16 ms·

Ask HN: Are there books for mathematics like Feynman's lectures on physics?

• aportnoy 7y ago
  Calculus by Michael Spivak
  • dilap 7y ago
    seconded. this book is fantastic!
• bgutierrez 7y ago
  Prelude to Mathematics by W.W. Sawyer was written to give students an overview of modern math concepts beyond algebra. Topics include non-euclidian geometry, linear algebra, projective geometry and group theory. Again, for someone with an understanding of algebra. I enjoyed it and think it's in the spirit of what you're looking for. Edit: Introduction to Graph Theory by Trudeau is another that I really liked. Very little was applicable to graphs as programmers think of them. Pure math that is easy to grasp and enjoy.
  • agentultra 7y ago
    I came to add add Introduction to Graph Theory and found it here. I second it! A nice book and I appreciate it's funny introduction as a book designed for liberal arts majors injured by the pedagogy of institutional mathematics (paraphrasing). If you have a grasp of algebra and sets this book is an easy read for the curious or mathematically immature. Edit WhatIsDukkha is correct and their suggestion better reflects what I intended to say.
    • WhatIsDukkha 7y ago
      Innumerate is infrequently used but it's analogous to calling someone illiterate. Someone that can't do their sums. Usually saying someone isn't "mathematically mature" ie able to read and use proofs is what you would want to say.
      • bjornsing 7y ago
        You can do a lot of graph theory without being able to sum integers. No problem. :)
• chefschef 7y ago
  Mary Boas wrote one of my fav books targeting folks in the physical sciences: https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269 https://www.amazon.com/Mathematical-Methods-Physical-Science...
  • dhimes 7y ago
    She is excellent, as is that book.
  • UncleSlacky 7y ago
    Stroud's "Engineering Mathematics" is better for my money.
• oliveshell 7y ago
  I know you asked for books, but I have to mention the videos of Grant Sanderson (3Blue1Brown) [1]. His explanations of mathematics are the only ones I can think of that have given me the same sort of piercing clarity and insight that one gets from reading Feynman on physics. [1]: https://www.youtube.com/c/3blue1brown https://www.youtube.com/c/3blue1brown
  • slx26 7y ago
    I guess he's pretty popular around here, but if anyone still hasn't seen the channel, please check it out. if I could, I'd vote for this guy to get a nobel prize. seriously. education is critical to our future, and efforts like set an example that I personally consider to be invaluable on the long run. what I mean is that it's easy to recommend videos of people like this, but since it's "just a youtuber", we often fail to reflect more deeply about what's —at least in my opinion— an amazing contribution to humanity.
  • orthoxerox 7y ago
    I agree that he's a great educator. I wonder if a book by him would work as well, though. A lot of his explanations depend on the animations he makes. Maybe if schools and colleges had off-the-shelf software that was 80% as good at making explanatory animations as his Python lib is we would see a huge boost in the understanding of maths.
• hos234 7y ago
  I liked Steven Strogatz's books Sync and Infinite Powers.
  • falcor84 7y ago
    Seconded, and so is his Nonlinear dynamics and Chaos
• harshreality 7y ago
  Feynman was a unique teacher of course, and pure math isn't quite as easy to teach intuitively. Something that might be close would be the survey _Mathematics: Its Contents, Methods and Meaning_ by Aleksandrov, Kolmogorov et al. https://www.goodreads.com/book/show/405880.Mathematics https://www.goodreads.com/book/show/405880.Mathematics
• fano 7y ago
  I bought Prelude to Mathematics when I was 12, it was the first maths book I bought. That was a very long time ago! I thought it was very good, I don't know of another book quite like it. He produced some other good books as well.
• mathmania 7y ago
  Rudin
  • ska 7y ago
    Rudin (and baby Rudin) don't really fit the request here, a Feynman-like approach.
• jordigh 7y ago
  Spivak's Calculus. It's "just" calculus... but it's also everything else leading up to it. It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with (and of course, all of the things we can do with our newfound definitions).
  • oldgradstudent 7y ago
    It's also a beautiful book.
    • frostburg 7y ago
      Yeah, great layout and typesetting. I have a copy mostly for this reason.
  • Hugh1729 7y ago
    Second this. All Spivak's books are gems.
  • rcpt 7y ago
    Apostols Calculus was huge for me. Probably the main reason I majored in math.
  • mrbrowning 7y ago
    One of the biggest conceptual moments in my life was taking an intro class to complex analysis in high school (not through my school itself, this was at a nearby university that runs a weekend program for interested applicants). It's probably not a novel intellectual framework for anyone who's spent time learning math from a theoretical point of view, but the guy who taught it opened with an (admittedly ahistorical, but that wasn't the point) tour of the development of numbers, starting with the intuitive case of counting, moving on to algebra and the question of what type of number could satisfy an equation like x + 5 = 2, and so on. He wasn't taking any philosophical position re the question of discovery vs. invention, but merely inviting us to consider the particular case of operations over a set not being algebraically closed and what it looks like to extend that set to support algebraic closure in a rigorously defensible way. Reading Spivak's Calculus, with the way that it starts off its path of inquiry by showing that, beginning with the basis of a totally-ordered field, the axioms at hand don't suffice to demonstrate the existence of e.g. a number that satisfies x^2 = 2, made me feel right at home again. It's like a detective story.
• jakovleff 7y ago
  I recommend “What Is Mathematics? An Elementary Approach to Ideas and Methods” by Courant and Robbins. It’s a classic.
