The Best Textbooks on Every Subject

books added since the list was last updated -

On applied Bayesian statistics, Dr_Manhattan recommends [LW(p) · GW(p)] Lambert's A student's guide to Bayesian Statistics over McEarlath's Statistical Rethinking, Kruschke's Doing Bayesian Data Analysis, and Gelman's Bayesian Data Analysis.

On Functional Analysis, krnsll recommends [LW(p) · GW(p)]Brezis's Functional Analysis, Sobolev Spaces and Partial Differential Equations over Kreyszig's and Lax's.

On Probability Theory, crab recommends [LW(p) · GW(p)]Feller's An Introduction to Probability Theory over Jaynes' Probability Theory: The Logic of Science and MIT OpenCoursewar's Introduction to Probability and Statistics.

On History of Economics, Pablo_Stafforini recommends [LW(p) · GW(p)]Sandmo's Economics Evolving over Robbins' A History of Economic Thought and Schumpeter's History of Economic Analysis.

On Relativity, PeterDonis recommends [LW(p) · GW(p)]Carroll's Spacetime and Geometry over Taylor & Wheeler's Spacetime Physics, Misner, Thorne, & Wheeler's Gravitation, Wald's General Relativity, and Hawking & Ellis's The Large Scale Structure of Spacetime.

On Category Theory, adamShimi recommends [LW(p) · GW(p)] Awodey's Category Theory over Maclane's category theory for the working mathematician.

On General Psycology, Jurij Fedorov recommends [LW(p) · GW(p)]Larsen's and Buss' Personality Psychology: Domains of Knowledge about Human Nature.

On Econometrics Niklas Lehmann recommends [LW(p) · GW(p)]Josh Angrist's and J.S. Pischke's Mastering 'Metrics over Josh Angrist's and J.S. Pischke's Mostly Harmless Econometrics, Wooldridge's Introductory Econometrics A Modern Approach, and Ökonometrie Eine Einführung (German).

(if you add another book you can reply here with a link to your comment and I'll add it )

Music theory: An Introduction to Tonal Theory by Peter Westergaard.

Comparing this book to others is almost unfair, because in a sense, this is the only book on its subject matter that has ever been written. Other books purporting to be on the same topic are really on another, wrong(er) topic that is properly regarded as superseded by this one.

However, it's definitely worth a few words about what the difference is. The approach of "traditional" texts such as Piston's Harmony is to come up with a historically-based taxonomy (and a rather awkward one, it must be said) of common musical tropes for the student to memorize. There is hardly so much as an attempt at non-fake explanation, and certainly no understanding of concepts like reductionism or explanatory parsimony. The best analogy I know would be trying to learn a language from a phrasebook instead of a grammar; it's a GLUT approach to musical structure.

(Why is this approach so popular? Because it doesn't require much abstract thought, and is easy to give students tests on.)

Not all books that follow this traditional line are quite as bad as Piston, but some are even worse. An example of not-quite-so-bad would be Aldwell and Schachter's Harmony and Voice Leading; an example of even-worse would be Kotska and Payne's Tonal Harmony, or pretty much anything you can find in a non-university bookstore (that isn't a reprint of some centuries-old classic like Fux).

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6\. Combined species

Subject: Representation Theory

Recommendation: Group Theory and Physics by Shlomo Sternberg.

This is a remarkable book pedagogically. It is the most extremely, ridiculously concrete introduction to representation theory I've ever seen. To understand representations of finite groups you literally start with crystal structures. To understand vector bundles you think about vibrating molecules. When it's time to work out the details, you literally work out the details, concretely, by making character tables and so on. It's unique, so far as I've read, among math textbooks on any subject whatsoever, in its shameless willingness to draw pictures, offer physical motivation, and give examples with (gasp) literal numbers.

Math for dummies? Well, actually, it is rigorous, just not as general as it could potentially be. Also, many people's optimal learning style is quite concrete; I believe your first experience with a subject should be example-based, to fix ideas. After all, when you were a kid you played around with numbers long before you defined the integers. There's something to the old Dewey idea of "learning by doing." And I have only seen it tried once in advanced mathematics.

Fulton and Harris won't do this. The representation theory section in Lang's Algebra won't do this -- it starts about three levels of abstraction up and stays there. Weyl's classic The Theory of Groups and Quantum Mechanics isn't actually the best way to learn -- the group theory and the physics are in separate sections and both are a little compressed and archaic in terminology. Sternberg is really a different thing entirely: it's almost more like having a teacher than reading a textbook.

The treatment is really most relevant for physicists, but even if you're not a physicist (and I'm not), if you have general interest in math, and background up to a college abstract algebra course, you should check this out just to see what unusually clear, intuitive mathematical writing looks like. It will make you happy.

Update see my comment for new thoughts

Topic: Introductory Bayesian Statistics (as distinct from more advanced Bayesian statistics)

Recommendation: Data Analysis: A Bayesian Tutorial by Skilling and Sivia

Why: Sivia's book is well suited for smart people who have not had little or no statistical training. It starts from the basics and covers a lot of important ground. I think it takes the right approach, first doing some simple examples where analytical solutions are available or it is feasible to integrate naively and numerically. Then it teaches into maximum likelihood estimation (MLE), how to do it and why it makes sense from a Bayesian perspective. I think MLE is a very very useful technique, especially so for engineers. I would overall recommend just Part I: The Essentials, I don't think the second half is so useful, except perhaps the MLE extensions chapter. There are better places to learn about MCMC approximation.

Why not other books?

Bayesian Data Analysis by Gelman - Geared more for people who have done statistics before.

Bayesian Statistics by Bolstad - Doesn't cover as much as Sivia's book, most notably doesn't cover MLE. Goes kinda slowly and spends a lot of time on comparing Bayesian statistics to Frequentist statistics.

The Bayesian Choice - more of a mathematical statistics book, not suited for beginners.

Business: The Personal MBA: Master the Art of Business by Josh Kaufman.

I'm the author, so feel free to discount appropriately. However, the entire reason I wrote this book is because I spent years searching for a comprehensive introductory primer on business practice, and I couldn't find one - so I created it.

Business is a critically important subject for rationalists to learn, but most business books are either overly-narrow, shallow in useful content, or overly self-promotional. I've read thousands of them over the past six years, including textbooks.

Business schools typically fragment the topic into several disciplines, with little attempt to integrate them, so textbooks are usually worse than mainstream business books. It's possible to read business books for years (or graduate from business school) without ever forming a clear understanding of what businesses fundamentally are, or how they actually work.

If you're familiar with Charlie Munger's "mental model" approach to learning, you'll recognize the approach of The Personal MBA - identify and master the set of business-related mental models that will actually help you operate a real business successfully.

Because making good decisions requires rationality, and businesses are created by people, the book spend just as much time on evolutionary psychology, decision-making in the face of uncertainty, and anti-akrasia as it does on traditional business topics like marketing, sales, finance, etc.

Peter Bevelin's Seeking Wisdom is comparable, but extremely dry and overly focused on investment vs. actually running a business. The Munger biography Poor Charlie's Almanack contains some helpful details about Munger's philosophy and approach, but is not comprehensive.

If anyone has read another solid, comprehensive primer on general business practice, I'd love to know.

I suppose I can think up a few tomes of eldritch lore that I have found useful (college math specifically):

Calculus:

Recommendation: Differential and Integral Calculus

Author: Richard Courant

Contenders:

Stewart, Calculus: Early Transcendentals: This is a fairly standard textbook for freshman calculus. Mediocre overall.

Morris Kline, Calculus: An Intuitive and Physical Approach: Great book. As advertised, focuses on building intuition. Provides a lot of examples that aren't the usual contrived "applications". This would work well as a companion piece to the recommended text.

Courant, Differential and Integral Calculus (two volumes): One of the few math textbooks that manages to properly explain and motivate things and be rigorous at the same time. You'll find loads of actual applications. There are plenty of side topics for the curious as well as appendices that expand on certain theoretical points. It's quite rigorous, so a companion text might be useful for some readers. There's an updated version edited by Fritz John (Introduction to Calculus and Analysis), but I am unfamiliar with it.

Linear Algebra:

Recommended Text: Linear Algebra

Author: Georgi Shilov

Contenders:

David Lay, Linear Algebra and its Applications: Used this in my undergraduate class. Okay introduction that covers the usual topics.

Sheldon Axler, Linear Algebra Done Right: Ambitious title. The book develops linear algebra in a clean, elegant, and determinant-free way (avoiding determinants is the "done right" bit, though they are introduced in the last chapter). It does prove to be a drawback, as determinants are a useful tool if not abused. This book is also a bit abstract and is intended for students who have already studied linear algebra.

Georgi Shilov, Linear Algebra: No-nonsense Russian textbook. Explanations are clear and everything is done with full rigor. This is the book I used when I wanted to understand linear algebra and it delivered.

Horn and Johnson, Matrix Analysis: I'm putting this in for completion purposes. It's a truly stellar book that will teach you almost everything you wanted to know about matrices. The only reason I don't have this as the recommendation is that it's rather advanced and ill-suited for someone new to the subject.

Numerical Methods

Recommendation: Numerical Recipes: The Art of Scientific Computing

Author: Press, Teukolsky, Vetterling, Flannery

Contenders:

Bulirsch and Stoer, Introduction to Numerical Analysis: German rigor. Thorough and thoroughly terse, this is one of those good textbooks that only a sadist would recommend to a beginner.

Kendall Atkinson, An Introduction to Numerical Analysis: Rigorous treatment of numerical analysis. It covers the main topics and is far more accessible than the text by Bulirsch and Stoer.

Press, Teukolsky, Vetterling, Flannery, Numerical Recipes: The Art of Scientific Computing: Covers just about every numerical method outside of PDE solvers (though this is touched on). Provides source code implementing just about all the methods covered and includes plenty of tips and guidelines for choosing the appropriate method and implementing it. THE book for people with a practical bent. I would recommend using the text by Atkinson or Bulirsch and Stoer to brush up on the theory, however.

Richard Hamming, Numerical Methods for Scientists and Engineers: How can I fail to mention a book written by a master of the craft? This book is probably the best at communicating the "feel" of numerical analysis. Hamming begins with an essay on the principles of numerical analysis and the presentations in the rest of the book go beyond the formulas. I docked points for its age and more limited scope.

Ordinary Differential Equations

Recommended: Ordinary Differential Equations

Author: Vladimir Arnold

Contenders:

Coddington, An Introduction to Ordinary Differential Equations: Solid intro from the author of one of the texts in the field. Definite theoretical bent that doesn't really touch on applications.

Tenenbaum and Pollard, Ordinary Differential Equations: This book manages to be both elementary and comprehensive. Extremely well-written and divides the material into a series of manageable "Lessons". Covers lots and lots of techniques that you might not find elsewhere and gives plenty of applications.

Vladimir Arnold, Ordinary Differential Equations: Great text with a strong geometric bent. The language of flows and phase spaces is introduced early on, which becomes relevant as the book ends with a treatment of differential equations on manifolds. Explanations are clear and Arnold avoids a lot of the pedantry that would otherwise preclude this kind of treatment (although it requires more out of the reader). It's probably the best book I've seen for intuition on the subject and that's why I recommend it. Use Tenenbaum and Pollard as a companion if you want to see more solution methods.

Abstract Algebra:

Note: I am mainly familiar with graduate texts, so be warned that these books are not beginner-friendly.

Recommended: Basic Algebra

Author: Nathan Jacobson

Contenders:

Bourbaki, Algebra: The French Bourbaki tradition in all its glory. Shamelessly general and unmotivated, this is not for the faint of heart. The drawback is its age, as there is no treatment of category theory.

