Hacker News new | past | comments | ask | show | jobs | submit login
Ask HN: Do you read math & hard science books? How?
68 points by zkz on June 20, 2009 | hide | past | favorite | 56 comments
Do you buy and read math books? do you read them cover to cover or do you just use them as a reference book?

I typically buy a lot of math and physics, hard cs books, etc., but they take a lot of time to read so I end up collecting them, while reading them slowly (because hard science books could take months to read, at least if you don't have a lot of time for that!). Is that a typical hacker thing or is it just me?

I'm asking because I keep buying books about stuff I want to learn, but I also look at my library and I ask myself: "why don't I read these first?" Who knows, maybe today I want to learn something different than yesterday.

I was a theoretical physicist for 13 years, and struggled a lot with this question. I found it very useful to develop several different styles for reading mathematics and physics. Mostly I did this in the context of reading papers, not books, but the comments below are easily adapted to books.

One unusual but very useful style was to set a goal like reading 15 papers in 3 hours. I use the term "reading" here in an unusual way. Of course, I don't mean understanding everything in the papers. Instead, I'd do something like this: for each paper, I had 12 minutes to read it. The goal was to produce a 3-point written LaTeX summary of the most important material I could extract: usually questions, open problems, results, new techniques, or connections I hadn't seen previously. When time was up, it was onto the next paper. A week later, I'd make a revision pass over the material, typically it would take an hour or so.

I found this a great way of rapidly getting an overview of a field, understanding what was important, what was not, what the interesting questions were, and so on. In particular, it really helped identify the most important papers, for a deeper read.

For deeper reads of important papers or sections of books I would take days, weeks or months. Giving lectures about the material and writing LaTeX lecture notes helped a lot.

Other ideas I found useful:

- Often, when struggling with a book or paper, it's not you that's the problem, it's the author. Finding another source can quickly clear stuff up.

- The more you make this a social activity, the better off you'll be. I organize lecture courses, write notes, blog the notes, and so on. E.g. http://michaelnielsen.org/blog/?p=252 (on Yang-Mills theories) and http://michaelnielsen.org/blog/?page_id=503 (links to some of my notes on distributed computing).

- On being stuck: if you feel like you're learning things, keep doing whatever you're doing, but if you feel stuck, try another approach. Early on, I'd sometimes get stuck on a book or a paper for a week. It was only later that I realized that I mostly got stuck when either (a) it was an insubstantive point; or (b) the book was badly written; or (c) I was reading something written at the wrong level for me. In any case, remaining stuck was rarely the right thing to do.

- Have a go at proving theorems / solving problems yourself, before reading the solution. You'll learn a lot more.

- Most material isn't worth spending a lot of time on. It's better to spend an hour each seriously reviewing 10 quantum texts, and finding one that's good, and will repay hundreds of hours of study, than it is to spend 10 hours ploughing through the first quantum text that looks okay when you browse through it in the library. Understanding mathematics deeply takes a lot of time. That means effort spent in identifying high quality material is often repaid far more than with (say) a novel or lighter non-fiction.

Agree with Michael's points. My strategy: Buy problem books instead of text books!

- I KNOW I won't be able to finish them. That means it's OK not to, so I don't feel bad - but also that I shouldn't buy too many.

- The material within is bite-sized. Early problems teach you what you need for later ones, and you can always stop and come back later.

- Constant feedback is rewarding. Also, some say you only understand what you create for yourself.

- If I'm not advancing at all in a problem book, then I find open books on the internet, or (better!) I buy the Dover Publications paperback of the book by a master/inventor of the field, usually for $7 or so.

Here's my list of distributed papers, I think you're missing quite a few good ones:


But, more importantly, I'm curious about the 15/3-routine. How often do you do this? Recently I subscribed to the arxiv RSS (astro-ph.co, gr-qc), there's lots of papers uploaded daily, but most don't look very interesting, so 15 interesting ones would be ~1 weeks worth for me.