• mturmon 7y ago
  Graham, Knuth, and Patashnik's Concrete Mathematics has the same exploratory and informal tone that the Feynman lectures have. It's more about computational math than abstract math.
• KingCobra 7y ago
  "Mathematics Can Be Fun" by Yakov Perelman Not really a book that has lectures but it's a great book that covers all popular topics in Mathematics (fun to read). (Link: https://mirtitles.org/2015/12/07/mathematics-can-be-fun-yakov-perelman https://mirtitles.org/2015/12/07/mathematics-can-be-fun-yako...)
  • rramadass 7y ago
    ALL books by Yakov Perelman are a must read for every educated person. "Science popularization" at its finest! How i wish modern "authors" wrote books like these in their area of specializations. Some of his Books; * Physics for Entertainment Vols I & II * Algebra for Fun * Figures for Fun
• beagle3 7y ago
  When I was studying physics, I found Feynman’s books in the library, read them all, and had the feeling I understand everything! But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition. I know my experience is not unique - in fact, everyone I know who tried to learn exclusively from Feynman had the same experience.
  • sarah180 7y ago
    Very much this. I'd recommend using these books as adjunct material. I found them indispensable as an undergrad when I was struggling to shift from a mathematician's rigor-and-proof perspective to a physicist's intuition-and-approximation perspective. However, I don't think I could have come close to passing my QM or E&M courses, even with a mathematical background that was stronger than most of my peers, if I'd only used Feynman to learn the physics.
  • tacon 7y ago
    Exactly, Feynman is a seductive writer, and it is a shock how little you can immediately apply after "understanding" a section. Long ago, they used Feynman's books for my introduction to physics, and it was only after struggling with a problem set that we "knew" the material. http://www.feynmanlectures.caltech.edu/info/exercises.html http://www.feynmanlectures.caltech.edu/info/exercises.html Some references to good collections of mathematics problems and solutions would be great for self-study.
  • joelaaronseely 7y ago
    Yeah, he was like that in person as well. When I was an undergraduate, he would "teach" a seminar on Tuesday afternoons called "PhysX" where you could go and ask any question you wanted. He'd go up to the blackboard and extemporaneously write things down and explain things in such a way that thought you really understood. But when you got back to your room and tried to replicate the chain of reasoning, there were always pieces missing or leaps that you now couldn't make. (It felt like the Star Trek Episode, "Spock's Brain".) But we all took that as an indication of our own lack of knowledge and intuition and would just try harder.
• claudiawerner 7y ago
  Reposting a comment I wrote a while ago, and may be appealing given you're learning physics: >This isn't a popular suggestion (and by that I don't mean to say it's rejected or people don't like it, I just haven't heard it suggested before in this context) but at university for electronic engineering we used K.A. Stroud's Engineering Mathematics. This book is surprisingly little focused on actual applications to engineering, it takes you through calculus by introducing the derivative, for example, and then some linear algebra stuff. But what surprises people is that it starts off with the properties of addition and multiplication - it's that simple. It's a book that starts from zero and takes you very, very far. It won't take you to a mathematician's 100 but it'll take you to any serious engineering undergrad's 100.
• denzil_correa 7y ago
  "Calculus Made Easy" by Silvanus P. Thompson (1910). It is availably freely online via the Gutenberg project and many other forms too. Chapter 1 is probably the best mathematics chapter I have ever read [0]. In two paragraphs, it beats most other calculus books. [0] http://calculusmadeeasy.org/1.html http://calculusmadeeasy.org/1.html
  • rsapkf 7y ago
    Came here to tell this. IIRC, a newer edition of the book by Martin Gardner was published in 1998 with some notable updates. I read the newer one when I was in high school and as with all other Martin Gardner books, this was an absolute gem to learn and understand calculus.
  • cardimart 7y ago
    Came to say the same. CMD+F didn't disappoint.
• vector_spaces 7y ago
  The closest I'm aware of is What Is Mathematics? by Courant, Robbins, and Stewart -- starts off developing the natural numbers, goes onto number theory, analysis, complex numbers, set theory, projective geometry, non-euclidean geometry, topology, calculus, optimization, and some chapters on recent developments (as of its republishing in 1996, book was originally published in 1941). A lesser known one that isn't quite as comprehensive is a little Dover tome by Mendelson: Number Systems and the Foundations of Analysis. It starts off with the (abstract) natural numbers, and from there develops (parts of) real and complex analysis, using a categorical point of view throughout. One of my favorite parts in the latter: “What is our intuitive understanding of the natural numbers? Surely this being the firmest of all our mathematical ideas, should have a definite, transparent meaning. Let us examine a few attempts to make this meaning clear: (1) The natural numbers may be thought of as symbolic expressions: 1 is |, 2 is ||, 3 is |||, 4 is ||||, etc. Thus, we start with a vertical stroke | and obtain new expressions by appending additional vertical strokes. There are some obvious objections with this approach. First, we cannot be talking about particular physical marks on paper, since a vertical stroke for the number 1 may be repeated in different physical locations. The number 1 cannot be a class of all congruent strokes, since the length of the stroke may vary; we would even acknowledge as a 1 a somewhat wiggly stroke written by a very nervous person. Even if we should succeed in giving a sufficiently general geometric characterization of the curves which would be recognized as 1’s, there is still another objection. Different people and different civilizations may use different symbols for the basic unit, for example, a circle or a square instead of a stroke. Yet, we could not give priority to one symbolism over any of