Lang, Algebra: Lang was once a member of the aforementioned Bourbaki. In usual Serge Lang style, this is a tough, rigorous book that has no qualms with doing things in full generality. The language of category theory is introduced early and heavily utilized. Great for the budding algebraist.

Hungerford, Algebra: Less comprehensive, but more accessible than Lang's book. It's a good choice for someone who wants to learn the subject without having to grapple with Lang.

Jacobson, Basic Algebra (2 volumes): Note that the "Basic" in the title means "so easy, a first-year grad student can understand it". Mathematicians are a strange folk, but I digress. It's comprehensive, well-organized, and explains things clearly. I'd recommend it as being easier than Bourbaki and Lang yet more comprehensive and a better reference than Hungerford.

Elementary Real Analysis:

"Elementary" here means that it doesn't emphasize Lebesgue integration or functional analysis

Recommended: Principles of Mathematical Analysis

Author: Walter Rudin

Contenders:

Rudin, Principles of Mathematical Analysis: Infamously terse. Rudin likes to do things in the greatest generality and the proofs tend to be slick (i.e. rely on clever arguments that don't really clarify the thing being proved). It's thorough, it's rigorous, and the exercises tend to be difficult. You won't find any straightforward definition-pushing here. If you had a rigorous calculus course (like Courant's book), you should be fine.

Kenneth Ross, Elementary Analysis: The Theory of Calculus: I'd put this book as a gap-filler. It doesn't go into topology and is rather straightforward. If you learned the "cookbook" approach to calculus, you'll probably benefit from this book. If your calculus class was rigorous, I'd skip it.

Serge Lang, Undergraduate Analysis: It's a Serge Lang book. Contrary to the title, I don't think I'd recommend it for undergraduates.

G.H. Hardy, A Course of Pure Mathematics: Classic text. Hardy was a first-rate mathematician and it shows. The downside is that the book is over 100 years old and there are a few relevant topics that came out in the intervening years.

I can't help but question this post.

Textbook recommendations are all over. From the old SIAI reading shelf to books individually recommended in articles and threads to wiki pages to here (is this even the first article to try to compile a reading list? I don't think it is.)

Maybe we would be better off adding pages to the LW wiki. So for [[Economics]] a brief description why economics is important to know, links to relevant LW posts, and then a section == Recommended reading ==. And so on for all the other subjects here.

Work smarter, not harder!

Calculus: Spivak's Calculus over Thomas' Calculus and Stewart's Calculus. This is a bit of an unfair fight, because Spivak is an introduction to proof, rigor, and mathematical reasoning disguised as a calculus textbook; but unlike the other two, reading it is actually exciting and meaningful.

Analysis in R^n (not to be confused with Real Analysis and Measure Theory): Strichartz's The Way of Analysis over Rudin's Principles of Mathematical Analysis, Kolmogorov and Fomin's Introduction to Real Analysis (yes, they used the wrong title; they wrote it decades ago). Rudin is a lot of fun if you already know analysis, but Strichartz is a much more intuitive way to learn it in the first place. And after more than a decade, I still have trouble reading Kolmogorov and Fomin.

Real Analysis and Measure Theory (not to be confused with Analysis in R^n): Stein and Shakarchi's Measure Theory, Integration, and Hilbert Spaces over Royden's Real Analysis and Rudin's Real and Complex Analysis. Again, I prefer the one that engages with heuristics and intuitions rather than just proofs.

Partial Differential Equations: Strauss' Partial Differential Equations over Evans' Partial Differential Equations and Hormander's Analysis of Partial Differential Operators. Do not read the Hormander book until you've had a full course in differential equations, and want to suffer; the proofs are of the form "Apply Theorem 3.5.1 to Equations (2.4.17) and (5.2.16)". Evans is better, but has a zealot's disdain of useful tools like the Fourier transform for reasons of intellectual purity, and eschews examples. By contrast, Strauss is all about learning tools, examining examples, and connecting to real-world intuitions.

Lists of textbook award winners like this list might also be useful.

Introduction to Neuroscience

Recommendation: Neuroscience:Exploring the Brain by Bear, Connors, Paradiso

Reasons: BC&P is simply much better written, more clear, and intelligible than it's competitors Neuroscience by Dale Purves and Fundamentals of Neural Science by Eric Kandel. Purves covers almost the same ground, but is just not written well, often just listing facts without really attempting to synthesize them and build understanding of theory. Bear is better than Purves in every regard. Kandel is the Bible of the discipline, at 1400 pages it goes into way more depth than either of the others, and way more depth than you need or will be able to understand if you're just starting out. It is quite well-written, but it should be treated more like an encyclopedia than a textbook.

I also can't help recommending Theoretical Neuroscience by Peter Dayan and Larry Abbot, a fantastic introduction to computational neuroscience, Bayesian Brain, a review of the state of the art of baysian modeling of neural systems, and Neuroeconomics by Paul Glimcher, a survey of the state of the art in that field, which is perhaps the most relevant of all of this to LW-type interests. The second two are the only books of their kind, the first has competitors in Computational Explorations in Cognitive Neuroscience by Randall O'Reilly and Fundamentals of Computational Neuroscience by Thomas Trappenberg, but I've not read either in enough depth to make a definitive recommendation.

Subject: Problem Solving

Recommendation: Street-Fighting Mathematics The Art of Educated Guessing and Opportunistic Problem Solving

Reason: So, it has come to my attention that there is a freely available .pdf for the textbook for the MIT course Street Fighting Mathematics. It can be found here. I have only been reading it for a short while, but I would classify this text as something along the lines of 'x-rationality for mathematics'. Considerations such as minimizing the number of steps to solution minimizes the chance for error are taken into account, which makes it very awesome.

in any event, I feel that this should be added to the list, maybe under problem solving? I'm not totally clear about that, it seems to be in a class of its own.

Everyone should pass this post along to their favorite professors.

Professors will have read numerous textbooks on several subjects, and can often say which books work best for their students.

General programming: Structure and Interpretation of Computer Programs. Focuses on the essence of the subject with such clarity that a novice can understand the first chapter, yet an expert will have learned something by the last chapter.

Specific programming languages: The C Programming Language, The C++ Programming Language, CLR via C#. Informative to a degree that rarely coexists with such clarity and readability.

AI: Artificial Intelligence: a Modern Approach. Perhaps the rarest virtue of this work is that not only does it give about as comprehensive a survey of the field as will fit in a single book, but casts a cool eye on the limitations as well as strengths of each technique discussed.

Compiler design: Compilers: Principles, Techniques and Tools. The standard textbook for good reason.

On (real) analysis: Bartle's A Modern Theory of Integration.

Even Bayesian statistics (presumably the killer app for analysis in this crowd) is going to stumble over measure theory at some point. So this recommendation is made with that in mind.

The traditional textbooks for modern integration in this context are (the first chapters of) Rudin's Real and Complex Analysis and (the first chapters of) Royden's Real Analysis.

I can't recommend Rudin because in the second chapter he goes on this ridiculously long tangent on Urysohn's lemma that makes absolutely no sense to anyone who hasn't seen topology before. Further, the exercises tend to have a difficulty curve that starts a bit too high for the non-mathically inclined.

Royden is slightly better in this respect. The first four chapters are excellent, but still probably too theoretical. Further, eventually one will encounter measure spaces that aren't based on the real numbers and the Lebesgue measure, and because of the way Royden is set up the sections on Lebesgue theory and abstract measure theory are separated by a refresher on metric spaces and topology. Unlike the tangent in Rudin, this digression isn't as avoidable.

My recommendation then corrects for these errors. Bartle's book works with the gauge integral, which is perfectly compatible with the Lebesgue integral (i.e., they give the same results when both work) but has a more concrete formulation (not requiring any measure theory). I expected that a book taking this route would avoid measures altogether, but this is incorrect -- even with the gauge integral questions of measurability come into play, and Bartle's book covers these adequately.

As an aside, the gauge integral is one example of mathematicians failing to update, in a sense. It's pretty superior to the Lebesgue integral in terms of conceptual simplicity and applicability, but practically no one uses it.

Recommending Ben Lambert's "A student's guide to Bayesian Statistics" as the best all-in-one intro to *applied* Bayesian statistics

The book starts with very little prerequisites, explains the math well while keeping it to a minimum necessary for intuition, (+has good illustrations) and goes all the way to building models in Stan. (Other good books are McEarlath Statistical Rethinking, Kruschke's Doing Bayesian Data Analysis and Gelman's more math-heavy Bayesian Data Analysis). I recommend Lambert for being the most holistic coverage.

I have read McEarlath Statistical Rethinking and Kruschke's Doing Bayesian Data Analysis, skimmed Gelman's Bayesian Data Analysis. Recommend Lambert if you only read 1 book or as your first book in the area.

PS. He has a playlist of complementary videos to go along with the book

Subject: Introductory Decision Making/Heuristics and Biases

Recommendation: Judgment in Managerial Decision Making by Max Bazerman and Don Moore.

This book wins points by being comprehensive, including numerous exercises to demonstrate biases to the reader, and really getting to the point. Insights pop out at every page without lots of fluffy prose. The recommendations are also more practical than other books.

Alternatives:

• Rational Choice in an Uncertain World by Reid Hastie and Robyn Dawes. A good, well-rounded alternative. Its primary weakness is the lack of exercises.
• Making Better Decisions: Decision Theory in Practice by Itzhak Gilboa. Filled with exercises, this book would be a great supplement to a course on this subject, but it wouldn't stand alone on self-study. This book specializes in probability and quantitative models, so it's not as practical, but if you've read Bazerman and Moore, read this next if you want to see more of the economic/decision theory approach.
• How to Think Straight about Psychology by Keith Stanovich. Slanted towards what science is and how to perform and evaluate experiments, this is still a decent introduction.
• Smart Choices by John Hammond, Ralph Keeney, and Howard Raiffa. Not recommended. Few studies cited and few technical insights, if my memory is correct. The book doesn't go far beyond "clarify your problem, your objectives, and the possible alternatives".

Here is a very similar post on Ask Metafilter. (It is actually Ask Metafilter's most favorited post of all time.)

Luke -- I wonder if either permalinks to comments answering the task, or direct quotes of them could be added to your main post (say, after two+ weeks have passed)? I know in other posts where a question is asked it can be very difficult to sift through the "meta" comments and the actual answers, especially as comments get into the 100-200+ range!

I'd love to give recommendations on probability, but I learned it from a person, not a book, and I have yet to find a book that really fits the subject as I know it. The one I usually recommend is Grimmett and Stirzaker. It develops the algebra of probability well without depending on too much measure theory, has decent exercises, and provides a usable introduction to most of the techniques of random processes. I found Feller's exposition of basic probability less clear, though his book's a useful reference for the huge amount of material on specific distribution in it. Feller also naturally covers much less ground (probability and stochastic processes has developed a lot since he wrote that book). Kolmogorov's little book (mentioned elsewhere in the threads) is typical Kolmogorov: deliciously elegant if you know probability theory and like symbols. I would love to be able to recommend Radically Elementary Probability Theory by Nelson, and it's certainly worth a read as a supplement to Grimmett and Stirzaker, but I would hesitate to hand it to someone trying to understand the subject for the first time.

For statistics, I favor Kiefer's 'Introduction to Statistical Inference'. It begins with the decision theoretic foundations and builds from there, skipping or bypassing huge numbers of standard topics, and using a notation I can only describe as Baroque, but it is the best source of real understanding and intuiton I know of. Hogg and Craig's 'Introduction to Mathematical Statistics' is a pretty nice text as well, but less precisely pitched than Kiefer's (and it covers a lot more of the standard topics). Casella and Berger's 'Statistical Inference' and Lehmann's two books 'Point Estimation' and 'Hypothesis Testing' are the more typical graduate statistics texts, but are hard going compared to my other recommendations.