That's an interesting list on distributed computing, thanks.

As regards how often I do this: I go through periods where I do it a lot (sometimes several times in a week), and then months where I don't do it at all. I do it thematically (i.e., with closely related papers), so I've never tried doing something like what you suggest with the arXiv's recent papers. They're usually not all that closely connected.

I approach this in the same pattern. There are some technological tricks that have recently made it much easier, though.

In addition to Arxiv and preprints I can find online, there's Google Scholar and Amazon Previews (I'm still missing many journal articles, especially in engineering, due to a lack of university access, luckily they're often compiled in journals on Amazon). By flipping through Amazon's book previews using the search feature, I can read an arbitrary number of pages in any given book, and the world's library is at my lap. I can then 'photocopy' the relevant/interesting sections using ctrl-shift-command-4 on my Mac, and paste them into my Evernote. In this way I can locate and collate a large number of papers and texts, and organize them along the way without even dipping into LaTeX. After that, I can past those copies into Mathematica, which has a very workable equation typesetter, with the additional advantage of the equations being computable.

Lately I make a lot of use of Evernote, however, which I can pretty much paste anything into, and I can 'photocopy' any part of a text on the computer by using ctrl-shift-command-4 on my Mac.

I think that especially with the Internet not bounding paper lengths any longer, authors should write more comprehensive versions of their papers (or at least include an appendix).

In most cases, the succintness of the papers is what makes them difficult to read, both in terms of skipping steps in proofs and in terms of hidden assumptions of the reader's knowledge.

Psyklic, our UW QSE group felt the same way, and to remedy these problems we wrote a 96-page "Practical Recipes" article on quantum simulation, which appeared this month in the (open source) New Journal of Physics.

This length permitted our QSE Group to explain practical methods for quantum system engineering at a mathematical level that was well-matched to our quantum system engineering students.

On the other hand, the peer review of articles of this length is a lot of extra work for all concerned---reviewers, editors, and authors ... to say nothing of the effort demanded of the readers.

If they don't take a good bit of time to read, then you're not doing it right. These are books full of tools for the mind. The best way to read them is a little at a time, taking the parts that click in your mind and trying them out on problems that seemed insurmountable before. The first time you open a big box of strange tools, it won't be immediately apparent to you what they are all for.

Finding a good math book is like stumbling into that room full of all of the weapons on your first time through Doom...

Yeah, this is exactly right. To a decent approximation, I spent college and grad school just basically plowing through math and physics texts. In eight or so years, with extensive help from the faculty of two universities, I grew to understand the contents of several dozen thick hard science and math books, and for my efforts they gave me two degrees.

Since quitting school I've dragged myself through a small pile of classic CS texts, and have learned a ton (and, as a side effect, become nicely employable as a programmer). It is insanely hard (and rewarding) work. If it's hard, then you're learning something; keep it up!

> If they don't take a good bit of time to read, then you're not doing it right.

Thanks, I needed to know this. I was starting to feel silly, thinking "maybe I don't understand them quick enough, people must read them faster or something".

Yup. Hard science books take a long time to digest. But the trick to keep at it is to keep a self check: is this something you're really interested in learning? Perhaps you'll find out within a few chapters that it's not worth it. And that's ok.

In my student days, before I became a working programmer, I was desperately poor and couldn't afford all the books I wanted to buy. So I got into the habit of buying books when I had money in my account to avoid a future in which I have to look longingly at a book and not have money to buy it. So, yes your "buying a book and reading a few years later" situation is something i am familiar with.

