly appreciate the intricacies of Analysis. Similarly, books like _Counterexamples in Probability and Real Analysis_ are of great help too. - The Way of Analysis by Robert S. Strichartz. This books is AMAZING for laymen like me. You'd want someone to *explain* how concepts emerge, and how intuitions evolve. To become good at maths by doing maths, so the following books used to help me a lot: - Problems and Proofs in Real Analysis - Putnam and Beyond. I still suck at maths, but those well designed problems in Putnam really taught me how to seek insights in higher maths. - Piotr's Problems in Mathematical Analysis. But really, any problem books that challenge you will do. I'd recommend you find problem sets from the website of university courses. They cover essential techniques, and will not be as overwhelming as the books.
• kevinventullo 4y ago
  This is a bit of an odd suggestion, but I learned the basics of category theory from the appendix to Weibel’s “An Introduction to Homological Algebra”. I’m not sure why, but I think the fact that it’s an appendix meant the author had no motivation to inflate the content unnecessarily. So it’s more like a pamphlet; only about 30 pages IIRC, and it’s really just the bare-bones definitions and facts. The full-on textbooks dedicated to category theory have way too much superfluous content IMO, unless your aim is to be a researcher in that field specifically.
  • enriquto 4y ago
    This happens a lot! For example, at the appendix of an advanced book on PDE (e.g. Evans') you find a three-page summary of main definitions and results in integration theory and L^p spaces. Or at the appendix of a book on differential geometry (e.g. do Carmo's) you find a succinct compendium of elementary differential calculus, explained in the most efficient way. These kind of condensed summaries, or fascicules de résultats, are rarely found on books that deal with the subject matter directly.
• kbelder 4y ago
  I don't think there is any book I've read as an adult that was particularly special. If I wasn't already good at math, I wouldn't be reading these books in the first place. Not that there weren't good and helpful books, but I wouldn't say any of them were revolutionary to me. But I'd like to mention two books I read as a child which had a life-altering effect. They probably wouldn't do any good for an adult, but might really help your kids... Unfortunately, I don't remember the specific titles or authors (I was probably around 10 yrs old). The first was similar to this book: "Speed Math for Kids: The Fast, Fun Way To Do Basic Calculations." This gave all sorts of advice and tips to quickly do math in your head... simple things, mostly. For example, to multiply by 18 just double, multiply by 10, and subtract 10%; or how it's frequently faster to multiply numbers by moving from most significant digits to least, which is opposite of how we're taught; or how to quickly estimate square roots. This really didn't teach new concepts, but by making routine and tiresome math operations faster and easier, it made the entire field more enjoyable to engage with. The second book was a guide to slide rulers, and I couldn't even find a similar book on Amazon. But learning advanced slide ruler techniques can trigger an epiphany; you learn mathematical relationships, how you can transform how numbers are represented. It was the first time I really saw an elegant structure behind the math.
• Buttons840 4y ago
  All the Math You Missed by Thomas A. Garrity. I have not read it, but it looks interesting and is on my list. It is aimed at new graduate students who need a quick refresher that is still detailed enough to be useful for postgraduate math.
• thanatos519 4y ago
  Mathematics, a Human Endeavor: A Book for Those Who Think They Don't Like the Subject by Harold R. Jacobs
• imranq 4y ago
  Counter-intuitively, reading Tim Ferris and his DSSS approach made me much better at math Deconstruct: Break down the math you want to know into big problems and concepts. Pick a math-related goal that is Measurable and Time-Bound Selection: What the 20% of math concepts, that if made really strong, would solve 80% of math problems Sequencing: What order of material should you study for maximal progress Stakes: Find some incentive to complete the problem. Some nice view of mathematical terrain, as part of a masters program, applications to another field, a prize, a cookie. Anything that motivates you to actually make progress towards the goal This approach helped me learn a bunch of high level math like abstract algebra, analysis, linear algebra, etc.
• s-xyz 4y ago
  Optimization by Jan Brinkhuis https://books.google.com/books/about/Optimization.html?id=UWKYDwAAQBAJ https://books.google.com/books/about/Optimization.html?id=UW...