I'm going to disagree about Griffiths for electromagnetism, but admit that I don't have a really good alternative to offer. I found the second volume of Feynman clearer. Jackson is utterly opaque, a book length exercise in Green's functions methods in linear partial differential equations, and one without mathematical rigor. Schwinger's 'Classical Electrodynamics' is actually a remarkably useful text. I would probably recommend Purcell's 'Electricity and Magnetism', but it's out of print.

For thermodynamics, Hatsopoulos and Keenan's 'Principles of General Thermodynamics' is the best text I know. It's certainly better than any of the recommendations I received in my physics department. There are lots of beautiful texts -- Fermi's, Sommerfeld's, the opening couple chapters of volume 5 of Landau and Lifshitz, etc. -- but they all assume a developed conception in the student's mind of the nature of a thermodynamic system, while Hatsopoulos and Keenan spell it out in utter clarity. My only caveat about this book is that their exercises are given in Imperial units.

For statistical mechanics, I still think that Landau and Lifshitz volume 5 is the best text I know of. Sethna's 'Entropy, Order Parameters, and Complexity' is really neat, and touches on a lot more modern techniques, but has less real meat, less direct physics, than L&L. After that I think Reichl is probably my favorite, and he does set things up in a nice way, but not as nicely as Sethna.

Despite six years of wearing the big white suit in a tuberculosis laboratory, I am unaware of a microbiology textbook that should be read instead of burned.

Subject: Basic mathematical physics

Recommendation: Bamberg and Sternberg's A Course in Mathematics for Students of Physics. (two volumes)

Reason: It is difficult to compare this book with other text books since it is extremely accessible, going all the way from 2D linear algebra to exterior calculus/differential geometry, covering electrodynamics, topology and thermodynamics. There is potential for insights into electrodynamics even compared to Feynman's lectures (which I've slurped) or Griffith's. For ex: treating circuit theory and Maxwell's equations as the same mathematical thing. The treatment of exterior calculus is more accessible than the only other treatment I've read which is in Misner Thorne Wheeler's Gravitation.

In Bayesian statistics, Gelman's Bayesian Data Analysis, 2nd ed (I hear a third edition is coming soon) instead of Jaynes's Probability Theory: The Logic of Science (but do read the first two chapters of Jaynes) and Bernardo's Bayesian Theory.

Subject: Warfare, History Of and Major Topics In

Recommendation: Makers of Modern Strategy from Machiavelli to the Nuclear Age, by Peter Paret, Gordon Craig, and Felix Gilbert.

I recommend this book specifically over 'The Art of War' by Sun Tzu or 'On War' by Clausewitz, which seem to come up as the 'war' books that people have read prior to (poorly) using war as a metaphor. The Art of War is unfortunately vague- most of the recommendations could be used for any course of action, which is sort of a common problem with translations from chinese due to the heavy context requirements of the language. Clausewitz is actually one of the articles in Makers of Modern Strategy- the critical portions of On War are in the book, in historical context.

The important part of Makers of Modern Strategy is that each piece (the book is a collection of the most important essays in the development of military thought through the ages, starting with the medieval period and through nuclear warfare. I have other recommendations for the post-nuclear age of cyberwarfare and insurgency and I'll post them separately.) is placed in context and paraphrased for critical details. Military strategy is an ongoing composition, but the inexperienced read a single strategic author and think they have everything figured out.

This book is great because it walks you through each major strategic innovation, one at a time, showing how each is a response to the last and how each previous generation being sure they've got everything figured out is how their successors defeat them. My overall takeaway was one of humility- even the last section on nuclear war has been supplanted by cyber and insurgent warfare, and it is a sure bet that someone will always find a way to deploy force to defeat an opponent. This book walks you through how to defeat naive and inexperienced combatants in a strategic sense. Tactics, as always, are contingent on circumstances.

I don’t know how relevant improv is to Less Wrongers, but I find it helpful for everyday social interactions, so:

Primary recommendation: Salinsky & Frances-White’s The Improv Handbook.

Reason It’s one of the only improv books which actually suggests physical strategies for you to try out that might improve your ability rather than referring to concepts that the author has a pet phrase for that they use as a substitute for explaining what it means. Not all of the suggetions worked for me, and they’re based on primarily on anecdotal evidence (plus the selection effect of the authors having run a reasonably successful improv group in the hostile London climate and only then written a book), but I know of no other book that has as constructive an approach. It also has a number of interview sections and similar, which are eminently skippable – only half the book is really worth reading for performance advice, but fortunately the table of contents make it pretty clear which half that is.

I’m recommending it over Keith Johnstone’s ‘Impro’ and ‘Impro for Storytellers’, whose ideas it incorporates, breaks down and structures far better, over Chris Johnston’s ‘The Improvisation Game’, which is an awful mishmash of interviews and turgid academic writing, over Charna Halpern’s ‘Truth in Comedy’, which has quite a different set of ideas but spends more time boasting about how good they are than explaining them, over Jimmy Carrane and Liz Allen’s Improvising Better, which has a few nice tips and is mercifully short, but doesn’t have anything close to a coherent set of principles, ‘The Improvisation Book’, which I haven’t read in depth but seems to be little more than a list of games, and Dan Patterson and Mark Leveson’s ‘Whose Line is It Anyway’, which unsurprisingly is very heavily focused on emulating the restrictive format of the show of the same name.

Secondary recommendation: Mick Napier’s Improvise, which comes from a different school of thought to TIH’s – the same one as ‘Truth in Comedy’.

Reason It's the only one of any of those I’ve mentioned (TIH included) to explicitly suggest scientific reasoning in developing and assessing improv methods. After the author’s initial proclamation to that effect, he doesn’t really communicate how he’s tried to do so, and his advice seems to assume you’re already quite comfortable with being in an unspecified scene with no preset rules (one of the hardest things for an improviser to find himself in, IME), so I wouldn’t recommend it as a beginner’s guide.

Non-relativistic Quantum Mechanics: Sakurai's Modern Quantum Mechanics

This is a textbook for graduate-level Quantum Mechanics. It's advantages over other texts, such as Messiah's Quantum Mechanics, Cohen-Tannoudji's Quantum Mechanics, and Greiner's Quantum Mechanics: An introduction is in it's use of experimental results. Sakurai weaves in these important experiments when they can be used to motivate the theoretical development. The beginning, using the Stern-Gerlach experiment to introduce the subject, is the best I have ever encountered.

While the following isn't really a textbook, I highly recommend it for helping you to improve your skill as a reader. "How to Read a Book" by Mortimer Adler and Charles Van Doren. It covers a variety of different techniques from how to analytically take apart a book to inspectional techniques for getting a quick overview of a book.

I never knew how to read analytically, I had never been taught any techniques for actually learning from a book. I always just assumed you read through it passively.

http://www.amazon.com/How-Read-Book-Touchstone-book/dp/0671212095

Subjects: algorithms/computational complexity, physics, Bayesian probability, programming

Introduction to Algorithms (Cormen, Rivest) is good enough that I read it completely in college. The exercises are nice (they're reasonably challenging and build up to useful little results I've recalled over my programming career). I think it's fine for self-study; I prefer it to the undergrad intro level or language-specific books. Obviously the interesting part about an algorithm is not the Java/Python/whatever language rendering of it. I also prefer it to Knuth's tomes (which I gave up on finishing - not enough fun). Knuth invents problems so he can solve them. He explains too much minutia. But his exercises are varied and difficult. If you like very hard puzzles, it's a good place to look.

Introduction to Automata Theory, Languages, and Computation (Hopcroft+Ullman) was also good enough for me to read. I've referred to it many times since. However, it's apparently not well-liked by others; maybe because it's too dense for them? I haven't read any other textbooks in the area.

The Feynman Lectures on Physics are also fun to read. But I doubt someone could use them as an intro course on their own. Because they're filled with entertaining tidbits, I was tempted to read through them without actually following the math 100%. Obviously this somewhat defeats the purpose. That's always a danger with well written technical material consumed for pleasure. I had already taken a few physics courses before I read Feynman; his lectures were better than the course textbooks (which I already forgot).

I didn't care for Jaynes. I only read about 700 pages, though. I remember there was some group reading effort that stopped showing up on LW after just a few chapters :)

For plain old programming, I've read quite a few books, and really liked The Practice of Programming - it was too short. I read Dijkstra's a discipline of programming and loved it for its idea to define program semantics precisely and to prove your code correct (nobody really practices this; it's too slow and hard compared to "debugging"), but it's probably not worth the price - I checked it out from a library.

I also agree with rwallace's recommendations also, except that the AI text is not especially useful (not that I know of a better one). I would not give SICP to a novice, though. Although I had done everything described in the book before (and already knew lisp), it did increase my appreciation of using closures and higher order functions as an alternative for the usual imperative/OO stuff. It also covers interpretation and compilation quite well (skipping the character-sequence parsing part - this is lisp, after all).

For Elliptic Curves:

I recommend Koblitz' "Elliptic Curves and Modular Forms"

It stays more grounded and focused than Silverman's "Arithmetic of Elliptic Curves," and provides much more detail and background, as well as more exercises, than Cassel's "Lectures on Elliptic Curves."

Is this thread still being maintained? There was a recommendation for it to be a wiki page which seems like a great idea; I'd be willing to put the initial page together in a couple weeks if it hasn't been done but I don't think I can commit to maintaining it.

Request for textbook suggestions on the topic of Information Theory.

I bought Thomas & Cover "Elements of Information Theory" and am looking for other recommendations.

World War II.

"A World at Arms" by Gerhard L. Weinberg is my preferred single book textbook (as a reference) on World War II.

It is a suitably weighty volume on WW2, and does well in looking at the war from a global perspective, it's extensive bibliography and notes are outstanding. In comparison with Churchill's "The Second World War" - in it's single volume edition, Weinburg's writing isn't as readable but does tend to be less personal. Churchill on the other hand is quite personal, when reading his tome, it's almost as if he is sitting there having a chat with you. Churchill is quite frank in revealing his thought processes for making decisions, in fact LWer's might particularly enjoy reading Churchills' account for that reason. Weinberg's A World at Arms is better at looking at multiple view points of the war, whereas Churchill tends to present everything from his point of view. "The Politics of War" by David Day is an Australian centric view point of WW2, it stands as an excellent reference from that perspective, but isn't able to provide an overall picture equal to either Weinburg or Churchill.

For topology, I prefer Topology by Munkres to either Topology by Amstrong or Algebraic Topology by Massey (the latter already assumes knowledge of basic topology, but the second half of Munkres covers some algebraic topology in addition to introducing point-set topology in the first half).

Both Armstrong and Massey try to make the subject more "intuitive" by leaving out formal details. I personally just found this confusing. Munkres is very careful about doing everything rigorously at the beginning, but this lets him cover much more material more quickly later, because he can safely talk about something without wondering whether the reader will correctly guess an implication, because the reader (in theory) understands the background material completely and will be able to tell what is going on.

Munkres' treatment is also far more comprehensive.

Munkres also has a lot of really good exercises, although I didn't get far enough into the other two books to really evaluate how good their exercises are.

One caveat: in topology it is easy to push definitions around without understanding what's going on. It helps to be able to draw pictures of e.g. Haussdorf condition to be able to figure out what's going on.

It really depends on your learning style, and whether you learn best through examples=>generalizations or generalizations=>examples.

Similarly, some people may learn faster from a non-rigorous approach (and fill in the gaps later), while others may learn faster from a more rigorous approach. Some people might stare at a text for hours, but might be able to motivate themselves to learn the material much faster if they had some concrete examples first (using the Internet as a supplementary resource can help in that). I actually find it easier to learn molecular cell biology through Wikipedia articles than through textbooks, because Wikipedia articles often contain more of the information that's more emotionally significant to many people (even if not epistemically significant).

For example, I really do feel that I would have learned physics and math much faster if I learned them through computer simulations (proofs could be done later - I tend to just stare at proofs if they're presented first). I'm an inductive learner, not a deductive learner, and I tend to stare at texts that are overly deductive (part of it owes to my severe inattentive ADD, but maybe some non-ADDers are in the same boat as I am there)

In general, I find lectures extremely inefficient, unless there is space for significant amounts of one-to-one feedback, either through insanely small classes or a teacher who allows you to be their pet. Since these rarely happen in college, I generally find learning from textbooks more efficient. Podcasts/video lectures are often VERY inefficient ways to learn since you can read MUCH faster than you can listen, and it's much more of a hassle to repeat a part you don't quite understand.

Here's a quote I really like:

"Similarly, no one has been able to confirm any certain limits to the speed with which man can learn. Schools and universities have usually been organized as if to suggest that all students learn at about the same rather plodding and regular speed. But, whenever the actual rates at which different people learn have been tested, nothing has been found to justify such an organization. Not only do individuals learn at vastly different speeds and in different ways, but man seems capable of astonishing feats of rapid learning when the attendant circumstances are favorable. It seems that, in customary educational settings, one habitually uses only a tiny fraction of one's learning capacities." Encyclopedia Britannica, Philosophy of Education

====

That being said, here's a list of books I wish I had studied from instead of the standard textbooks: http://www.amazon.com/gp/richpub/syltguides/fullview/R2BKS9X5I8D9Y/ref=cm_sylt_byauthor_title_full_1

Also, Razib Khan has collected some pretty amazing books (you can find them on http://www.gnxp.com).

I made a post with ideas for what to do if you can't find a textbook in this thread that covers the subject you want to learn.

Subject: Introductory Real (Mathematical) Analysis:

Recommendation: Real Mathematical Analysis by Charles Pugh

The three introductory Analysis books I've read cover-to-cover are Lang's, Pugh's, and Rudin's.

What makes Pugh's book stand out is simply that he focuses on building up repeatedly useful machinery and concepts-a broad set of theorems that are clearly motivated and widely applicable to a lot of problems. Pugh's book is also chock-full of examples, which make understanding the material much faster. And finally, Pugh's book has a very large number of exercises of varying difficulty-Pugh has more than 500 exercises total.

In contrast, Rudin's book tends to focus on "magic." Rudin uses the shortest possible proofs for a given theorem. The problem is that the shortest proofs aren't necessarily the most instructive-while Baby Rudin is a beautiful work of Math qua Math, it's not a particularly good book to learn from.

Finally, Lang's book is frankly subpar. Lang leaves out critical details of some proofs (dismissing one 6 page proof as trivial!), is poorly motivated by examples, and has a number of mistakes.

If you want to really understand Mathematical Analysis and get to the point where you can use the concepts to create proofs and solve problems, Pugh is the best book on the topic. If you want a concise summary of undergraduate analysis to review, pick Rudin's book.

For abstract algebra I recommend Dummit and Foote's Abstract Algebra over Lang's Algebra, Hungerford's Algebra, and Herstein's Topics in Algebra. Dummit and Foote is clearly written and covers a great deal of material while being accessible to someone studying the subject for the first time. It does a good job focusing on the most important topics for modern math, giving a pretty broad overview without going too deep on any one topic. It has many good exercises at varying difficulties.

Lang is not a bad book but is not introductory. It covers a huge amount but is hard to read and has difficult exercises. Someone new to algebra will learn faster and with less frustration from a less advanced book. Hungerford is awful; it is less clear, less modern, harder, and covers less material than Dummit and Foote. Herstein is ok but too old fashioned and narrow, and has too much focus on finite group theory. The part about Galois theory is good though, as are the exercises.

It's not exactly a textbook series, but I've found the videos at khan academy http://www.khanacademy.org/#browse to be really helpful with getting the basics of a lot of things. The most advanced math it covers is calculus, which will get you a long way, and the language of the videos is always simple and straightforward.

... Guess I need to recommend it against other video series, to keep to the rules here.

I do recommend watching the stanford lecture videos http://www.youtube.com/user/StanfordUniversity?blend=1&ob=5 , but I recommend Khan over them for simplicity's sake on getting the basics. (Then watch stanford for a more complex understanding)

And though it just covers abiogenesis and evolution, cdk007 http://www.youtube.com/user/cdk007?blend=1&ob=5#p/a does have quite a bit of overlap with khan's biology section. But it's a lot more narrow than what khan covers, and pretty much is just there to counter creationists. While that's a pretty good goal, and the videos are good, it's not as good for learning in my opinion.

Subject: Electromagnetism, Electrodynamics

Recommendation: Introduction to Electrodynamics by David J. Griffiths

I first received this textbook for a sophomore-level class in electrodynamics. It was reused for a few more classes. I admit that I don't have much to compare it with, though I have looked at Feynman's lectures, a couple giant silly freshman physics tomes, and J. D. Jackson's Electrodynamics, and I know what textbooks are like in general.

I was repeated floored by the quality of this book. I felt personally lead through the theory of electrodynamics. In general, he does go from the simple and specific to the complex and general, as any mind requires. But at every stage, he knows exactly where there is risk of conceptual confusion, and he knows exactly how to correct it. He brings every clarification and result back to the the fundamentals of the subject, and he keeps you radiantly aware of the context. After this kind of developed enlightenment, you walk away with a rationalist's mastery, at least in this specific subject. He does all this, from vector calculus review to special relativity, in 2 centimeters thick.

Subject: Economics

Recommendation: Introduction to Economic Analysis (www.introecon.com)

This is a very readable (and free) microecon book, and I recommend it for clarity and concision, analyzing interesting issues, and generally taking a more sophisticated approach - you know, when someone further ahead of you treats you as an intelligent but uninformed equal. It could easily carry someone through 75% of a typical bachelor's in economics. I've also read Case & Fair and Mankiw, which were fine but stolid, uninspiring texts.

I'd also recommend Wilkinson's An Introduction to Behavioral Economics as being quite lucid. Unfortunately it is the only textbook out on behavioral econ as of last year, so I can't say it's better than others.

Since many people will be buying books here, this is a good place to recommend that people use a book-price search engine to find the best possible price on a book. I have found the best one to be BooksPrice. DealOz is also decent. I am not affiliated with either of these in any way.

Subject: Microeconomics

Recommendation: My Textbook

Obviously I have some massive bias issues in evaluating my own book, but the kind of person who regularly reads and contributes to LessWrong is probably the kind of person who would write a textbook LessWrongers might want to read. Plus, a used copy costs only $3 at Amazon.

My book even briefly discusses the singularity.

Mankiw's Principles of Microeconomics and Heyne's The Economic Way of Thinking are also good.

I don't have any recommendations yet, but want to note that some Books can be read and downloaded at archive.org, for example Spivak's Calculus: https://archive.org/details/Calculus_643. For some Books you'll have to sign up to "loan" a Book Online.

It would be useful for me if some of you guys shared your methodology of choosing textbook / course / whatever for learning X, especially if X has something to do with math, computer science or programming.

My methodology (in no particular order):

• Go to this thread and look at recommendations
• Go to libgen, search for the keyword and sort by the publisher or by year
• Check rating on goodreads and/or on amazon
• Check top comments by usefulness on goodreads and/or amazon
• Download the book, look at the Contents section, see how much I like what I see
• Google best textbook on ${subject name}, ${book title 1} vs ${book title 2}. Pay special attention to results on stackexchange. Do the same google search with site:reddit.com

Subject: Commutative Algebra

Recommendation: Introduction to Commutative Algebra by Atiyah & MacDonald

Contenders: the introductory chapters of Commutative Algebra With a View Towards Algebraic Geometry by Eisenbud and the commutative algebra chapters of Algebra by Lang.

Atiyah & MacDonald is a short book that covers the essentials of Commutative Algebra, while most books cover significantly more material. So this review should be seen as comparing Atiyah & MacDonald to the corresponding chapters of other Commutative Algebra books. There are a few reasons why Introduction to Commutative Algebra is better than most other books:

• Better abstractions. The abstractions Atiyah & MacDonald use (especially towards rings and ideals) are simply more broadly applicable and make several proofs simpler. Conversely other books tend to use an older set of abstractions which make the same proofs significantly more complex.

• Exercise-driven approach. Atiyah & MacDonald's exercises are beautifully structured so that you build up important parts of the theory yourself. There's a very satisfying feeling of castle-buildng: each exercise draws upon your understanding of the previous problem, and they come together to form very nice results. Many books can give you the feeling of understanding Commutative Algebra, but this one helps you discover it, which is much more enjoyable and provides a much deeper understanding.

• The right kind of conciseness. Atiyah & MacDonald's book is short because they cover a limited range of topics, but they do cover all the essential tools that are widely used. In contrast most books tend to bloat by trying to cover too many things, or tend to leave out critical parts of the theory.

Related: The Best Intro Book for Any Topic.

I would like to request a book on Game Theory. I went to my school's library and grabbed every book I could find, and so I have Introduction to Game Theory by Peter Morris, Game Theory 2nd Edition by Guillermo Owen, Game Theory and Strategy by Philip Straffin, Game Theory and Politics by Steven Brams, Handbook of Game Theory with Economic Applications edited by Aumann and Hart, Game Theory and Economic Modeling by David Kreps, and Gaming the Vote by William Poundstone because I also like voting theory.

My brief glances make Game Theory and Strategy look like a fun, low level read that I'll probably start with to whet my appetite for the subject. Introduction to Game Theory looks like a good, well written intro textbook, but it was written in 1940 and was only updated once in 1994, and I would hope something new would have happened in that time. Game Theory 2nd Edition looks like a good, moderately modern (1982) and incredibly boring book. The others look worse.

I'll read at least portions of all of them and at least two or three completely unless somebody suggests anything. If no one does before I read them I'll post an update.

Machine learning: Pattern Recognition and Machine Learning by Chris Bishop

Good Bayesian basis, clear exposition (though sometimes quite terse), very good coverage of the most modern techniques. Also thorough and precise, while covering a huge amount of material. Compared to AI: A modern approach it is much more clearly based in Bayesian statistics, and compared to Probabilistic robotics it's much more modern.

For elementary economics: "Macroeconomics" by Mankiw, is without a doubt the best on the market. It is incredibly well written, and it's so good once you've read the book it fools you into thinking you understand absolutely everything on the topic! "Intermediate Microeconomics" by Varian, is arguably the one to get. It can be a tad dry, and he uses lots of maths. If you don't like the idea of that then "Microeconomics" by Katz and Rosen is a very readable and less mathematical, though not quite as comprehensive as Varian.

Any recommendations for Mechanism Design [? · GW] textbooks?

In Introduction to Mechanism Design [LW · GW] Badger recommended A Toolbox for Economic Design (2009) and An Introduction to the Theory of Mechanism Design (2015).

In the the preface to the latter, the author mentions a few other books too:

• Designing Economic Mechanisms (2006) by Leonid Hurwicz and Stanley Reiter. "The focus of this text is on informational efficiency and privacy preservation in mechanisms. Incentive aspects play a much smaller role than they do in this book."
• Communication in Mechanism Design: A Differential Approach (2008) by Steven R. Williams "This book covers material similar to that of Hurwicz and Reiter. The emphasis that both books place on the size of the message space in a mechanism differentiates them from more modern treatments of mechanism design."
• A Toolbox for Economic Design (2009, also recommended by Badger) by Dmitrios Diamantaras, with Emina I. Cardamone, Karen A. Campbell, Scott Deacle, and Lisa A. Delgado. "This book is closest to mine among those listed here, but it covers more than I do, such as the theory of Nash implementation, the theory of matching markets, and empirical evidence on mechanisms. Sometimes I wish I had written this book. My own book is more narrowly focused, perhaps goes somewhat into greater depth, and places a greater emphasis on the relation between game theoretic foundations and mechanism design."
• Mechanism Design, A Linear Programming Approach (2011) by Rakesh Vohra. "This is a superb book, demonstrating how large parts of the theory of mechanism design can be developed as an application of results from linear programming. Vohra puts less emphasis than I do on the game theoretic aspects of mechanism design."