So anyways, I ended up having a few hundred technical books (and a couple of thousand non technical books). The future of not having money to buy books never came (yet, touch wood) and the biggest advantage of having this huge collection of books is I can cross reference them to get better info on what I am looking for. On the other hand, moving is a huge pain :-)

EDIT:(example of buying a book and then using it years later) I am now (slowly) working through Cormen et al's "Introdcution to Algorithms" (second edition) book. The idea is to do all the exercises and proofs and so on. Should be done by the end of the year I think.I bought this book a few years ago and am using it(seriously) only now. (There's a third edition out now for anyone planning to buy. second ed is good enough for my purposes)

Ah, maybe that's why. When a child I was desperate for books, it was hard for me to get those (I had books, but I read them a lot faster than I could get them, I was always re-reading them). So I guess when I started having money I just started buying them, like in a rush, to compensate or something. I should realize it makes no sense anymore. Thank you.

Oh no! There's a third edition out now? I haven't cracked the 2nd yet!

EDIT: Ok, the 3rd won't be out 'til Sept.

From the book's web page: "The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrence (now called "Divide-and-Conquer"). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition."

I studied computer science using Cormen et al., and it struck me that this might be one way to 'use' these oft-impenetrable tomes. (Though I really found Cormen very accessible.)

Look around for a university course that teaches using the book, and see if you can find notes, or - better - problems based on the text. Often gives you a sense of where to begin with the larger books.

You can get podcasts based on this book, from the MIT's itunes page; MIT 6.046J introduction to algorithms.

Its not quite as good as seeing it on the page but it might help if your out for a walk or in the car.

The problem with math books. Succinctness. There you have it. This is the single most annoying problem with succinctness. When you go over a line of text sometimes it is justified to spend 3 hours with it. But sometimes its not, its just something that you are not seeing. The thing with math books is you cant tell if it needs 3 hours or 2 minutes because all the lines look the same and the succinct ones kinda jump at you without warning. Succinctness is Power, but if you are facing a powerful person in combat you wont be singing the glories of origins of your foes power.

The way I go about these books is to work the theorems myself. It will take a loooong time to get through the first few chapters because that is where you are getting oriented towards that kind of thinking. The second chapter is usually the hardest! Stick with it. Do not try to calculate how long it is going to take to complete this book at this rate. Because the thing gets faster as you read it. Some kinda exponential function at work, the more you read the faster you can read since you have an intuition for the succinct parts and you can sense them from far. Many times you don't have to complete the book since the later chapters are on a need to know basis and the fundamentals are covered in the first half of the book. Also the thing gets faster once you cross the second chapter since you know the language now.

Why you should work the theorems yourself: When you read them you feel like you know them, but this is a bias. ( I use that word as an umbrella term to refer to all unintentional consequences of the way our mind works ). Once you try to reconstruct the theorem, that is when you get to understand all the gaps, holes and whole craters in your knowledge with such clarity.

Clearly knowing what you don't know is the last but one step before you know it. This is like finding the exact line in which the bug occurs, 95% of the times when I have done this the fix is immediately obvious to me. The remaining 5% of the times the bug is a consequence of the architecture (fondly referred to as a feature). To think of a parallel to this in learning: these are the times when you feel an Ah ha moment where whole areas of darkness come to light.

You need a guru by all means to guide you. Not all the information about the difficulty of a topic is captured by a book. You wont understand the consequences of a particular way of thinking unless you have spent a few years doing it wrong. So find a person who has been down that path to guide you. Also a buddy group makes the whole experience much more manageable and fun.

I'm surprised that nobody has made online math books where you can click on a succinct line of clever math and expand it, in place, to the two-page explanation.

Are you? Care to explain why you are suprized ?

I think its because the web is a such a big and diverse place, that he assumes any idea that sounds good and is describable in one sentence is already implemented.

It's kind of like Rule 34, but not just for porn.

Well, I think such a book would be useful, and strikes me as a pretty obvious idea, with plenty of analogies in related areas (ie. zoomable user interfaces; code folding).

Currently, if you are reading math and hit something you don't understand, you can refer to other references (which may not use the same notation or approach things in quite the same way), and/or try to work out the details yourself, or get help from someone else. Working through yourself and looking at other sources certainly helps one learn, but can be very inefficient, and there can be a high energy barrier to success.