• geocrasher 4y ago
  "How to use Calculators" by R. U. Kiddinme
• jordibc 4y ago
  For sure I got significantly(?) better with classics like Spivak, Apostol, Rudin. "Real and Complex Analysis" by Rudin, and the two books both named "Calculus" from Spivak and Apostol. But also from Apostol his more concise and far-reaching "Mathematical Analysis". And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me. Other than more "classic math" books, I also wanted to mention two outliers that I found eye-opening and generally awesome: * Street-Fighting Mathematics, by Mahajan (http://streetfightingmath.com/ http://streetfightingmath.com/). Intuitive, useful and fun. * Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra, this is the one that made it for me.
  • dorchadas 4y ago
    > * Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra, this is the one that made it for me. I've tried to read several of them, and, sadly, I feel most geometric algebra books fail at explaining it. It's a shame as it's part of what kindled my interest in pure mathematics and I still feel I'm nowhere nearer understanding it despite working through several other mathematics textbooks, including just plain algebra. But, it did spark my interest and now I've moved on to other interesting topics, though Geometric Algebra is still my white whale.
    • jordibc 4y ago
      In case it helps: In addition to "Geometric Algebra for Physicists" (whose first two chapters I'd recommend to get a nice overview), I found Hestenes' "New Foundations for Classical Mechanics" to be very good and readable. Also, there are many good resources in https://bivector.net/ https://bivector.net/ , including videos, papers, presentations and programs. Finally, an interesting paper (that got me kickstarted) is "Imaginary Numbers Are Not Real—The Geometric Algebra of Spacetime" by Gull, Lasenby and Doran.
• d0m 4y ago
  Quantum Mechanics: The Theoretical Minimum --> Great book to learn about quantum mechanics and as a side effect math
• 6gvONxR4sf7o 4y ago
  Probabilistic Graphical Models by Koller & Friedman. In anything statistics and ML related, being able to deal with complicated probabilitistic things that are all related is really useful. This book gives you that toolkit. It's a "strong foundations" kind of book, rather than a bunch of methods you'll use directly.
• ForHackernews 4y ago
  The Art and Craft of Problem Solving https://archive.org/details/the-art-and-craft-of-problem-solving https://archive.org/details/the-art-and-craft-of-problem-sol... This is only math book I've ever read that teaches the mindset needed to work mathematics problems, rather than mathematical concepts or techniques.
• brainzap 4y ago
  something with gamedev probably
• dqpb 4y ago
  Not a book, but I loved this: * The Natural Number Game https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g...
• moomin 4y ago
  Baby Rudin opened my eyes to what you can do with maths.
• aught 4y ago
  A decade of the berkeley math circle and concrete mathematics
• agumonkey 4y ago
  If the HN crowd is up for it, I'd love similar book threads for physics, chemistry and biology.
• siavosh 4y ago
  Best "math book" for kindling interest in mathematical thinking in an elementary school kid?
  • alimw 4y ago
    There are some Lockhart books mentioned on this page.
• chkhd 4y ago
  * The Language of Mathematics: Utilizing Math in Practice by Baber https://www.amazon.com/Language-Mathematics-Utilizing-Math-Practice/dp/0470878894 https://www.amazon.com/Language-Mathematics-Utilizing-Math-P... really helped me "get it", as I always found programming natural but math hard. This one is written by a CS professor and it really makes all the difference. * How to Solve it by Polya https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie... and How to Prove it by Velleman https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995 https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... helped strengthen that understanding. * This year I am trying to master https://www.amazon.com/Methods-Mathematics-Calculus-Probability-Statistics/dp/0486439453 https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... which focuses on how to "connect the dots". * I am using Geometry and the Imagination by Hilbert https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publishing/dp/0821819984 https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... as an attempt to "immerse" myself in Geometry. I just love this book.
• actinium226 4y ago
  Elementary Differential Equations by Boyce and DiPrima I'm not sure I'd say that it made me significantly better at math, but I keep coming back to it time and again, and usually via very different paths.