He also wrote this about prerequisites:

This book is meant for advanced undergraduate and graduate students of economics who have a good understanding of game theory. Fudenberg and Tirole (1993) contains more than the reader needs for this book. I shall also assume a basic knowledge of real analysis that can, for example, be acquired from Rudin (1976). 

For category theory, I would recommend Category Theory by Awodey instead of Category Theory for the Working Mathematician by Maclane. Awodey gives a lot of intuition, and explain through examples many of the subtleties, while still being formal. Maclane is a great reference book, but it is to terse for first learning the field, in my opinion.

Is this list still being maintained and/or discussed over ?

I feel like the ML text-book being recommended *could* at least use an alternative in the form of: http://www.deeplearningbook.org/ , it takes a purely frequentist perspective (but consider that's basically the "practical" perspective at the moment, with even the bayesianNN work being... not so Bayesian), but it's much more concise, does a good job at explaining the math and skips over historical stuff that people either know of already (e.g DT) or that is essentially useless outside of niche applications and legacy systems (e.g. kernel trick).

Or possibly even the fast-ai course http://course18.fast.ai/ml , granted, it's no a text-book per-say, but the combination of the notes is textbook-like.

At least it would be worth creating a "Modern automatic differentiation modeling" section or something for it, if people disagree that ML can be essentially reduced to "whatever the top papers on paperswithcode are doing in the last 4 or 5 years".

Question: what are the recommended books on the following topics?

*Entrepreneurship

*Innovation management

*Inspiration (how to get inspiration for yourself and for others)

*Social Science research methods

Cheers!

This guy reviewed 5 freely available calculus textbooks and chose Elementary Calculus: An Approach Using Infinitesimals by Jerome H. Keisler as his favorite. Note that the book uses a nonstandard approach.

Here are some physics and quantum mechanics recommendations that may not meet the "read three books" requirement.

Another strategy for finding good textbooks is to surf around Amazon and see what seems to have good reviews.

Special relativity: Spacetime Physics by Taylor and Wheeler is excellent. It reminds me of the general style of the Feynman lectures, but is in depth and has good problem sets. Like the Feynman lectures it is based on developing intuition, which is important for relativity because, like QM, every single human is born with the wrong intuition. It takes time and practice to develop. Also like Feynman, the writing style isn't akin to a barren wasteland like most textbooks. It is written to teach, not as an accompaniment to a university course. Finally, the problem sets are the best I've ever run into in any physics book.

The Feynman lectures has a few chapters about special relativity but they're short and not nearly as good as the rest of the lectures.

The first time I learned this material was through the book Modern Physics by Harris. Dodge this book at all costs. The writing is as clear as a muddied lake, or maybe a blizzard sky of deepest winter. The problems are numerous and boring. Rote physics indeed.

The MIT intro to special relativity is decent, but very dry like all the other MIT intro books. Not recommended for self study, but great as a class companion.

These are all that I've read, but there are many many more out there. This site is a bit dated but contains lots of good books. It recommended spacetime physics which turned out to be amazing. One book I see overlooked often is Einstein's own explanation of the subject. Be careful what printing you buy, or download it off of Gutenberg. It is somewhat outdated and very short, but if you only have a few hours to spare it will give you a good outline of both theories. Since it's free and short I'd recommend giving it a go before buying a textbook. I personally find SR fascinating, but others might not and this will help you decide.

I'd like to request Best Textbook suggestions for: climate science and/or climate policy.

Chris

Recommended for LINGUISTICS: "Contemporary Linguistics", by William O'Grady, John Archibald, Mark Aronoff, & Janie Rees-Miller. Truly comprehensive, addressing ALL the areas of interesting work in linguistics -- phonetics, phonology, morphology, syntax, semantics, historical linguistics, comparative linguistics & language universals, sign languages, language acquisition and development, second language acquisition, psycholinguistics, neurolinguistics, sociolinguistics & discourse analysis, written vs spoken language, animal communication, & computational/corpus linguistics. Each chapter is sharp & targetted; you will really know what you want to read next after studying this text.

NOT recommended: "Linguistics: An Introduction to Linguistic Theory", edited by Victoria A. Fromkin & authored by Bruce Hayes, Susan Curtiss, Anna Szabolcsi, Tim Stowell, Edward Stabler, Dominique Sportiche, Hilda Koopman, Patricia Keating, Pamela Munro, Nina Hyams, & Donca Steriade. This text provides a solid guide to generative phonology, generative syntax, and formal semantics -- but only in their mainstream (aka Chomskian) formulations, and with no reference to actual language use (which, for theoretical reasons, is anathema to the Chomskian crowd). Interestingly, at least 8 of the authors I recognize as faculty from UCLA, which makes the text a bit ingrown for my taste.

NOT recommended: "Syntax: A Generative Introduction", by Andrew Carnie. First problem: This book covers syntax and only syntax, and does so solely from a generative perspective. Second problem: Although Carnie is a reknowned expert in Irish Gaelic syntax and doubtless knows his stuff, he can't write a clear expository textbook to save his soul. This is the most confusing book on linguistics that I've ever read.

In the wake of publishing Scientific Self-Help: The State of Our Knowledge, I realized there is another subject on which I have read at least three textbooks: self-help!

Subject: Self-Help

Recommendation: Psychology Applied to Modern Life by Weiten, Dunn, and Hammer

Reason: Tucker-Ladd's Psychological Self-Help is a 2,000 page behemoth of references from a passionate, life-long researcher in self-help. It was a work-in-progress for 20 years, and never mass-published. It's an excellent research resource, though it's now out-of-date. John Santrock's Human Adjustment is a genuine university textbook on self-help, but it is not as mature, well-organized, or well-written as Weiten, Dunn, and Hammer's Psychology Applied to Modern Life.

In college, I found most of the time that the professor's lecture notes contain almost everything of value that both the textbook and the lecture contains, but they contain ten times less text. This led me to believe that textbooks are a terribly inefficient way to convey facts, by comparison to the format of lecture notes. Books are words, words, words, flowery metaphors, digressions, etc. Hell, I don't know what they spend all those words on. But I know that, potentially, lecture notes are one fact after another.

Software engineering: everything by Andrew Tanenbaum. The standard texts in the field for good reason.

the absolutely wonderful thing about textbooks is that you can often pick up older editions for the price of a paperback novel.

Sometimes two textbooks on the exact same topic serve completely different purposes. There are "I want to learn this thing I don't know" textbooks, and there are "I am an expert but I still want this book on hand as a tool to help me with my experting". Below I describe the most extreme examples I am aware of, which are unfortunately on different topics:

Nonlinear Dynamics and Chaos by Strogatz  is incredibly readable. You can sit with it on a train and read non-stop without needing to look anything up and you will keep wanting to relate the next amazing thing you have learned to the poor stranger sat next to you. You emerge from it with a new conceptual framework, and then you never look at it again because if their is ever a detail or issue you can't remember this book is the wrong place to check it.

Statistical Methods in Quantum Optics by Carmichael is a fantastic book. But, if you are new to the topic of quantum optics you should NOT touch it at all. It is an almost useless teaching aide. If you can't remember whether the quantum regression theorem is dependent on the Markovian, Born or Secular approximations then this is the book for you. If you don't know what any of those things are and want to find out then stay away! Find something else.

The same book cannot be ideal at both, their is a trade-off in optimising towards these two objectives.

Is this list still being updated? Does anyone have any recommendations for linguistics, specifically the study of how languages change over time?

Personality Psychology: Domains of Knowledge about Human Nature by Randy J. Larsen, David M. Buss

I have looked into maybe 40 general psychology textbooks. Not read them all though, but read quite a few. This one is still by far the best intro to general psychology. But you may put it under personality psychology even though that's basically all of psychology minus the philosophical and political part. I try to read many more textbooks to review them. I'll inform people if I find something on this level again. The problem is that it very fast gets into pseudoscience/guesswork territory with psychology so there are a ton of really bad textbooks out there.

For Functional Analysis, I'd recommend Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis. Some alternatives often suggested are the books by Kreyszig or Lax. Where they fall short depends on what your purpose of study is. To me, most students are learning functional analysis as a tool, usually for PDEs at the level of Evans or John and Brezis is the most versatile book for this or other purposes. It's exposition is lucid and the exercises come with partial solutions. Kreyszig has a lot of overlap but it's more restrictive in its proofs and presentation. Lax's presentation of the topics is non-standard a number of times and should be used as a complementary text to Brezis. All this being said, for PDE I would always recommend learning Harmonic Analysis and the Theory of Distributions in conjunction with what is considered the classical functional analysis course centered around the results of Banach. Harmonic Analysis is hard to find a good singular reference for (at this level, serving this purpose) but there are bits and pieces of notes online that I patched together to gather some understanding and the Theory of Distributions could probably be learned from a combination of Folland's chapter 9, Stein-Shakarchi Book 4, and the book by Friedlander.

Does anyone have a recommendation for a comprehensive history textbook, covering ancient as well as modern history, and several geographical regions? Just something to teach me about major events and dates, wars, rulers & dynasties, interactions between civilisations, etc., without neglecting the non-geopolitical aspects of history. College-level, please. (A dumbed-down alternative to what I'm asking would be to start looking for my old high school textbooks, but obviously that wouldn't be very satisfactory.) Comprehensive accounts of single civilisations in a single period could work as well, but I'm looking for a book that is mainly didactic in purpose and with a broad subject matter.

Also: should I supplant whatever I'm studying with Wikipedia, so that I have the option of going in as much depth as I like? Or is it too unreliable even for basic learning purposes?

On philosophy, I think it's important to realize that most university philosophy classes don't assign textbooks in the traditional sense. They assign anthologies. So rather than read Russell's History of Western Philosophy or The Great Conversation (both of which I've read), I'd recommend something like The Norton Introduction to Philosophy.

Just so you know, the title of Spivak's book has been misspelled as 'Caclulus.'

Subject: Animal Behavior (Ethology)

Recommendation: Animal Behavior: An Evolutionary Approach (6th Edition, 1997) Author: John Alcock

This is an excellent, well organized, engagingly written textbook. It may be a tiny bit denser than the comparison texts I give below, but I found it to be far and away the most rewarding of the three (I've just read the three). The natural examples he gives to illustrate the many behaviors are perfectly curated for the book. Also, he uses Tinbergen's four questions to frame these discussions, which ensured a rich description of each behavior. The author gives a cogent defense of sociobiology in the last chapter, which was icing on the cake.

Other #1: Principles of Animal Behavior (1st Edition, 2003) Author: Lee Alan Dugatkin

This was one I had to read for a class; it's a bit shorter than Alcock, and maybe it has been improved upon since this inaugural edition, but I found the fluff-to-substance ratio to be concerningly high. It was much more basic than Alcock, perhaps better suited for a high school audience. The chapters were written like works of fiction and the author maintained this style throughout, which I found distracting (though others may like it). Bottom line: If you have had a decent college level class in biology, you would definitely be better off going straight to an older edition of Alcock.

Other #2: Animal Behavior: An Evolutionary Approach (9th Edition, 2009) Author: John Alcock

I read through this edition too (I think there's a 10th out now) while writing my undergraduate thesis to make sure I hadn't missed any important updates in the field (I hadn't). The new edition had ~100 fewer pages; it was long on pictures (quite a few more than its predecessor) and short on content. It's been several years now and I can't remember exactly the ways in which it differed, but “watered down” comes to mind. I would highly recommend picking up an older edition unless this one is specifically required.

For someone who currently has a teacher's-password understanding of physics and would like a more intuitive understanding, without desiring to put in the work to obtain a technical understanding (i.e. learning the math), I would recommend Brian Green's Fabric of the Cosmos, which I feel does for physics (and the history of physics) what An Intuitive Explanation of Bayes Law does for Bayesian probability. It goes through history, starting with Newton and ending with modern day, explaining how the various Big Names came up with their ideas, demonstrates how those ideas can explain reality incrementally better than the previous ideas by using easy-to-envision thought experiments, and also contains a skippable explanation of the mathematic principles behind the new ideas for those who want that, although the book is valuable even without these sections. In this way, it's like a popular science book with an optional textbook component.

It has a couple weaknesses, like taking M-theory seriously, but in general I would say that it accomplishes its goal of imparting an intuitive understanding better than other popular physics books with similar goals, like Hawking's A Brief History of Time, The Universe in a Nutshell, or Green's The Elegant Universe.

For organic chemistry, all the textbooks have more or less the name "Organic Chemistry", The best, if most rigorous, is by Clayden, Greeves, Stuart Warren (main author) and Wothers. Much less rigorous are the books by McMurray, or Jan Smith or many others. I find the Wm. Brown book well written but rather similar to all the rest. The market requires that the book prepare one for the MCATs which means all chemistry discovered after about 1980 is omitted. Perhaps that is why Clayden is good, it is English. Modesty prevents me from naming the one I wrote, but I would suggest that if you want to organize your thoughts, writing a textbook is not a bad way to do it.

Subject: Criminal Justice Recommendation: Criminal Justice: Mainstream and Crosscurrents/John R. Fuller

Reason: The other intro texts on the subject are somewhat dry and tend to be just recitations of the Uniform Crime Reports and other government documents, with little interpretation. There are books by several authors (Neubauer and Albanese are two), but Fuller's book takes a critical view of the system without demonizing the system or those who work in it. Fuller's writing is also better, making reading a pleasure, which is an unusual trait for textbook. Nearly all CJ intro books delve into criminological theory, which students (including me) hate, but Fuller makes the theories clear and easier to understand. He also introduces a bit more history. Personally, I like to know where criminal justice practices come from and why. So much of it is based on common law, custom, and precedent!

This article showed up on the front page of HackerNews and on the front page of metafilter today.

Recommendation requests: Intro to calculus. I know about derivatives and I can use them and I sort of understand integrals but my knowledge is very fragmented. For instance, I don't know what half of the notation is supposed to actually represent. Also, I want strategies for solving problems rather than being given a bunch of (apparently) unrelated tools and told to just figure it out.... yea, I didn't have a good math teacher

Set theory and other discrete mathematics.

Psychology.

Something or other on the scientific method (how to design experiments)

Biology. General, human, micro, intro or advanced... Just trying to make the list more comprehensive

Chemistry. See above.

Physics. There are already some here but I want more topics (thermodynamics is the first that comes to mind).

In recommendations, I would suggest another criteria be added related to learning type. Some books are being praised for their concreteness and others for their topical comprehensiveness and others for their pedagogical comprehensiveness (addresses most common misconceptions etc.) and other sometimes mutually exclusive traits. Just a way of systematizing this and making it easier for people to get the type of book that they are looking for.

Edit: Another topic: writing. I have read elements of style but I haven't read anything else on the subject. I would like to see how it compares to other (newer?) books.

Subject: Meta-ethics

Recommendation: Miller, An Introduction to Contemporary MetaEthics

Reason: Jacobs' The Dimensions of Moral Theory is shorter and easier, for beginners, but it doesn't explain contemporary debates hardly at all. Miller's books is more comprehensive, precise, and contemporary, and even includes some original arguments (the section on Railton is particularly good). I'd like to see an updated third edition, but the 2nd edition from 2003 is still the best thing out there for an overview of meta-ethics. Smith's Ethics and the A Priori is pretty good, but of course it's the opinion of just one philosopher's views, and not good for an overview.

I would like to request a recommendation for a text that provides a comprehensive introduction to Lisp, preferably one with high readability.

Thank you for this post. It is profoundly useful. I noted it when it first appeared and recently had the need for a textbook on a subject. Came over here and found a great one.

Added the recommendations by joshkaufman, realitygrill, and alexflint.

Thanks, gang! Keep 'em coming.

Hard to answer without knowing your background. I might try online courses or ask Chat-GPT here for advice.

Subject: Theories of Policy Process (decision making in government and other organizations)

Recommendation: Understanding Public Policy: Theories and Issues (2nd Edition) by Paul Cairney (or his blog https://paulcairney.wordpress.com/).

Reason: The interdisciplinary (or transdisciplinary) field of policy studies is essential for understanding decision-making in organizations (notably how governments make policy decisions), research and normative debates on the use or non-use of evidence in decision-making processes, and advising or influencing those who make policy. The field is broad and fuzzy around all its many edges, but several theories or related debates have spawned concepts—such as bounded rationality or decision windows—that are essential in other fields discussed on Less Wrong. 

The Scottish scholar Paul Cairney makes nearly all of the material in his excellent books on policy-making available on his blog https://paulcairney.wordpress.com/. Note his interesting experiments with summarizing key ideas in 1000-, 750-, and 500-word posts (and 1000-second audio lectures, which equals about 16 minutes). If you'd prefer a book format, his key textbook is Understanding Public Policy: Theories and Issues (2nd Edition), which reviews most of the major theories about policymaking and much more. A follow-up to that textbook is his The Politics of Policy Analysis. For both good advice on the politics surrounding the use of evidence in government decisions and a survey of the research on what some call "knowledge utilization," see his The Politics of Evidence-Based Policy Making.  I think most of the material for the first and third books can be found on his blog. I'm not sure about the middle one listed. There are several alternatives to his textbook, but none are as equally succinct and broad. 

If the major theories are covered too quickly by Cairney, then Theories of Policy Processes (5th Edition) by Paul A. Sabatier and Christopher M. Weible (Editors) contains a half-dozen or so chapters each reviewing one major school of thought and a few more chapters making comparisons across theories and considering the future of policy process research. Alternatively, if you want a single textbook with a quicker look at many theories mingled with more on the goals and pitfalls of policy analysis, there is The Public Policy Theory Primer (3rd Edition) by Kevin B. Smith and Christopher Larimer. 

However, I prefer Cairney as he brings the theories along with related discussions in the social sciences (determinism, social construction, power, chaos or complexity theory, Marxism, etc.). In short, if the phrases garbage can model, advocacy coalition framework, and punctuated equilibrium (as applied to policy making) aren't familiar to you, but you are interested in decisions in organizations, then you might give Cairney's blog a look and then consider his books. 

What I have found to be the best textbooks for economic theory, and econometrics based on my experiences at econ grad school (graduate level, so more mathematical than suggestions above)

Microeconomic theory  - individual decision making/production/general equilibrium - Kreps, Microeconomic Foundations 1: Choice and Competitive Markets. Better then Mas-Collel, Whinston and Green, Microeconomic Theory, and Varian, Microeconomic Analysis

Microeconomic theory - game theory - Osborne and Rubenstein, A Course in Game Theory. Better than Mas-Collel, Whinston and Green, Microeconomic Theory, and Tadelis, Game Theory: An Introduction.

Macroeconomic Theory - growth theory - Acemoglu, An Introduction to Economic Growth

Macroeconomic Theory - business cycles - Lundqvist and Sargent, Recursive Macroeconomic Theory

General econometrics: Cameron and Trivedi, Microeconometrics: Methods and Applications

Microeconometrics/causal inference: Angrist and Pishke, Mostly Harmless Econometrics, and also Cunningham, Causal Inference: the Mixtape

Bayesian Econometrics: Greenburg, Introduction to Bayesian Econometrics

Subject: Econometrics

Recommendation: Mastering 'Metrics by Josh Angrist and J.S. Pischke

Reason: The book uniquely explains the intuitive ideas behind econometric methods. There is also a video series by MRU on the book. Other books that I have read on the subject:

- Mostly Harmless Econometrics, by the same authors. Kind of an earlier version of Mastering Metrics, more in depth, less fun and engaging.

- Introductory Econometrics A Modern Approach, by Wooldridge. Excellent for hands-on projects, very detailed, not as intuitive and easy to read as the others, packed with supplementary math, strong focus on different data structures (cross-section data vs. timeline and panel)

- Ökonometrie Eine Einführung (German) , similar to the above but way less content, stronger focus on potential errors and wrong presumptions. 

Furthermore I recommend reading The Book of Why (popular science) by Judea Pearl for a greater understanding of causal inference as a whole. The book also delves into the history of causal inference, bayesian networks and artificial intelligence.

We should migrate this post to a Github Awesome list. That medium works best for this kind of semi-distributed curation. 

https://www.reddit.com/r/AskReddit/comments/c4glci/professionals_and_experts_of_reddit_what_is_the

Hi, I am currently building a website to find recommended textbooks for specific topics, because I personally wanted this tool and I thought it might help other students like me, and I just randomly found this webpage a few days ago. I was wondering if I could use some of the comments here for my website, I just want to share your recommendations with more people and I will obviously add links back to this webpage and include the acknowledgements . Would that be ok with you?

By the way, the website is: www.books2learn.com

I just started this project a few weeks ago, so if you have any ideas to make it better I'm open to suggestions.

Regards

Post the title of your favorite textbook on a given subject.
You must have read at least two other textbooks on that same subject.
You must briefly name the other books you've read on the subject and explain why you think your chosen textbook is superior to them.

Subject: Probability Theory

Recommendation: Feller's An Introduction to Probability Theory is better than Jaynes' Probability Theory: The Logic of Science and MIT OpenCourseware: Introduction to Probability and Statistics

Jaynes' book probably has more insight for someone who already knows probability theory very well. MIT course should be better if you want ot learn some probability theory and statistics very fast skipping proofs and other stuff. Feller's book is better if you want to learn a lot of probability theory, you have a lot of time and Jaynes' book is too difficult for you.

Relativity

Recommendation: Spacetime and Geometry

Author: Sean Carroll

This is an expanded version of Carroll's lecture notes on relativity, which he has used to teach courses and which are available for free online (see the "Lecture Notes" tab on the page linked to above). I find it to be an excellent introduction to the subject, which covers the mathematical tools used, the basics of the theory, and the most common applications, all in a straightforward fashion. I have recommended this text (or its corresponding lecture notes) many times on Physics Forums as a reference for people who want a good introduction to the subject.

Other Textbooks Read:

Spacetime Physics, by Taylor & Wheeler. The text that I first learned Special Relativity from, and still a good introduction, with an emphasis on building physical intuition. However, it does not cover General Relativity. (Taylor apparently has a follow-on text covering GR at least as it applies to black holes, but I have not read it.)

Gravitation, by Misner, Thorne, & Wheeler: The classic text, and still a good comprehensive reference even though it was published in 1973. However, it is very comprehensive and detailed, has a somewhat idiosyncratic style, and can be difficult if you don't already have considerable background in the subject. It also weighs enough to seem like it might undergo gravitational collapse and become a black hole. :-)

General Relativity, by Robert Wald. Another classic, with a more abstract mathematical approach than MTW, not as comprehensive but covering some topics in more detail and from a different viewpoint than MTW. Published in 1984, so it also covers some topics, such as quantum fields in curved spacetime, that were too new to be covered when MTW was published. Not as recent as Carroll's text (published in 1984), and going into topics that are probably too advanced for readers who are being introduced to the topic for the first time.

The Large Scale Structure of Spacetime, by Hawking & Ellis. The definitive text on global geometric methods and causal structure in GR. It covers the classic singularity theorems of Hawking & Penrose in detail. However, it is really a monograph, not a comprehensive GR text, and requires the reader to already have considerable background in the subject.

The Usenet Physics FAQ has a long list of relativity references here:

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

For Biology 101, Life by David Sadava is amazing. I wasn't even particularly interested in the subject and just needed the course credit, but it was a fascinating page turner and made everything so clear.

https://www.amazon.com/Life-Science-Biology-David-Sadava/dp/1464141266

I don't know if this counts as a textbook, but Python for the Absolute Beginner is so good for beginning programming. Python is a great language to learn programming with. This book is just so perfectly paced. It's the exercises that make it work so well. It increments the difficulty just a smidgeon with each exercise to gradually get you used to more and more concepts.

https://www.amazon.com/Python-Programming-Absolute-Beginner-3rd/dp/B00B7RE628/ref=sr_1_1?s=books&ie=UTF8&qid=1470565643&sr=1-1&keywords=python+for+absolute+beginners#navbar

On introductory non-standard analysis, Goldblatt's "Lectures on the hyperreals" from the Graduate Texts in Mathematics series. Goldblatt introduces the hyperreals using an ultrapower, then explores analysis and some rather complicated applications like Lebesgue measure.

Goldblatt is preferred to Robinson's "Non-standard analysis", which is highly in-depth about the specific logical constructions; Goldblatt doesn't waste too much time on that, but constructs a model, proves some stuff in it, then generalises quite early. Also preferred to Hurd and Loeb's "An introduction to non-standard real analysis", which I somehow just couldn't really get into. Its treatment of measure theory, for instance, is just much more difficult to understand than Goldblatt's.

Subject: Written style and composition

Recommendation: Rhetorical Grammar: Grammatical Choices, Rhetorical Effects, by Martha Kolln and Loretta Gray

Reason: After reading Pinker's The Sense of Style, I wanted a meatier syllabus in the mechanics of writing well. My follow-up reading was Rhetorical Grammar and Joseph Williams' Style: Ten Lessons in Clarity and Grace.

I would actually recommend reading all three. Rhetorical Grammar is the most textbook-y of the recommendations, and The Sense of Style is more like a weighty, popular book on the subject, with Ten Lessons being more of an extended exposition/workbook on (you will be unsurprised to learn) ten broad principles of clear writing. All three books have similar messages and convergent positions on the subject matter. Rhetorical Grammar wins out for being the book I imagine one would learn most from.

As opposed to not elevating any particular hypothesis out of the hypothesis-space before there is enough evidence to discern it as a possibility. Privileging the Hypothesis and all that.

There is a thread on calculus textbook recommendations here. And here are some useful textbook recommendations on mathematical logic, math foundations and computability theory, courtesy of Vladimir_M.

On the basics of (normative) decision theory, I recommend Peterson's An Introduction to Decision Theory over Resnik's Choices: An Introduction to Decision Theory and Luce & Raiffa's Games and Decisions. Peterson's book has clearer explanations and is more up to date than these others. It's main failing is to ignore the work on decision theory in computer science and in Bayesian statistics, but the other two standard decision theory textbooks (Resnik; Luce & Raiffa) skip those subjects, too.

In statistical decision theory you've got Chernoff & Moses and Berger, but they're kinda out of date now and perhaps too difficult for the beginner.

For transport phenomena (momentum, mass, heat) I recommend Bird, Stewart, Lightfoot over Welty, Wicks, Wilson, Rohrer or Deen. WWWR is good if you need a quick reference and Deen is great for mathematical treatments, but nothing beats BSL if you are trying to actually learn transport phenomena.

For Physical Chemistry, McQuarrie and Simon is better than Atkins.

For basic Calculus, James Stewart has the best treatment.

Logic:

--mathematical

Enderton, "A mathematical introduction to logic" then Shoenfield's classic "Mathematical logic"

Cori and Lascar, "Mathematical logic: a course with exercise" for exercises for self-study

Manin, "A course in mathematical logic" for additional enrichment

--computational

Van Dalen's "Logic and Structure" and then Fitting, "First Order Logic and Automated theorem proving" to fill in the gaps

--philosophical

From Frege to Goedel: a sourcebook in mathematical logic

additional works by Frege and Cantor in dover reprints or in the original.

"Goedel's Proof" by Nagel

"Goedel, Escher and Bach" by Hofstadter

--modal and fuzzy

Goldblatt, "Logics of Time and Computation" (Introduction to modal logic through temporal logic)

Bergmann, "An introduction to many valued and fuzzy logic"

Calculus:

Apostol, "Calculus" 2 volumes (Still a classic)

Demidovich, "Problems in mathematical analysis" (Classic drill book)

Topology:

Viro, "Elementary Topology Problem Textbook" (Based on a classic course)

Modern Abstract Algebra:

Jacobson, "Basic Algebra" volumes 1 and 2

History of Western Philosophy:

Basic primary sources in western philosophy (Not a textbook!)

• Algorithms and Theory of Computation Handbook, Second Edition
• Computer Science Handbook, Second Edition

These two books are great for those who want to study Computer Sciense in a breadth-first manner. While each topic is not discussed in great details, the number of covered topics is mind-boggling. From trivial ones such as Sorting and Searching to more esoteric matter like Pricing Algorithms for Financial Derivatives, etc.

Subject: Automated Theorem Proving

Recommendation: Harrison, Handbook of Practical Logic and Automated Reasoning

Reason: Afraid I'm going to break the rules here, I haven't read any other books on the subject but as there's nothing posted here on ATPs I thought this might be useful to someone. The book is an excellent introductory text for someone who has a CS background but not in logic, and who wants to learn about theorem provers for from a practical perspective.

Updated again. Thanks, people! Keep 'em coming!

I would like to request a book recommendation on probability theory.

Following the rules if possible.

On systems theory, I'll recommend "Thinking in Systems: A Primer" is a great general audiences book, with a great nontechnical approach.If you are looking for something more mathematical, you'll need to ask someone else; I'm just not well read enough. (Despite being a math major back in school.)

"The Fifth Discipline: The Art & Practice of The Learning Organization" is a great book, but not as useful for systems theory in general, it's a more domain specific book. (I would recommend it, but not as the best book on the subject generally)

"Introduction to Systems Thinking" by Kim is just not as good; it's a fine book, but small and not at all comprehensive.

There are some great, slightly more technical books on the subject, like An Introduction to General Systems Thinking by Weinberg, as well, I am sure, as others. I haven't read enough of them to say that that specifically stands out among technical books on the subject. (If anyone has recommendations on the technical side, I'd love to hear them, as I would like to see more.)

I would like to request a recommendation for a text that introduces one to Utilitarianism.

But what exactly do you want to learn? If you study widely, surely you are trying to learn something different from what specialists in their respective fields try to learn. They might for example forgo a general understanding for specialist knowledge, because that is how they could best hope to contribute something unique to their field and hence reap the rewards of status. They might overemphasize certain methods of their fields since only discoveries through the use of such methods can hope to contribute results to their field.

An example:

the introductory course is increasingly tailored not for the majority of students for whom it will be their only economics course, but for the negligible fraction who will go on to become professional economists. Such courses focus on the mathematical models that have become the cornerstone of modern economic theory. These models prove daunting for many students and leave them little time and energy to focus on how basic economic principles help explain everyday behavior.

from here

Perhaps it's better to have textbooks written for other academics outside of a specialty, since such textbooks are forced to be tolerable/comprehensible to outsiders they are less susceptible to disciplinary navel gazing. They might aim to show off their specialty to others, instead of showing off the author's prowess within the specialty, but even this is an improvement, since they must achieve that through appealing to a wider audience with diverse interests/aptitudes.

What would be a general solution? Michael Vassar's idea of 'lightness of curiosity' helps I think. You should always make sure your curiosity tracks your goals. Do not rely on Schmidhuber's notion of curiosity as compression, because a discipline can hoodwink you by introducing difficult and enticing subproblems within the field which only practitioners would be interested in solving.

Note: I've only just realized all my suggestions are from actual film directors. No theorists or critics.

Subject of filmmaking, the best textbooks are Jerry Lewis's (yes, glavin) The Total Filmmaker which being transcribed from lectures he gave at USC around the time that George Lucas was a student it presents a soup to nuts overview of the nuts and bolts of screenwriting, principal photography including camera coverage, directing actors, editing and post production. Including some of the most salient observations on the avant-garde artistry of Stanley Kubrick/2001:A Space Odyssey I have read anywhere. It is a highly practical treatise, including tips such as how to develop mnemonics to remember shots, or how to balance the self-criticism of being a performer-director, or why you should leave an extra frame between a cut from an A to B camera.

Surprising to an outsider, but not surprising to those who know how much Lewis longed to be taken 'seriously' not much of the book is about comedy and there is a very simple reason for this - because the technical information is much the same irrespective of tone or genre. 

While Lewis avoids explicating a 'theory of comedy' he does have some salient observations such as "the snowball is always thrown at the top hat, not the battered fedora". It also introduced me to what has become a mantra for me

Who is doing what to whom?

Every time I write a scene, make an edit, direct someone I ask myself this question.

I would rate it above Vsevolod Pudovkin's The Film Technique especially for beginners. Pudovkin's book is still great, as Stanley Kubrick opined  in a 1969 interview with Joseph Gelmis 

“The most instructive book on film aesthetics I came across was Pudovkin’s Film Technique, which simply explained that editing was the aspect of film art form which was completely unique, and which separated it from all other art forms.”

I'm inclined to agree. In the book Pudovkin gives the example of a rally or parade down the street and describes all the different types of camera coverage that could be used to frame the events that take place within it. Pudovkin was also clearly a great observer of the innovations of storytelling that were happening in Hollywood at the time and internalized the way to produce a good climax.

Kubrick compares Pudovkin's book to the essays and in particular the book The Film Sense of his contemporary Sergei Eisenstein (the Battleship Potemkin) and I'm inclined to agree that the latter's work is much more opaque and preoccupied with a prescriptive use of juxtaposition to create a visual equivalent of Marxist Dialectic whereas Pudovkin's book I felt was much more Descriptivist and observational of technique.

That being said I found the most illuminating explanation of Eisenstein's theories wasn't the Film Sense at all but an essay found in Grierson on Documentary by John Grierson. Grierson was a propagandist for the British Empire, including Canada, and was instrumental in setting up the documentary industries. He manages to describe the importance rhythm in Eisenstein's theories with much more lucidity than any translator of Eisenstein ever has.

The go-to text book in most Film Schools is of course Michael Rabinger's Film Techniques and Aesthetics. When I studied documentary film my supervisor pointed us to Rabinger's other book "Directing the Documentary". While my memory is foggy I remember Directing the Documentary being a fine book on the topic, discussing many of the practical (and interpersonal) difficulties a documentary filmmaker may face.

I could name many other useful or practical books (especially Judith Weston's Directing Actors), but I've tried to restrict this comment to all-encompassing textbooks on the techniques and aesthetics and practicalities useful for film directors.

On Quantum Information I (Mark) recommend Quantum Computation and Quantum Information by Nielsen and Chuang. It is not the newest book but it is better written than many other newer introductory books on the topic. https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176

On Quantum Computation I recommend Quantum Computing Since Democritus by Scott Aaronson. https://www.amazon.com/Quantum-Computing-since-Democritus-Aaronson/dp/0521199565

A further note I want to add is that in maths and physics it is easy to read something and make yourself believe that you understood the concept when in fact you haven't. A good way to check for this bias that you can do on your own is to solve the problems in the book and check the solution afterwards.

Maybe not terribly relevant to LessWrong, and is not really a textbook per se, but considering that a lot of Yous are aspiring authors:

How to NOT write a novel by Mittelmark and Newman

What I also read: 

Writing a Novel in 30 days

Writing the Novel from Plot to Print

On Becoming a Novelist - Gardner, John

Why? HtNWaN condenses all the good advice similar books have into extremely memorable snippets that stay with you. It will not make you a great writer, but it prevents you from being a terrible one, by instilling in you certain useful "taboos" against typical bad writing pitfalls. Its less of a guide and more of a crude memetic tool to bludgeon your own imagination with until a readable novel emerges.

What astrophysics textbook would y'all suggest?

On storytelling (developing a movie script in particular).

John Truby, The Anatomy of Story. 22 Steps to Becoming a Master Storyteller

I haven't actually read other books on movie scripts, but I have read a number of comparision reviews  that overwhelmingly recommend this one. I have also read Joe Vitale's books, Springboard by Demming, a number of books on Seth Godin and Made to Stick and other books by Heath brothers. Truby's book excels as a textbook. He also taught tens of thousands of people.

About solid rocket engine principle: recommend Tang Jinlan's solid rocket engine principle (it's a Chinese book)

Subject: phonological theories
Recommendation: Routledge's Handbook on Phonological Theory
Strengthes: each chapter on an approach is written by a specialist in that approach, clearly explaining what the ideas are.
Alternatives: the relevant section of Kodzasov & Krivnova's "Obshchaya fonetika" (short and obscuring some very important points, as well as leaving out some approaches); Philip Carr's "Phonology" (somewhat outdated - 1993 - and makes that unpleasant trick with "this is our current theory... now let's look how it's wrong and adopt a better theory... and again... and again" - while this is akin to how scientific thought goes it doesn't necessarily do justice to the theories in question).

Does someone have a suggestion for an anthropology book?

Subject: History of Economics

Recommendation: Economics Evolving, by Agnar Sandmo

Reason: A superbly clear overview of the history of economics, from Adam Smith until the 1970s. Each chapter provides a guide to further reading. I found this book much better than the alternatives in the genre that I consulted, including Lionel Robbins' opinionated A History of Economic Thought and Joseph Schumpeter's chaotic History of Economic Analysis.

As a companion, I recommend Keynes' Essays in Biography, a collection of wonderfully written (and astonishingly well-researched) essays on some of the great English economists, including Malthus, Jevons, Edgeworth and Marshall.

Regarding the McAfee economics book, the link appears to have changed. I believe this link directs to the appropriate text

http://www.mcafee.cc/Introecon/IEA2007.pdf

Another attempt to do something like this thread: Viva la Books.

Does anyone know some good textbooks for animal anatomy and ecology? I haven't found any good ones so far...

I'd like some recommendations for precalculus textbooks. I'll be starting university in the fall and I'll taking calculus I honors, as well as other math courses. I'll likely be doing a math major. But I'm not confident in my knowledge/ability to do rigorous math, so am spending the summer reviewing past material. I'd like to make sure that I master the basics before moving on, so to speak. I already know a bit of calculus, and I know from that studying that two of my weaknesses are with logarithms and trigonometry,

For Introduction to Computational Fluid Dynamics, the book I would recommend is "Numerical Heat Transfer and Fluid Flow" by S. V. Patankar.

Most common Finite Volume codes used for incompressible flows are based on a method (SIMPLE) originally created/invented by the author, Patankar and this book has a from-the-horse's-mouth appeal and doesn't disappoint. The book is somewhat limited because everything builds up to explain the SIMPLE algorithm and the focus is narrow. However it does this very well. Another limitation is that it is short on worked out examples thought it does have end of the chapter problems. The other issue is that the last edition is from early 80s and so there is very little coverage of anything that has happened in this field since then, which is quite a lot. Still, the book is very good for what it does and quite short too.

Other books that address some of the shortcomings of Patankar's book are:

1A) "An introduction to computational fluid dynamics: The finite volume method" by HK Versteeg and W Malalasekera. This contains a lot of nice worked out examples that help explain the concepts well. I would happily recommend this book as a replacement for Patankar's book - it was a tossup. They keep adding more stuff to each edition though and you should get this book too.

2) "Computational Methods for Fluid Dynamics" by Joel Ferziger and Milovan Peric - this is an excellent book too. It is more of a general CFD book and covers much more of the subject that the first 2 books, though not with as much detail on any one subject. There are little or no worked out examples in this book.

3) One of the standard books for CFD is the book "Computational Fluid Mechanics and Heat Transfer" by Richard Pletcher , John C. Tannehill , Dale Anderson. It is a classic.

4) Numerical Methods for Internal and External Flows by C Hirsch is quite comprehensive too.

Would love to hear from others on what books they use, both from academics and people in the industry.

I'd like to request a book on Mathematical Economics that teaches you the basics of building and solving utility based microeconomic models (without strategic behavior).

Can anyone think of a good textbook on research in nursing? The one I have is abysmal and I literally cannot read it, thus I have a C in the class. Something in English might help. (I'm taking the class in French and although I'm almost equally fluent in both, I do find it harder work to read in French.)

Any recommendations for a textbook on cryptography?

I haven't had much success with textbooks. I have found them to be mostly boring and riddled with errors. I interpret boredom to mean that I'm not learning anything.

Here's a possible explanation for the boringness. Are you familiar with the experience of not being able to understand how you didn't get something, right after you've got it? The same presumably applies in the minds of professors.

It's hard for them to imagine not understanding the ideas. One can't know what the reader knows and doesn't know and what his misconceptions are. Teaching generations of students helps, but not much, and it won't help at all with tacit knowledge communicated face-to-face, but not via text.

Incidentally, that's probably why textbooks are so full of mistakes: not only do they contain arcane symbols which cause typos, but, being boring, nobody reads them anyway and the errors remain uncorrected.

The solution I think is to make two texts: one main text, which can be edited online to fix errors, and accompanying notes written by readers, with links to better material wherever possible.

Subjects: algorithms, computation, physics, Bayesian probability, programming

Introduction to Algorithms (Cormen, Rivest) is good enough that I read it completely in college. The exercises are nice (they're reasonably challenging and build up to useful little results I've recalled over my programming career). I think it's fine for self-study; I prefer it to the undergrad intro level or language-specific books. Obviously the interesting part about an algorithm is not the Java/Python/whatever language rendering of it. I also prefer it to Knuth's tomes (which I gave up on finishing - not enough fun). Knuth invents problems so he can solve them. He explains too much minutia. But his exercises are varied and difficult. If you like very hard puzzles, it's a good place to look.

Introduction to Automata Theory, Languages, and Computation (Hopcroft+Ullman) was also good enough for me to read. I've referred to it many times since. However, it's apparently not well-liked by others; maybe because it's too dense for them? I haven't read any other textbooks in the area.

The Feynman Lectures on Physics are also fun to read. But I doubt someone could use them as an intro course on their own. Because they're filled with entertaining tidbits, I was tempted to read through them without actually following the math 100%. Obviously this somewhat defeats the purpose. That's always a danger with well written technical material consumed for pleasure. I had already taken a few physics courses before I read Feynman; his lectures were better than the course textbooks (which I already forgot).

I didn't care for Jaynes. I only read about 700 pages, though. I remember there was some group reading effort that stopped showing up on the site after just a few chapters :)

For plain old programming, I've read quite a few books, and really liked The Practice of Programming - it was too short. I read Dijkstra's a discipline of programming and loved it for its idea to define program semantics precisely and to prove your code correct (nobody really practices this; it's too slow and hard compared to "debugging"), but it's probably not worth the price - I used a library.

I also agree with rwallace's recommendations also, except that the AI text is not especially useful (not that I know of a better one). I would not give SICP to a novice, though. Although I had done everything described in the book before (and already knew lisp), it did increase my appreciation of using closures and higher order functions as an alternative for the usual imperative/OO stuff. It also covers interpretation and compilation quite well (skipping the character-sequence parsing part - this is lisp, after all).

Macroeconomics: Olivier Blanchards Macroeconomics is a concise, yet in-depth tour of standard macroeconomic theory. I recommend it as a starting point for studying topics such as monetary policy and international trade.

Subject: Introductory Real (Mathematical) Analysis:

Recommendation: Real Mathematical Analysis by Charles Pugh

The three introductory Analysis books I've read cover

Okay, I'm going to take your word for it! So I just got The Great Conversation, Sixth Edition in the mail and it looks very good. But if I want to know more about Gottlob Frege or the philosophy of language or analysis, and I'm a layperson who needs something accessible, where should I go for that? Should I just get Meaning and Argument?

There's a brand new edition of Meaning and Argument. I'm gonna get it.

I do not have the expertise to review all the books, but this is a reddit/r/compsci produced list canonical introductory textbooks covering the major branches of computer science.

link

I should mention that on "machine ethics", "Moral Machines" is not exactly a textbook but it is currently the best source for a view of the entire field. I do not have other books to compare it to because at the moment they do not exist.

CORRECTION: The Andersons' Machine Ethics has been released, so I'll review that and update this.

What a wondrous idea! And, the contributions to date are outstanding. Thank you!

(This title already mentioned, but not as a top-level comment) For general Artificial Intelligence, Artificial Intelligence a Modern Approach by Russell and Norvig. It's very broad but still deep enough to get a feel for a lot of areas, with some advantages of scale due to certain exmples and consistent notation being used across many areas. It's also a much easier read than Bishop's ML book already mentioned for Machine Learning stuff, though Bishop's book is much more specialized.

To get an idea of the difference in scope AIMA covers planning algorithms, NLP, decision theory and even FAI (though pretty much by mention only).

Added the recommendations by Davidmanheim and Alex_Altair.

I'd personally appreciate a rule-following recommendation on A.I.

On Linear Algebra:

I was immensely impressed by the original ideas I hadn't seen elsewhere in the following books at the library. After my skim reading I'm gonna go back to borrow them and recommend them to ya'll. The marketing books are exceptions - the titles just look compelling, didn't flick through them. Hope I get time to get round to finding them again.

why it sells by 'danesh', critical marketing,

quantiative methods in marketing,

data driven business models,

aesthetics in marketing,

controversy in marketing theory.

Too lazy to get the links for the rest. They are: psychology of marketing, values in organizations emerging perspectives

economics

against utility based economics, first principles in economics, rationality in economics, why economics is not yet a science, the economics anti-textbook and the philosophy of the australian liberal party.

Wlll these be a waste of time? I doubt they're all the best in their niches or that those niches are important.

Subject: Economics

Recommendation: Introduction to Economic Analysis (www.introecon.com)

This is a very readable (and free) microecon book, and I recommend it for clarity and concision, analyzing interesting issues, and generally taking a more sophisticated approach - you know, when someone further ahead of you treats you as an intelligent but uninformed equal. It could easily carry someone through 75% of a typical bachelor's in economics. I've also read Case & Fair and Mankiw, which were fine but stolid, uninspiring texts.

I'd also recommend Wilkinson's An Introduction to Behavioral Economics as being quite lucid. Unfortunately it is the only textbook out on behavioral econ as of last year, so I can't say it's better than others.

Since different people have different tastes and different needs, I doubt that there is a best textbook on any subject. As for 'every subject', what can that possibly means?

Subject: Metallurgy

Recommendation: Mechanical Metallurgy by George Dieter

I have not actually read this book myself, as I learned all the metallurgy I need through different methods. However, it appears to be a favorite among humans.

Unfortunately, it requires expenditure of a relatively high amount of USD to access in full. For those of you who (like me) can only access things on the internet or which cost little USD, you can go try here.

EDIT: Those who are voting this post down are bad humans. I'm just trying to help you learn metallurgy and provide both quality and free methods for doing so.