A 'zoomable' math text would require a lot of work to create, but the writing could be done collaboratively (or even partly automatically). There is some software to be written to implement this idea, but given the large number of computer and other scientists who depend on learning and using math, it is surprising to me that there hasn't been more experimentation with different ways to present it.

I guess I should try to write it...

For what it's worth, we've already got wikipedia which does math pretty well. Even though it doesn't have the fancy-sounding zoomable user interface (which imho suck w.r.t. usability), it does offer plain old, get this, hypertext, which allows you to perform further exploration.

As for your idea, I don't want to minimalize it [because well, with ideas, you never know for sure which ones are good and which ones are bad (w.r.t. how successful they are) until after they are deployed], but it seems to me it would be a lot of work, with an end-result that might be totally crap usability-wise, and of limited interest to a large part of the population. Plus it would (for the moment) require a computer to read it. And computers suck as devices to read books on.

This is really interesting advice. I have spent a lot of time lately considering how I could become more effective at teaching myself math. The community aspect is fundamental to my success as a programmer, but that is something that I have not come across for math. Where would you suggest someone find peers and or mentors?

If you are a good programmer its very easy to become friends with math/phys/cs profs. They typically have many projects that they are not looking at at the moment for lack of programming power. Offer a few hours a week of your time to a particular project that you feel interested in. You will learn crazy lots. This is what a "Grad Student" is. But IMO this is much better than being a grad student and suffocating through the bureau-crazy.

This is how I got started programming professionally. During my freshman year, my CS prof had funding for a climate research project and he first set me up as a UNIX admin then a C and Perl programmer. In addition to learning UNIX and programming, it paid about 3 times as much as any other work study job, and I got to put "participated in NSF funded research" on my resume. I wasn't even a good programmer, I just wasn't as bad as everyone else.

Are you suggesting trading programming time for mentoring time, or just programming a math teacher's projects as a means to learn?

How would you initiate something like that anyway? I would feel more than a little awkward wandering on to a local campus and knocking on doors in the math dept. Are there any online resources/communities?

First Question: Both.

Second Question: Read online about the interests of a prof. Select a few. Watch a few of their introductory lectures to see if you like how they explain stuff. Select one. Look up the office hours. Wander into the room and state your mind.

there's a #math channel on irc.freenode

Basically, this is just a classic inventory control problem. If the inventory is piling up, you need to either decrease the rate of acquisition, increase the rate of consumption, or (preferably) both.

I can't say how typical the situation is, but it's definitely not just you. I have quite the stack of books on my "to read" list, but I keep working my way through them (and adding more to the pile.) So it goes.

I had this same inventory control problem with cookbooks. I solved it by making a rule for myself: No new cookbooks until I cook 30% of the recipes in all the ones I already have.

I have this same inventory control problem with computer science books. Good textbooks are expensive. If you implement a utilization rule like this, you can save yourself a lot of money on books you never end up reading. B&N, Borders and their ilk have liberal return policies, as does Amazon. This will help save lots of money. Also, the utilization rule prevents you from disadvantageous conditioning. The retail pleasure of acquisition can drive you to buy books faster than your actual reading rate.

I have quite the stack of books on my "to read" list, but I keep working my way through them (and adding more to the pile.) So it goes.

I have the same phenomenon with Irish Trad tunes I want to learn. The list is ever growing. (There are at least 30,000 of those.) My solution? I only learn the tunes I fall in love with. Life is short, so why waste time with something that's just "nice?" I think I'm going to apply this to books and other contexts.

Buy older editions of textbooks and also the "Eastern Economy" (read: china/india printed on cheap paper) editions. You will save a pretty penny, and thermodynamics hasn't changed much since 1975.

(Obviously this won't work for machine learning.)