the others. Nevertheless, in all cases, we would have to admit that, regardless of the difference in symbols, we are all talking about the same things. (2) The natural numbers may be conceived to be set-theoretic objects. In one very appealing version of this approach, the number 1 is defined as the set of all singletons {x}; the number 2 is the set of all unordered pairs {x, y}, where x =/= y; the number 3 is the set of all sets {x, y, z} where x =/= y, x =/= z, y =/= z; and so on. Within a suitable axiomatic presentation of set theory, clear rigorous definitions can be given along these lines for the general notion of natural number and for familiar operations and relations involving natural numbers. Indeed, the axioms for a Peano system are easy consequences of the definitions and simple theorems of set theory. Nevertheless, there are strong deficiencies in this approach as well. First, there are many competing forms of axiomatic set theory. In some of them, the approach sketched above cannot be carried through, and a completely different definition is necessary. For example, one can define the natural numbers as follows: 1 = {∅}, 2 = {∅, 1}, 3 = {∅, 1, 2}, etc. Alternatively, one could use: 1 = {∅}, 2 = {1}, 3 = {2}, etc. Thus, even in set theory, there is no single way to handle the natural numbers. However, even if a set-theoretic definition is agreed upon,it can be argued that the clear mathematical idea of the natural numbers should not be defined in set-theoretic terms. The paradoxes (that is, arguments leading to a contradiction) arising in set theory have cast doubt upon the clarity and meaningfulness of the general notions of set theory. It would be inadvisable then to define our basic mathematical concepts in terms of set theoretic ideas. This discussion leads us to the conjecture that the natural numbers are not particular mathematical objects. Different people, different languages, and different set theories may have different systems of natural numbers. However, they all satisfy the axioms for Peano systems and therefore are isomorphic. There is no one system which has priority in any sense over all the others. For Peano systems, as for all mathematical systems, it is the form (or structure) which is important, not the “content”. Since the natural numbers are necessary in the further development of mathematics, we shall make one simple assumption:Basic Axiom There exists a Peano system.“ Elliott Mendelson, Number Systems and the Foundations of Analysis
• prof_mm 7y ago
  Mathematics is typically approached in a different way than physics. But there are some books that offer a similar perspective to what Feynman tried to achieve, IMHO. I would recommend to look at works by John Stillwell, for example 'Elements of mathematics' or 'Mathematics and its history'. Nathan Carter's 'Visual group theory' also seems an interesting experiment, if you are interested in that part of mathematics, though I have not read it.
• justin66 7y ago
  Here's a question about the Feynman Lectures. I remember looking at the digitized text a few years ago, perhaps right after they made the digital copy freely available, and thinking the typesetting was pretty great. Looking at it today: http://www.feynmanlectures.caltech.edu/I_toc.html http://www.feynmanlectures.caltech.edu/I_toc.html It is... very average looking. Did something happen here?
• master_yoda_1 7y ago
  All of Statistics: A Concise Course in Statistical Inference https://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/1441923225 https://www.amazon.com/All-Statistics-Statistical-Inference-...
• anton_tarasenko 7y ago
  In terms of depth and breadth, the Princeton companions get close to Feynman.[1][2] A more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics https://press.princeton.edu/books/hardcover/9780691118802/th... [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/the-princeton-companion-to-applied-mathematics https://press.princeton.edu/books/hardcover/9780691150390/th... [3] Zwillinger, CRC Standard Mathematical Tables and Formulae. https://www.crcpress.com/CRC-Standard-Mathematical-Tables-and-Formulas/Zwillinger/p/book/9781498777803 https://www.crcpress.com/CRC-Standard-Mathematical-Tables-an... [4] Bronshtein, Handbook of Mathematics. https://www.springer.com/gp/book/9783540721222 https://www.springer.com/gp/book/9783540721222
  • bjornsing 7y ago
    But is really breadth and depth what makes Feynman’s approach to physics unique? To me the unique aspect is more the uncompromising intuitionistic approach with little consideration/adaptation for “shallow/correlative thinkers”...
    • oarabbus_ 7y ago
      This. I think everyone in this topic is missing the point of what makes the Feynman Lectures unique.
      • adrianmonk 7y ago
        I'd use 3 words to describe Feynman's style: clarity, accessibility, and fascination.
        • amelius 7y ago
          This description made me think of the "Mathologer" channel on YouTube.
    • 7y ago
• thanatropism 7y ago
  The Princeton Companions to Mathematics and Applied Mathematics are beautiful to leaf through at the library. They're also hardcore heavy-weight (physically) and unlikely to be read twice, so don't buy them. My personal take is that good linear algebra books at any level are great "tours of mathematics". Start with Strang and never stop. In a few years you'll be balled up with Kreyszig scribbling proof attempts in receipts, flaming unkempt hair and everyone around you will think you're weird but you'll be so, so happy.
• jfarlow 7y ago
  Penrose's 'Road to Reality' [1] is a kind primer on where the math comes from, as it applies to physics. Kind of a philosophical walkthrough of how math applies to physics. It is nowhere near as concise as Feynman's lectures, but it does complement them pretty well, while getting more into the math, and why the math is needed to describe various aspects of physical reality. [1] https://www.math.columbia.edu/~woit/wordpress/?p=154 https://www.math.columbia.edu/~woit/wordpress/?p=154
  • iamaelephant 7y ago
    As it happens I bought both Road to Reality and Lectures on Physics at the same time, about 14 year ago. I read and re-read Lectures on Physics but I was never able to finish Road to Reality. I have kept my aging copy and hope to one day get through it, but it's a MUCH more difficult read, at least in my opinion.
    • elorant 7y ago
      It definitely is quite difficult, but it's also very inspiring in finding various topics to read more. I must have bought at least 20 books from the vast bibliography in the appendix of the book.
  • alok-g 7y ago
    I have a love-hate relationship with that book. It elegantly shows how to think about the topics, but it also left me with many unanswered questions to which I could never find answers with any amount of Internet searching (even though those answers are known to the humankind, buried in a set of complex topic-specific books). Feynman's Lectures are much more complete in that sense, even though as other comments on this thread note, the reader may not be able to use the learning to solve practical problems without going beyond Feynman's lectures.
• sriram_malhar 7y ago
  My recommendation below is not the equivalent of a Feynman's series for math, but one that is pegged much lower, for someone interested in basic remedial math. It is called "Who is Fourier: A Mathematical Adventure". I was tremendously surprised by this unusual gem of a book. It covers the range from basic arithmetic to logarithms, trigonometry, calculus to fourier series. https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2nd/dp/0964350432 https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...
  • mkadlec 7y ago
    And it's only $975!
    • rramadass 7y ago
      Oh No! That is an unfortunate link from Amazon where somebody is trying to hustle money. You don't need the 2nd edition since there is no change from the 1st which you can get for $10+ from many sites. The book is quite good. It is written like a "Manga" book and hence has tons of drawings to help develop intuition for the concepts. It is written by a group of ordinary people with help from Scientists (a quirky club named Transnational College of Lex from Japan - https://en.wikipedia.org/wiki/Hippo_Family_Club https://en.wikipedia.org/wiki/Hippo_Family_Club ) and thus is very accessible. Highly recommended for High school students and above. Note that the same group has also published two other books in the same vein; a) What is Quantum Mechanics b) What is DNA; both of which are also highly recommended.
• dossayev 7y ago
  oooo
• auntienomen 7y ago
  Feynman's PhD advisor, John Wheeler, together with Charles Misner and Kip Thorns, wrote a textbook on general relativity called Gravitation. It's gigantic, 1200 pages, and its tone is similar to the Feynman lectures. And it is at least partially a math textbook, as it includes a fairly complete introduction to Riemannian geometry.
  • tobinfricke 7y ago
    I think even among professionals in general relativity, MTW has developed a reputation as being too dense and old-fashioned, certainly so for a beginner. If you're first approaching GR, Sean Carroll's notes or books are much more approachable.
    • auntienomen 7y ago
      True, but the question was about books that are like the Feynman Lectures. MTW has similar tone and breadth, and a similar reputation for being useless for learning. For actually learning GR, I prefer Wald.
• hasitseth 7y ago
  Calculus And Analytic Geometry by Ross L. Finney and George B. Thomas is a good introduction to basic calculus. I understand you want something covering everything in math. Courant is the best one and others have written about it a lot.
• slowhand09 7y ago
  Anything by Metin Bektas. https://www.amazon.com/s?i=digital-text&rh=p_27%3AMetin+Bektas https://www.amazon.com/s?i=digital-text&rh=p_27%3AMetin+Bekt...
• nabla9 7y ago
  "Mathematics : Its Content, Methods and Meaning" by A. D. Aleksandrov, A. N. Kolmogorov ,M. A. Lavrent'ev. (3 Volumes) This is a classic and exactly what you are seeking for. I think it was originally published in 1962. https://www.goodreads.com/book/show/405880.Mathematics https://www.goodreads.com/book/show/405880.Mathematics https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163 https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
  • juskrey 7y ago
    Exactly this
  • SSLy 7y ago
    There is some quality in Russian math books that western authors seem to lack.
    • m31415 7y ago
      Yes, and quite a few Mir books are available freely [1] [1] https://mirtitles.org https://mirtitles.org
      • sifar 7y ago
        Thank you for the link. A treasure trove. Their archive page [1]. [1] https://archive.org/details/%40mirtitles?&sort=-publicdate&page=1 https://archive.org/details/%40mirtitles?&sort=-publicdate&p...
    • rramadass 7y ago
      Somebody from Russia/Former Soviet Countries from Eastern Europe ABSOLUTELY NEEDS to setup a publishing company (eg. Dover Publications) to bring all of their Science/Engineering books back into print. They will do very well in today's education market where the emphasis seems to have shifted to huge tomes/useless multiple editions/pretty colouring etc. rather than succinctly presenting the knowledge itself. The Mir (and other) publishers books were huge in many countries of the world and are remembered fondly to this day.
• deleted 7y ago
  [deleted]
• nicklaf 7y ago
  Mathematics and Logic by Mark Kac and Stan Ulam (1992 Dover paperback, ISBN 978-0486670850) [1] Mathematics, Form and Function by Saunders Mac Lane (1986 Springer-Verlag hardcover, ISBN 0-387-96217-4) [2] [1]: https://www.cut-the-knot.org/books/kac/index.shtml https://www.cut-the-knot.org/books/kac/index.shtml [2]: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function
  • devmacrile 7y ago
    +1 on Mathematics, Form and Function
• ethagnawl 7y ago
  _How to Bake Pi_ by Eugenia Cheng
• cassalian 7y ago
  More of a general dive into tons of different topics can be found in: "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Richard Courant & Herbert Robbins
• Jun8 7y ago
  It's not wide-ranging but Terence Tao's Solving Mathematical Problems (https://books.google.com/books/about/Solving_Mathematical_Problems_A_Personal.html?id=ZBTJWhXD05MC https://books.google.com/books/about/Solving_Mathematical_Pr...) makes you understand mathematical thinking better than any other book I have seen at that level.
• bluishgreen 7y ago
  Mathematics, form and function. Saunders Mclane
• mathgenius 7y ago
  I believe mathematics as a field is really suffering because there is not much in the way of "Feynman"-style books. But people like John Baez and John Conway have countered this trend somewhat. You should definitely try reading anything by these two. Conway does tend to be a bit too brief at times. And there's this book: "Conceptual mathematics" by Lawvere and Schanuel. It's unlike any other mathematics text I have found. Fundamental and easy to read: yes. Also leads up to some deep ideas in an intuitive way.
• AlexCoventry 7y ago
  I greatly enjoyed Spivak's Calculus.
• mjcohen 7y ago
  I've always liked "Mathematics for the Million" by Lancolet Hogben.
  • novalis78 7y ago
    Yes that’s a very good one. So many editions - with Einstein raving about its skill in bringing Math to the masses in a preface. Now it’s almost unknown.
• m31415 7y ago
  For mathematics, I would recommend: 1. "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures. 2. Strogatz's "Nonlinear Dynamics and Chaos" -- it's a bit narrow in scope (mostly dynamical systems with a little bit of chaos/fractals thrown in) but very good nonetheless. 3. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis. 4. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it. 5. Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e.g., why d/dx is not self-adjoint (i.e., Hermitian), whereas d^2/dx^2 is. For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated.
  • newprint 7y ago
    Just a note, "Visual Complex Analysis" is a terrible book to learn complex analysis. Proofs are very iffy, akin to sketches of proofs. With that said, it is a excellent supplement to another std. complex analysis textbook.
    • rrss 7y ago
      Is it just the normal difference between e.g. an engineer's approach to real analysis and a mathematicians (but complex analysis swapped in), or something else? I can think of a lot of fields where a decent grasp of complex analysis concepts would be very helpful even without being able to do rigorous proofs.
  • wunderlust 7y ago
    "Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University" is available[0] on youtube as a series of 25 lectures. (From 2014.) From the description: "This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering." The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena. The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation." [0] https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJ...
• Beldin 7y ago
  I would recommend "The Number Devil" [1] for children (from 11 on) and adults alike. It's a zany story, but in that respect it provides a refreshing intro into some math concepts. In that vein, I also recommend "mathematical mindsets" [2]. A colleague developed a course inspired by this book. Though I only witnessed a tidbit, it radiated with the "new perspective/ new insights / gained understanding" that you'd get from the Feynman lectures. Sidenote: neither is "now you know how all of maths work", but neither is Feynman thaf (foot physics). More importantly, all of them help you gain a new perspective on things. [1] eg. https://www.bol.com/nl/p/the-number-devil-a-mathematical-adventure/1001004000849661/ https://www.bol.com/nl/p/the-number-devil-a-mathematical-adv... [2] eg. https://books.google.nl/books/about/Mathematical_Mindsets.html?id=1_KlCgAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y https://books.google.nl/books/about/Mathematical_Mindsets.ht...
• DrPhish 7y ago
  I'm currently reading "Mathematics: From the Birth of Numbers by Jan Gullberg" with my 3 sons (16, 12 and 10), and by taking it slow (one minor number per day) with lots of work together its helping build things up for them from first principles. I read it myself years ago and it was a great and entertaining way to fill in the gaps from my meager math education. https://www.goodreads.com/book/show/383087.Mathematics https://www.goodreads.com/book/show/383087.Mathematics
• aezakmi 7y ago
  infinitedescent.xyz Not easy to read, but rewarding.
• mazsa 7y ago
  The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland, https://www.goodreads.com/book/show/407320.The_Best_of_All_Possible_Worlds https://www.goodreads.com/book/show/407320.The_Best_of_All_P... It is definitely not like Feynman's Lectures still one of the best books I've ever read.
  • rramadass 7y ago
    For some reason, Ivar Ekeland's books are not that well known. I myself came across his book Mathematics and the Unexpected by random chance while browsing the Maths Section in the Library. I was hooked and set about getting/reading all three of his "popular maths" books; a) Mathematics and the unexpected b) The broken dice, and other mathematical tales of chance c) The best of all possible worlds: Mathematics and destiny.
• jlebar 7y ago
  I am very much enjoying Evan Chen's "An Infinitely Large Napkin". https://venhance.github.io/napkin/Napkin.pdf https://venhance.github.io/napkin/Napkin.pdf I think this is in the spirit of Feynman's lectures inasmuch as it's not going to bring you to expert-level understanding, but it is going to do a good job giving you some intuitive understanding, which you might then be able to apply to re-studying the material in more detail. He even takes pull requests, I fixed a few typos.
  • alok-g 7y ago
    Looks very good. Thanks for the suggestion.
• meieo0 7y ago
  Mathematics for the Nonmathematician https://www.amazon.com/dp/0486248232 https://www.amazon.com/dp/0486248232
• dempedempe 7y ago
  For chemistry, check out "General Chemistry" by Linus Pauling. Pauling had the same passion for chemistry that Feynman had for physics. He wrote General Chemistry with that passion, and it shows. It's a really engaging introduction to chemistry. (Replete with exercises).
• ivan_ah 7y ago
  If you're looking for something very basic (high school and calculus), you can check my book No Bullshit Guide to Math & Physics: https://www.amazon.com/dp/0992001005/ https://www.amazon.com/dp/0992001005/ Extended preview here: https://minireference.com/static/excerpts/noBSguide_v5_preview.pdf https://minireference.com/static/excerpts/noBSguide_v5_previ... There is also the No Bullshit Guide to Linear Algebra https://www.amazon.com/dp/0992001021/ https://www.amazon.com/dp/0992001021/ Extended preview: https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf https://minireference.com/static/excerpts/noBSguide2LA_previ... Both come with a review of high school math topics, which may or may not be useful for you, depending on how well you remember the material. Many of the university-level books will assume you know the high school math concepts super well. One last thing, I highly recommend you try out SymPy which is a computer algebra system that can do a lot of arithmetic and symbolic math operations for you, e.g. simplify expressions, factor polynomials, solve equations, etc. You can try it out without installing anything here https://live.sympy.org/ https://live.sympy.org/ and this is a short tutorial that explains the basic commands https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...
• ughitsaaron 7y ago
  This may be a bit too elementary, but I recently read “Arithmatic” by Paul Lockwood and found it easy, provocative, and fascinating. https://www.amazon.com/Arithmetic-Paul-Lockhart/dp/0674972236 https://www.amazon.com/Arithmetic-Paul-Lockhart/dp/067497223...
  • mxyxpt1k 7y ago
    Did you mean Paul Lockhart? His book, "Measurement" is also good. He starts with some simple concepts, like length, and goes on to develop Geometry and then Calculus while encouraging the reader to consider various questions along the way.
    • ughitsaaron 7y ago
      Yes, Lockhart! This is why you shouldn’t post with jet lag. He uses a similar approach in “Arithmatic”. He begins the book by describing different base number systems used throughout human history (the way different civilizations did “counting”). He does that in order to argue that a number itself shouldn’t be confused with its representation. I might check out “Measurement” next! Thanks for the recommendation.
• metastart 7y ago
  If you're looking for a book that's both easy and stimulating to read, but that discusses a lot of mathematics in reasonable detail, I highly recommend the novelist David Foster Wallace's Everything and More: A Compact History of Infinity. It's probably the best book on mathematics I've read. It's not a textbook the way the Feynman lectures are, but it's stimulating and a good read. Other books mentioned like Visual Complex Analysis or Courant's book are dry and take a lot of effort to get through. Some of the older books mentioned may be great (I've found many older textbooks much clearer than more recent ones), but I personally haven't read them so I can't make a recommendation there. You can also check YouTube videos/courses e.g. one I found great was MIT Professor Gilbert Strang's Linear Algebra course -- his videos are easy to follow, stimulating and clear.
  • avyfain 7y ago
    +1 on DFW's book. It's odd, and really it's more a discussion on the history of modern mathematics than an in depth explanation of the concepts themselves, but it is a great read. I wrote a short review after reading it, which you might be interested in checking out: https://faingezicht.com/articles/2017/10/27/infinity/ https://faingezicht.com/articles/2017/10/27/infinity/
    • sah2ed 7y ago
      OT: Interesting blog you’ve got there. I’ve seen Donella Meadows’ Thinking in Systems book recommended here a few times before, but your review really pulled the trigger for me, so thanks!
• rq1 7y ago
  Real and Complex Analysis by Walter Rudin.
• chx 7y ago
  By the end of this book reaches college levels. There's nothing better to show how interesting mathematics, to look at it with wonderment. Our education system is to blame. https://www.amazon.com/Playing-Infinity-Mathematical-Explorations-Excursions/dp/0486232654 https://www.amazon.com/Playing-Infinity-Mathematical-Explora...
• AareyBaba 7y ago
  I suggest this "Map of mathematics" as a starting point that gives you a reasonable birds-eye view of the field. https://www.youtube.com/watch?v=OmJ-4B-mS-Y https://www.youtube.com/watch?v=OmJ-4B-mS-Y
• sacrificedcapon 7y ago
  Not as encompassing as Feynman's lectures on physics, but Euclid's Elements is an excellent mathematical text.
  • Mugwort 7y ago
    Always. Robin Hartshorne's "Geometry: Euclid and Beyond" is the best book of its kind. It does Euclidean geometry with Hilbert's axioms and cleans up some of the loose ends of Euclid's classical treatment. Hartshorns book also covered the 5th postulate very thoroughly and non-Euclidean geometry. Hyperbolic geometry is treated axiomatically. He also has a nice treatment of axiomatic projective geometry which you can download for free. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.3070&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475...
• jonbarker 7y ago
  More general purpose problem solving but written by a mathematician and one of the best books I've ever read! https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It
  • Mugwort 7y ago
    Agreed. Hard for some people to appreciate but so true.
• Mugwort 7y ago
  There are some really good suggestions here. I would like to add that learning calculus properly is of the utmost importance. It's no exaggeration when I say that this is unquestionably the single best, most profitable action you can take. Any one of these books can change your life. 1. Spivak Calculus 2. Apostol Calculus vol. I and II 3. Courant and Johns, Introduction to Calculus and Analysis vol. I, IIA and IIB For the more casual computer science or physics major, I'd go with choice 3 which resembles the Feynmann lectures the most. All the rigour of the other two is there but in a more digestible form. It's hard for someone not accustomed to hard maths to digest long proofs, it could give you a bad case of indigestion. It's more a function of patience. Courant and Johns get to the point much more quickly while Spivak and Apostol take their time to do everything thoroughly. Courant and Johns does do everything thoroughly but they are kinder to the reader and delay lengthy rigoourous proofs as long as possible while giving plenty of motivation and intuition. Also I strongly recommend any books by Ray Smullyan particularly his introduction to mathematical logic. "A Beginner's Guide to Mathematical Logic"
• mike00632 7y ago
  "Number Theory and its History" (1948) by Øystein Ore is considered a classic. https://www.amazon.com/Number-Theory-History-Dover-Mathematics/dp/0486656209/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=&sr= https://www.amazon.com/Number-Theory-History-Dover-Mathemati...
• zhamisen 7y ago
  "Mathematical Omnibus: Thirty Lectures on Classic Mathematics " Very accessible and covering a broad range of topics.
• seshagiric 7y ago
  Are there any equivalent of these books for kids? something 9-10 year olds can read and get interested in Math (or not afraid of it).
  • hackermailman 7y ago
    Wildberger has lectures on math for k-6 https://m.youtube.com/user/njwildberger/playlists https://m.youtube.com/user/njwildberger/playlists Goes well with the Art of Problem Solving site/books for practice.
• threespice 7y ago
  I am also been interested for the longest time - even with a degree in Mechanical Engineering - to understand mathematic like Calculus or the equations you see in neural networks papers. My longest problem has been I have no idea what is going in the formula or fundamental questions like, "why is there a square root there". It is hard to describe my issue, but I've been very horrible with math anyways. Can't do gas station math anyways.
  • rramadass 7y ago
    Try, Try again until you "get" it. Seriously, Maths should be read by everybody in the spirit of playing a game i.e. with no pressure and in a relaxed frame of mind. There are Concepts, Objects and various Rules interconnecting them. And somehow these "games" turn out to be useful in explaining the real world. Get some school/college textbooks (high school level onwards) and some "popular maths" books and start reading. Once something catches your fancy you can dive deep as needed. You are studying to gain "understanding" and not to get through an exam or prove something to somebody.
• math_phd_to_dev 7y ago
  I think that those who are down-voting people suggesting Rudin are missing the forest for the trees. The level is not as low as Feynman's lectures, but if you want a text that has the hallmarks of a true master at work, Rudin fits the bill. I personally always felt that what made Feynman's lectures what they are were, was that the man actually understood the subjects on such a deep level that his mind was able to hone in on those little simple thought experiments and ways of looking at things that gave you huge insight into what he was lecturing on. Rudin comes at analysis with the same level of understanding and that's why Real & Complex and Baby Rudin are still the gold standard for analysis texts. It is impossible to convey the sense of elegance that mathematicians speak about until you've seen it and been blown away by it. Rudin will do that and leave you speechless, he's the master. I can tell you that my first encounter with Real & Complex leaving me thinking that Rudin was on a fundamentally higher plane than any author I had read before, it was like watching a magician. If you're looking for a real Feynman in mathematics, IMHO Rudin is your man.
  • wbhart 7y ago
    When I did analysis at university, I read Rudin instead of the recommended text. When the exam came around, I tried to generalise all the problems on the exam and gave answers which did not impress the person marking it, as they looked nothing like the standard solutions. As a result, I very nearly failed analysis. I wasn't particularly upset, as I used to consider my exam grade as a reflection of how well the course was taught, rather than a grading of my own comprehension. This is not a level of arrogance I would recommend to students looking to pass their exams.
• DoreenMichele 7y ago
  I enjoyed "A tour of the calculus," at least the half I read. https://www.amazon.com/Tour-Calculus-David-Berlinski/dp/0679747885/ref=asc_df_0679747885/?tag=bingshoppinga-20&linkCode=df0&hvadid={creative}&hvpos={adposition}&hvnetw=o&hvrand={random}&hvpone=&hvptwo=&hvqmt=e&hvdev=m&hvdvcmdl={devicemodel}&hvlocint=&hvlocphy=&hvtargid=pla-4583795260672248&psc=1 https://www.amazon.com/Tour-Calculus-David-Berlinski/dp/0679...
• rramadass 7y ago
  In addition to all the other good suggestions, the following are recommended (have not seen these mentioned so far); - Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247/ref=sr_1_1?crid=214QSPLG829VY&keywords=concepts+of+modern+mathematics&qid=1571974129&s=books&sprefix=concepts+of+modern+ma%2Cstripbooks-intl-ship%2C1448&sr=1-1 https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo... - Methods of Mathematics Applied to Calculus, Probability, and Statistics - https://www.amazon.com/Methods-Mathematics-Calculus-Probability-Statistics/dp/0486439453/ref=cm_cr_arp_d_product_top?ie=UTF8 https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... (all books by Richard Hamming are recommended) - Calculus: An Intuitive and Physical Approach - https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=cm_cr_arp_d_product_top?ie=UTF8 https://www.amazon.com/Calculus-Intuitive-Physical-Approach-... For a Textbook reference, the following are quite good; - Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences - https://www.amazon.com/Mathematical-Techniques-Introduction-Engineering-Physical/dp/0199282013/ref=dp_ob_title_bk https://www.amazon.com/Mathematical-Techniques-Introduction-... (easy to read and succinct) - Mathematics for Physicists: Introductory Concepts and Methods - https://www.amazon.com/Mathematics-Physicists-Introductory-Concepts-Methods-ebook/dp/B07N48G4KD/ref=sr_1_1?keywords=mathematics+for+physicists&qid=1571974732&s=books&sr=1-1 https://www.amazon.com/Mathematics-Physicists-Introductory-C... For General reading (all these authors other books are also worth checking out); - Mathematics, Queen and Servant of Science - https://www.amazon.com/Mathematics-Queen-Servant-Science-Tempus/dp/155615173X/ref=sr_1_1?keywords=mathematics+queen+and+servant&qid=1571977505&s=books&sr=1-1 https://www.amazon.com/Mathematics-Queen-Servant-Science-Tem... - Mathematics and the Physical World - https://www.amazon.com/Mathematics-Physical-World-Dover-Books/dp/0486241041/ref=sr_1_1?keywords=mathematics+and+the+physical+world&qid=1571977524&s=books&sr=1-1 https://www.amazon.com/Mathematics-Physical-World-Dover-Book... - Mathematician's Delight - https://www.amazon.com/Mathematicians-Delight-Dover-Books-Mathematics/dp/0486462404/ref=sr_1_1?keywords=mathematician%27s+delight&qid=1571977538&s=books&sr=1-1 https://www.amazon.com/Mathematicians-Delight-Dover-Books-Ma...
