Ask HN: Best Mathematics book for complete noobie?

"An Introduction to Mathematical Reasoning" by Peter J Eccels. Teaches the vocabulary of mathematics, just the basics you need to think like a mathematician, not a mathematics user like most science texts.

"How To Solve It" George Polya. Heurists and problem solving skills, by a great mathematician.

Do a google search, specially in the sci.math newsgroup. Again, read books by mathematicians for mathematicians; they're often far more enjoyable and actually far more straightforward (I was often confused by the examples in my school work; I didn't care for "vehicle moving at speed X" or "object falling at from height Y". We all have a different internal visual mind and I tended to think in abstract patterns, usually colors, lines or nested bodies, without real physical objects distracting me.)

I heartily endorse reading the classic works of geometry as a way to both the subject as well as a way of thinking about math, proof, and argumentation.

Start with Euclid's _Elements_, and then move onto Archimedes' short books on levers and floating bodies, Apollonius's wonderful treatise on conic sections, and Ptolemy's _Almagest_.

They are excellent for self-education, providing both geometrical knowledge in itself, as well as extensive training in sound reasoning. Don't be fooled by the antiquity of their origin: they teach more clearly than most modern day texts, and their content is timeless.

What kind of math do you want to learn?

There's a lot of great resources out there, but you need to be more specific.

For example: I really enjoyed Gilbert Strang's course on Linear Algebra, available as a series of video lectures on MIT OCW (http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Cours...).

If you are interested in Discrete mathematics, Knuth's "Concrete Mathematics" is a great book--but it might not count as "basic" enough for your purposes, depending on your background.

If by "basics" you mean "the stuff you should have learned in high school or as an undergrad", the Standard Deviants videos are fun: http://www.sdlearn.com/default.asp

I know this doesn't answer your question since you asked about math in general, but in case anyone ever starts a "Best Physics books for complete noobie?" thread I'd like to go ahead and suggest Brian Greene's "Fabric of the Cosmos": http://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp...

I'm in the similar situation as you (OP). My high school education was interrupted quite badly and 13 years after graduating I lack confidence in my comp sci endeavors because my maths sucks so bad. I'd be interested to hear of any hackers who have missed education milestones (like high school maths) but gone and successfully filled in the gaps. The reason I'm asking is because I'm kind feeling that things like maths knowledge is layered on year after year and if you lack the foundation its really a huge amount of work to repair each successive layer.

Passing on some wisdoms to the young hackers around here... I wish someone had grabbed me by the face in highschool and told how important all these layers of skills/knowledge would be for getting the kind of jobs I want now. <I come from a blue collar background - by the time I realised how important education was (age 22) it was too late to do much about it>

I find the Khan Academy videos to be pretty helpful. They start with the absolute basics and go on up. http://www.khanacademy.org/

Have you seen this thread?

http://news.ycombinator.com/item?id=665029

I haven't picked it up yet, but I remember reading about "The Princeton Companion to Mathematics" on here a while ago. It looks like a pretty complete guide to all of modern mathematics and sounded like it was easy enough for a beginner to get through while still being able to teach math experts some new things.

Thanks for reminding me about it - I think I'm going to order my self a copy!

"Naive Set Theory" by Paul R. Halmos.

Here is some general advice.

First have some kind of goal. Do you want to be able to determine the orbit of an planet, evaluate the complexity of algorithms and computing models, study human interactions as walks on graphs, or use statistics to model and predict complex systems. Decide on this first, don't wonder around mathematics aimlessly.

Secondly, work the books. Maths can not be learned by observation, and reading proof after proof is simply observation. Memorize proofs, work from your current point back to first principles, and do all the problems you can. Of course there will be times when you simply can not find a means to start on a problem, and at that time find help or try and come back to the problem later.

"What is Mathematics" by Courant and Robbins is quite good and respected, but it will challenge you: http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-... It may be more advanced then what you're looking for though.

I've had pretty good luck using the MAA recommendations list for libraries: http://mathdl.maa.org/mathDL/19/?pa=content&sa=viewDocum...

I recommend reading Theodore Gray and Jerry Glynn's Brain Rot article for some ideas on what math skills are worth intensive study and development and which are less important: http://www.theodoregray.com/BrainRot/

There are several articles and blog postings on the topic of math self study that I found interesting and you might find useful in determining what and how to study: Developing your intuition for math: http://betterexplained.com/articles/developing-your-intuitio... Math every day (Steve Yegge): http://steve.yegge.googlepages.com/math-every-day Math for programmers (Steve Yegge): http://steve-yegge.blogspot.com/2006/03/math-for-programmers... How to read mathematics (Shai Simonson and Fernando Gouvea):http://web.stonehill.edu/compsci/History_Math/math-read.htm

If you go back and learn Algebra, Trig, Geometry, then I fully recommend the Cliffs Study Solver series of textbooks because they are very cheap and very thorough plus each day you do a chapter, you'll make cumulative progress.

You are introduced to a concept, given a set of practice problems to see the concept in action, then given a problem set to solve on your own.

http://www.amazon.com/Algebra-I-Cliffs-Study-Solver/dp/07645...

Each book is about 350 pages and you'll be up to speed in no time.

I came back to doing maths after a gap of over a decade. I found the student survival guide very clear and useful. I imagine it would be excellent to someone who is not good at maths.

I read the guide every evening while I was cooking (its not a difficult read) and my maths improved greatly.

http://www.netcomuk.co.uk/~jenolive/ http://www.amazon.com/Maths-Students-Survival-Self-Help-Engi...

That's depends on what you want to learn and for why, well, some people want to understand the formalism of a theory, as theoretical computer science or theoretical physics where others are only interested in applications, so I will take a generalist approach in the topics, yes topics not books, that I will advise you to learn. Unless the book is awful (and there are many out there that are) it will makes no difference which book you pick, you generally will not "read" a math book, the only case in which you will is when it's a book for divulgation (as Polya's "How To Solve It"). For me the basics is: Statistics (Descriptive and some Probability), Calculus, the idea of Limits, Derivatives and Integrals (for Multiple Variables) and applications, Linear Algebra and also some Applications (there are many), numerical Linear Algebra is totally necessary if you want to apply it in the real world, a basics in Differential Equations, some Numerical Analysis.

If you want to learn things closer to computer science then learn something of Number Theory, some Enumerative Combinatorics and Graph Theory as well. The list is extensive because I come from a mathematical background. If you learn at least a bit of these topics them the next step will be apparent for you.

Honestly I think Schaum's is pretty good because it does a bit of explanation, but you primarily learn through doing two dozen pages of problems per chapter.

Some years ago I took the same approach to start again from ground zero. I found Polya to be good, but a Mathematician's Delight is better and more accessible: http://www.amazon.co.uk/gp/product/0486462404?ie=UTF8&ta...

If you want to DO math, nothing beats working through a decent textbook. I have worked through several since I'm approaching 50 and don't use math enough to keep my skills up (and like any skill, you have to keep practicing to stay decently competent in math). The best Precalculus textbook I have used is Swokowski's "Algebra and Trigonometry with Analytic Geometry" which is clear, concise, and has lots of problems.

If you want to learn ABOUT math, Davis and Hersch's "The Mathematical Experience" is a fairly easy read about philosophy of math, how it is used, and a bit about studying math.

Eric Temple Bell's "Mathematics: Queen and Servant of Science" is a bit dated but an excellent history of math for someone interested in learning to do advanced math; the author's a bit biased towards algebra over analysis, number theory, and geometry, but not excessively so. Its biggest lack is only one short chapter on probability and statistics. This is not a particularly easy read since it covers things in some depth, but I think it is worth the effort.

For proof based mathematics, I found "How to Prove It:A Structured Approach" helpful.

I'm pretty at Mathematics and doing that takes a lot of work. And the Mathematics books for noobs are no good.

The better approach is to get a theoretical book, something like Spivak's Calculus or Linear Algebra by Friedberg, Insel and Spence. And then from there whenever you have difficulty with the material spread out laterally and you really start to gradually grow an understanding of mathematics.

And then perhaps, one day you'll be up for Spivak's Calculus on Manifolds!

The World of Mathematics edited by James Newman (a four-volume anthology) may give you a feel for and an interest in exploring math further. It's a great collection ranging from mathematical curiousities and puzzles to memoirs of mathematicians to a very moving short story by Aldous Huxley.

Also, One, Two, Three, Infinity by George Gamow (a great physicist) is a great intro.

Second the How To Solve It recommendations.

If you have some decent background in reasoning and logic, I would suggest Linear Algebra Done Right by Sheldon Axler. It provides a general introduction in mathematical reasoning as well as providing a strong framework for maths needed in many fields.

http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/...

For a "popular" treatment of mathematics that does go into some mathematical detail "Journey through Genius: The Great Theorems of Mathematics" by William Dunham is difficult to beat. It is by far one of the best "Math" books I have read that have kept me coming back to it. Also, try some of the books by John Derbyshire along similar lines.

I second the OCW reference. Some of the Calculus for Dummies, type books are good. Its good to remember that Calculus and Linear Algebra don't have to be that complicated. I also recommend scan the books before you buy them, I wasted far too much money at college on txtbooks that I ended up despising

It's not strictly math, and I can't recommend it from experience, but I've always been curious what a beginner's reaction to _Structure and Interpretation of Classical Mechanics_ might be. It's free here:

http://mitpress.mit.edu/SICM/book.html

"Scientific Notation and Other First Principles: Comprehensive Mathematics for Lawyers and Politicians," by Jacob Herwitz. Penguin, 1992.

Great introductory text which starts from algebraic first principles and goes through pretty much everything up until differential equations. Very thorough.

I think Kreyszig's Advanced Engineering Mathematics is an excellent text in applied math.

I'm not sure where you're at or what direction you want to study, but once you're familiar with calculus concepts this text is a good place to go to deal with ODE and analysis.

Concepts of Modern Mathematics

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

There are a few math books in the "Head First" series (which I always love). Those might serve more as refreshers for most people, but for a true math noob (like me), they have really helped.

'Zero: The Biography of a Dangerous Idea' by Charles Seif