Where do you buy such kind of books? I can't find them in Ebay anymore. Probably it was not legal to export them.

International Editions have saved me a ton of money. I found out about this when I started seeing big C++ books (the really thick ones) around the lab with a big sticker on it that read "not for sale in the USA" (or similar). These are the same book, though usually a bit more cheaply made, but at sometimes 10-20% of the price.

That's what you think.

asks perpetual motion powered hovering maid to replicate another iced tea

Nice rules. I started to do something similar to your "only learn what you fall in love with". For some of the older books I bought once and I never read, now I know I will never read, because now I know better and I know they are garbage (or I know of better material now). So I won't waste my time reading those just to remove them from my todo list.

I guess I shouldn't have bought them either.

As I was pondering here: http://news.ycombinator.com/item?id=664383 : why do I keep working my way through them like some sort of automaton? "So it goes"? It doesn't have to go like that. You could buy one book and read it and then stop. How much am I really benefitting from reading and how much am I using it as an escapist excuse? Would I be a better person if I read 8 five-star books from Amazon than if I read 8 four-star books?

Is it really better to read a well reviewed book? Isn't a horrible book better for you in the same way that walking uphill is better for you than driving uphill?

Isn't a horrible book better for you in the same way that walking uphill is better for you than driving uphill?

I feel like your analogy would be more akin to learning theorems by deriving them from first principles as opposed to taking them as gospel.

It's the material that should be hard, not gleaning information out of the book.

Sometimes you just read about things you want to learn. At least that's the case of the books I talk about in this thread. For example, I'm driven by the curiosity to understand how some theories of physics work, particularly relativity and quantum theory. I've learned some extremely basic stuff about them, and I want to learn more, and more, and the more I learn, the harder it gets (it needs more mathematical tools, etc.).

Maybe a key is to read books that drive you towards a goal? I can understand your feeling, and I really appreciated your thread when it appeared in hn. But in my case the problem is different: I want to know a lot of things, and learning all of that will take me years, and a symptom of that is that I end up collecting tons of books that I keep reading slowly.

Inventory is a buffer against scarcity. As there is generally no scarcity with books, perhaps one should keep no inventory?

I bought a Kindle b/c I don't have room for all my books. I recently had a child and his books already fill one of my bookshelves. So I've been cleaning out my physical books, only keeping those I really like. The Kindle DX might be the way to go for texts. So you get unlimited space (Amazon will keep your books online), access to all the classics for free (via gutenberg,etc) and your books are always with you (while you carry the device anyway).

Of all the things you can spend your money on, books are the best investment by far.

I tend to collect lots of books, usually at times when I'm not really reading much. However, I eventually (usually a matter of weeks or sometimes months) get back to reading and will crunch through endless amounts of books. I've managed to get through 500 page books in a day, every day for over two weeks before.

As for specifically science books, I tend to read them slower so I usually read a chapter or section of one and then read a chapter of a fiction novel. If I keep switching I find I can get through both quite quickly as reading the fiction novel will usually give enough motivation to read the non-fiction hard science book quickly too.

I often buy books and read some chapters that interest me. I get most out of such books months or even years later when I can appreciate their content better. It's good to know that I've the stuff at my hand, often there are explanations, algorithms, concepts in a depth one rarely finds on the net.

Textbooks are indispensable for really getting the material down, but I've found it much easier to read lectures.

Feynman has great examples of this type of work: "The Character of Physical Law" or "The Feynman Lectures on Computation" are both excellent. I've found that these books walk somewhere between textbook and popular science book. Easy to read but all the while teaching you the material.

I've found this type of work to be the crucial link between pop. science and a textbook. You learn enough that you can find your footing when you're in a textbook and and also the inspiration to actually read it.

Perhaps you just like the idea of reading all these books rather than the actual reading of them.

No, I really like reading them. But it's easy to buy them faster than reading them if reading them takes you so much time (for the hard science ones, not divulgation, fiction, etc.).