• williamscales 4y ago
  The three for me were: - Principles of Mathematical Analysis by Walter Rudin (aka “Little Rudin”) - Linear Algebra and its Applications by David Strang - Elementary Differential Equations and Boundary Value Problems by Boyce and Diprima
• Py-o7 4y ago
  Steele's The Cauchy-Schwarz Masterclass is actually quite good and seemingly designed for self study. (A lingering result of this book is I heavily use inequalities even outside of analysis.) Artin's Algebra probably has had the most impact on my math thinking. The development of groups and rings while tightly linking them to linear algebra was rather brilliant.
  • selimthegrim 4y ago
    Seconding Steele (cf. my comment)
• mdkl 4y ago
  The correct answer is, of course, Beast Academy, the lead-in to the Art of Problem Solving.
• Wistar 4y ago
  Not nearly as rarefied as many of the books cited here, for me it was John Saxon's excellent Algebra 1/2, Algebra 1, and Algebra 2. I didn't get a good enough grasp on basic Algebra in high-school. When I was in my early–mid 20s, a friend gave me these three algebra textbooks. In a marathon session lasting about two weeks, I went through all three books from end-to-end and really learned algebra. For whatever reasons, the Saxon books worked really well for me — better than any other learning I have ever gotten from a textbook. Although I was very motivated, I attribute a lot of my success learning algebra well to those three books. I still own them.
• orsenthil 4y ago
  For me, it was just practice with whatever the problem that I was doing, and the book which was in front of me.
• savryn 4y ago
  Abstract Algebra: A Student-Friendly Approach by Dos Reis Paperback layout feels like a workbook, not overwhelming-- beginner friendly
• Dalewyn 4y ago
  None. As far as I'm concerned, they all suck because academia goes about teaching math in all the wrong ways. I finally learned the point behind math thanks to dabbling in programming. All the math classes and teachers and textbooks in the world will never teach me what the importance of 1+1 is.
• zmgsabst 4y ago
  I really liked “Excursions in Modern Mathematics” and “The Shape of Space”. Not the most technical — but really influenced how I thought about mathematics.
• germamme 4y ago
  Differential and Integral Calculus (Volumes 1 & 2) – Nikolai Piskunov Not as colorful and attractive but the adage "do not judge a book by its cover" applies so well to this masterpiece. With brief and precise explanations and high quality exercises with solutions, I went from struggling to getting A+
• o4tuna 4y ago
  _Mathematics for the Million_ by Lancelot Hogben.
• bcbrown 4y ago
  In early high school in the 90s, I got my parents to buy me an (expensive) copy of Chaos and Fractals: New Frontiers of Science by Peitgen, Jurgens, Saupe. The end of each chapter was a Basic program for calculating and displaying various fractal/chaos theory images, and that's what got me started programming. It also included a bunch of mathematics involving "neighborhoods", meaning the set of all points within a distance of an arbitrarily small epsilon from some point X. Although I never did any of the math problems from the book, that early exposure to epsilon made calculus vastly easier to understand, and for that, it's close to my heart.
• djmips 4y ago
  A lot of people have mentioned Keith Devlin's book "Introduction to Mathematical Thinking" by Keith Devlin but for me his other book "Mathematics: The Science of Patterns" was something that really had a huge impact on me just to put mathematics in perspective. Probably has something to do with my own personal character and education but I needed that perspective before I could take the next step. Then the "Introduction to Mathematical Thinking" is a great following read. So it depends where you are.
• Twisol 4y ago
  As a child, I re-read The Number Devil constantly. It introduced me to some really cool mathematical ideas, couched in a cute story. The very last chapter includes a picture of the Principia Mathematica's proof of 1 + 1 = 2 -- mostly for shock value, I think, but also "even this is within your reach". I recently got to see a friend's copy of the Principia, and I realized just how much of it I actually did understand, which was a really nice closing of the loop. As an adult, Imre Lakatos' Proofs and Refutations gave me a much richer understanding of definitions in mathematics -- what job they're meant to do, and when it makes sense to change your definitions instead of adding premises to your theorems.
• Waterluvian 4y ago
  You know how Feynman has these lectures where he digs into physics but you don’t need to know any to get lots out of it? Is there that for math? Books or lectures that talk about math without doing the math?
  • SkyBelow 4y ago
    I've found YouTube videos can do a good job. Entry level: 3 Blue 1 Brown, Mathologer More advanced: Many random one offs which I haven't yet to establish a good pattern for, Richard E Brocherds seems to have a few series though I have to take them slowly as they are more akin to a college lecture. Number crunching examples: Michael Penn. Also should have some more theory based videos but I have only watched his problem solving ones. Avoid: Numberphile just ends up feeling empty and devoid of any depth. Maybe it works for someone so entry level that they don't follow along with Mathologer but I don't see any value and would like a way for YouTube to stop recommending their videos.
• iancmceachern 4y ago
  Math magic Https://www.amazon.com/Math-Magic-Calculator-Everyday-Problems/dp/0688104762
• teleforce 4y ago
  The Road to Reality: A Complete Guide to the Laws of the Universe In this book, Roger Penrose a Nobel Prize winner in Physics for his contributions in mathematical physics of general relativity and cosmology, provides background math to understand the book's contents in the first half of the book.
• musictubes 4y ago
  I read the first chapter of “Mathematics; Its Content, Form, and Meaning” (or something close to that) and it explained the entirety of my high school mathematics. If I had been given that to read back then I might have gone into mathematics in college. Instead I got burned out and quit doing any math for a decade or more. Sigh.
  • sonabinu 4y ago
    This is a great book! +1
• garbagecoder 4y ago
  Spivak, Abbott, Hubbard & Hubbard, Linear Algebra Done Right, Gallian’s Abstract Algebra, and believe it or not MTW taught me more good math than many math books.
• throwaway81523 4y ago
  It may be sacrilege but I learned a lot from "Numerical Recipes". Not in much depth, but enough to wet my feet in a number of areas that were new to me.
• selimthegrim 4y ago
  The Cauchy-Schwarz Master Class by J. Michael Steele Linear Algebra by A.O. Morris (out of print and tricky to find)
• volkanvardar 4y ago
  * The Man Who Loved Only Numbers, by Paul Hoffman https://www.goodreads.com/book/show/714583.The_Man_Who_Loved_Only_Numbers https://www.goodreads.com/book/show/714583.The_Man_Who_Loved... * Algorithms to Live By, by Brian Christian & Tom Griffiths (not really a Math book, mostly computer science, but still has some math algorithms and their implementations to real life) https://www.goodreads.com/book/show/25666050-algorithms-to-live-by https://www.goodreads.com/book/show/25666050-algorithms-to-l...
• Aromasin 4y ago
  Khan Academy. Not a book per-se, but have worked through the courses over the past few years, I'm confident that my college and university results would be about 2 or 3 grades higher we I to retake them. https://www.khanacademy.org/ https://www.khanacademy.org/
• I_complete_me 4y ago
  I got a lot out of "Unknown Quantity" by John Derbyshire. Subtitle a real and imaginary history of algebra. I particularly enjoyed the lead up to the Chapter "Assault on the Quintic". Also, I hold "The Dictionary of Curious and Interesting Numbers" close to my heart for the endless fun it brought me.
• lr1970 4y ago
  V.I. Arnold "Problems for children from 5 to 15" [0]. The book was discussed on HN in 2021 [1] (325 comments) If you have kinds and teach them math this book has mind-opening problems that even curious adults would enjoy. [0] https://www.imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf https://www.imaginary.org/sites/default/files/taskbook_arnol... [1] https://news.ycombinator.com/item?id=27884973 https://news.ycombinator.com/item?id=27884973
• odraude 4y ago
  Nonlinear Dynamics and Chaos by Strogatz - does a great job at explaining very complex mathematical topics with great examples. Not for beginners. Every applied math student should read this cover to cover.
• odraude 4y ago
  Nonlinear Dynamics and Chaos by Strogatz is a work of art
• mindentropy 4y ago
  Has anyone read "Common Sense Mathematics"? I really liked that book for shortcuts to elementary maths for mathematical analysis of everyday things.