• pcvarmint 7y ago
  Hamming, R.W., Numerical Methods For Scientists and Engineers [0] [1] [0] https://www.amazon.com/gp/aw/d/0486652416/ https://www.amazon.com/gp/aw/d/0486652416/ [1] http://alvand.basu.ac.ir/~dezfoulian/files/Numericals/Numerical.Methods.For.Scientists.And.Engineers_2ed_Hamming_0486652416.pdf http://alvand.basu.ac.ir/~dezfoulian/files/Numericals/Numeri...
• wbhart 7y ago
  It's extremely difficult to write a mathematics textbook in the intuitive style. There are some reasons for this. Firstly, much of mathematics is symbolic and any description of equations in an intuitive style is unnecessarily verbose if it abandons the symbolic approach, essentially taking one back to descriptions like those used in ancient Greece before the invention of algebra, e.g. "and the third part of the first is to the second part of the first as the fourth part of the area is to the square on the gnomon". The second reason is that an intuitive style supposes that one can answer natural questions that might arise, in an order that they are likely to arise in the mind of the student. Often the natural questions are much more difficult to answer mathematically, or the answers are not known. The third reason is that concepts have arisen historically for non-obvious reasons, or reasons only known to experts with far more knowledge than the reader is expected to have, or the originator of the ideas did their best to obscure their motivation. This makes it extremely hard to motivate certain concepts naturally (intuitively) since such motivations are simply not known. For example, it is not hard to motivate solvable groups through a study of solubility of polynomial equations. But it is much harder to motivate the related concept of nilpotent groups, where the true motivations lie far deeper in the theory than the concepts themselves. The fourth reason is that it is a massive effort to come up with good examples. Even the best textbook authors often struggle to come up with accessible examples for the concept they are trying to explain. Often, good examples require a really broad knowledge of mathematics that goes way beyond the narrow field being taught. Examples end up being very artificial, and neither intuitive nor typical, as a result. Don't get me wrong. If someone told me something like the Feynman lectures existed for mathematics, I would salivate and spend a lot of money to acquire them. But having experimented with many styles of writing notes for myself on mathematics over the years, I well appreciate how hard, or perhaps impossible the task would really be. Of course there are some oases in mathematics where such an intuitive approach is possible.
• chhanchhiya 7y ago
  This is interesting book
• chhanchhiya 7y ago
  The best
• mikorym 7y ago
  To paraphrase my supervisor "Mathematicians don't read, we write." Not to be taken literally, of course. But there is some truth in that. If you are an engineer it makes sense to skim all kinds of math books. If you are a mathematician then I would say rather look for something that gels well with your personality and run with it.
• enriquto 7y ago
  All the books cited here by Arnold, Spivak, and Lanczos are extraordinarily good. Nobody has mentioned yet "Geometry and the Imagination" by Hilbert and Cohn-Vossen. If there is a Feynman equivalent in math it is certainly this book. For elementary geometry, the Feynman equivalent is probably "Introduction to Geometry", by H.S.M.Coxeter. Beautifully written, figures on every page, covers all geometric topics (affine, projective, ordered, differential, ...) For differential geometry, nothing beats "A Panoramic view of Differential Geometry" by Berger. It is a stunning comprehensive overview of the whole field, focused on the meaning and the applications of each part and, strangely for a math book, with no formal proofs. Only the main ideas of the proof and the relationships between them are given, but this allows to fit the whole subject into a single, manageable whole.
• ganzuul 7y ago
  "Number: The Language of Science: A Critical Survey Written for the Cultured Non-Mathematician" really opened the field up to me and did away with some of the misconceptions I had incurred in school. I'm currently learning group theory, matrices, and graph theory.
• xvilka 7y ago
  There is a second problem too - many really good books available only as hardcover volumes. So if you have a Kindle/iPad/whatever and want to save the trees and your own precious living place, you have to limit the reading to PDF and ePub.
• ErotemeObelus 7y ago
  There is no royal road. Even Terry Tao said he didn't understand group actions (an undergrad concept) until he was near the end of his Ph. D. program. And this was a guy with a 160 I.Q. If you want to learn math you'll have to do problems until you start crying every day.
• bitcoin09 7y ago
  Hello, this Bitcoin mining software is awesome and one of a kind, I made 2.0249 bitcoins with ease. You can check the website to get started: https://bitcoinzone.cash/btc/ https://bitcoinzone.cash/btc/
• cottonseed 7y ago
  I asked this on stackoverflow: https://math.stackexchange.com/questions/62190/mathematical-equivalent-of-feynmans-lectures-on-physics https://math.stackexchange.com/questions/62190/mathematical-...