I have the same problem. I have TONS of Mathematics (mainly) and Physics books, but I've not really worked through most of them. I've spent a fortune on them so far. I always keep saying that I'll take a couple of years off to concentrate on nothing but hard science, but I know that will never happen.

I actually have a theory that good programmers are frustrated Mathematicians and Physicists who couldn't stomach the real thing and chose the easier way out.

Thanks HN, Many times a rhetorical question is answered in ways more than i can ask for. I have few attributes that I suspect are behind my depression. This being one of them. I have been doing the same- but unlike the OP and others, I get depressed that I bought a book and by not reading it completely, I didn't give its due. I take it very personally that I have Cormen's Algorithms and not gone past chapter1. It's like insulting the writers- i don't know if you get it. It's like you want to be the most passionate religious man on earth and the holy bible you really wanted to read and you know that is what you want is lying on the shelf, while you are trying to sort floating divs on a web page...and whenever i pick up a book, i will hit a block where it gets difficult to understand and because i am used to reading other books in a more casual way, i come to tell myself how dumb i am. i convince myself this to be true when i read about everyone i follow and all the books they have read...it's a vicious cycle that's been eating me inside out - in almost a literal sense.

...But many a times, I will just grab a book (anything - even non technical) and read it while sitting on the throne - read a few lines and ponder over it. my favorite is sicp - which i have not completed after having it well over a year. The few minutes of pondering is much more valuable compared to the regular day, when I am less patient and I want to do some "quick fix" things. I am so glad to find that I am not alone to read parts in between.

so @zkz, thank you for posting this question. The answers posted removed one more attribute which added to my depression. many more to overcome. what a day! I feel so relieved! - i would say this if I met you, so posted it here.

The throne method is surprisingly good! An ex-boyfriend of mine was a hacker (well.. most of them have been) and one of his peculiarities was to have a vast collection of academic and O'Reilly books next to the loo. Great for flicking through, though often one would end up spending far too much time in there...

Glad to know it helped you, thank you!

I read all the main theorems without even reading any of the definitions and examples for the first pass while at the same time I write down any questions I have with a reference to the theorem it pertains. For my second pass I go back and look at the examples to see if they answer any of the questions I wrote down and write down more questions referencing the examples. For the first two passes I don't try to answer any questions. I simply try to engage the material. Finally I try to answer all the unanswered questions and work some of the exercises and write down more questions if there are any left.

It takes me a while to read the books I have as well. I've bought lots of books than I haven't been able to read yet and my list of books to buy and read keeps growing as well. Another thing that adds to the amount of time it takes me to read a book is that I'm a very meticulous reader. I like looking up and cross referencing anything I don't understand, so for me that means looking up lots of stuff. I wonder if other people do this as well.

I used to buy math and science books all the time. I probably read 25% of the books I bought. I quit buying books in general after I moved. Moving 500 books sucks.

Now I only buy math and science books if I actually plan to work through them. I usually try to do the problems first and only go back to the writing if I can't figure the problems out. Other books for leisure reading, I just get them at the library.

Yeah, I have a wide variety of very interesting books collecting dust on my shelves. I don't know why really, I think maybe I spent my time in graduate school immersed in theory and these last few years I have been completely focused on understanding how that theory relates to practice. Maybe the pendulum will swing the other way again once I have more free time.

My parents are in academia & they've each amassed a huge collection of books. I learned very early on that I should be collecting digital books instead.

Definitely best to sift through them slowly, get the most out of them. No use hammering through a good book then taking nothing from it at the end.

I would try to take them cover-to-cover and then use them as reference. Also, perhaps, if you really wanted to learn the material, you would simply check them out of the library. There's been an article posted on the frontpage recently about how verbalizing a goal makes it less likely to be actualized: I think a parallel occurs with buying books (I experience the same phenomenon).

Get'em from the library, yo.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact