What's a good way to relearn college math on my own?

January 17, 2005 5:43 PM

Help set my feet on the road to math geekery [+].

Self-education is a passion of mine. For some time now I've been aware that mathematics is a major gap in my knowledge: All I retain from grammar school is some basic algebra and trigonometry. I've lost quadratics and definitely lost calculus. I'd like to address my ignorance and set a long-term goal of getting to a level of ability that where I have mastered secondary school maths and can look to studying the university-level mysteries.

I have no wish to enrol in a class, or hire a private tutor; I'm picky about having control of my personal time and who I see. I would much prefer to study from books or self-paced teaching packages. Any suggestions as to what books or software might be helpful?

posted by Ritchie to Education (22 answers total)

This is a good search engine for finding math books.
posted by mlis at 5:50 PM on January 17, 2005

What Is Mathematics?: An Elementary Approach to Ideas and Methods.
posted by Gyan at 5:53 PM on January 17, 2005

No specific books or software to recommend, but a suggestion as to technique: practice, practice, practice. Do as many problems as possible. Even if you understand the concepts, the mechanics of manipulating mathematical expressions won't become automatic for you without repeated drilling. For me, at least, having the basics down automatically makes reading and understanding more advanced texts much easier
posted by mr_roboto at 6:08 PM on January 17, 2005 [1 favorite]

You can find some great books at used book stores and at university book sales (my alum had them quarterly). Since the universities require new versions of the books so often, there are many "old revisions" for dirt cheap. Probably the most popular calculus book an academia is Stewart's.

I also recommend getting the matching 'answer guide' if you get any textbook - they come in handy if you get stuck. I picked up an "old" calculus book & the answer guide for 1$ each.
posted by escher at 6:44 PM on January 17, 2005

It depends how much you want to know and what level of awareness you want to touch. You can very easily master algebra, the fundamental aspects of calculus, some differential equations, and linear algebra on your own. Albiet, your knowledge won't be an exhaustive knowledge that might be demanded of you elsewhere. If it's for personal gain, it probably will suffice. That said, a big part of my amazement with math was watching hour long proofs. That wasn't something I could work through myself, or even understand the beauty of when it was displayed in a book. Math becomes (and is) a lot more beautiful than "learn the algorithm, apply the algorithm." It takes a focused immersion to start spinning it in your head.

In other words, if I was you I'd sneak into a big lecture hall for second semester calculus and see where it takes you.
posted by sled at 6:45 PM on January 17, 2005

I recommend sled's approach. Math can be a solitary pursuit but there is a lot to be gained from having a prof explain things. If you live near a large, good university, pick up a copy of the time schedules and find classes to sit in on. You can start with a pre-calc course and work your way up.

Or just wander to the bookstore and see what textbooks the students are using. I recommend Calculus by Spivak (hard but good) once you get there, although a more popular book with have more solutions sets to google (TA's post solutions online for classes at various universities, you can find these and sometimes lecture notes). Anyway most calc books have a review of pre-calculus in the front which will at least let you know what you need to relearn.

And don't limit yourself to the beaten path of calculus. Abstract Algebra, Graph Theory, and Topology can all be good fun and you can easily learn the basics yourself.

I also recommend the short topical books on math put out by dover. Only about ten bucks each on a variety of topics.
posted by mai at 7:55 PM on January 17, 2005

Good advice in this AskMe thread.

There is a series of books in a collection edited by the Mathematical Association of America called the New Mathematical Library. Many titles are available used on Amazon. They're written by professional mathematicians for curious but inexperienced people who are willing to put in a little time.
posted by stuart_s at 8:04 PM on January 17, 2005

MIT's OpenCourseWare project has placed all the raw coursework for its classes online here. The introductory calculus classes are 18.01 and 18.02. Differential Equations is 18.03.

The links include pdfs of each chapter from the required readings as well as lecture notes and problem sets.

OpenCourseWare discussion in the blue here.
posted by event at 8:15 PM on January 17, 2005

My friend Bruce has an online calculus tutorial which seems to be popular.
posted by greatgefilte at 8:20 PM on January 17, 2005

The most *popular* calc book may be Stewart's, but I firmly dislike it from a teacher's perspective. Larson & Holstetter's (sp?) is better.

I'll second the "practice" mantra.
posted by notsnot at 9:33 PM on January 17, 2005

I suggest you study Linear Algebra. Wicked-cool.
posted by five fresh fish at 9:43 PM on January 17, 2005

Along the lines of Linear Algebra, check out these videos from a great teacher:

Professor Strang's Linear Algebra Class Lecture Videos
posted by AmaAyeRrsOonN at 9:49 PM on January 17, 2005 [2 favorites]

Linear Algebra meets Dynamic Systems in Hirch and Smale's great book "Differential Equations, Dynamical Systems, and Linear Algebra". It's a great book, taking you from calculus up through some really nice systems theory and great ways of looking at interdisciplinary math many of us wish we got much earlier.
posted by freebird at 11:35 PM on January 17, 2005

Math in the real world (ie physics, engineering, etc) is entirely impromptu -- one merely needs to know what is out there. Competence in any particular mathematical branch is only necessary when you want to publish... (And picking up a math or two is trivial.)
posted by theatrical matriarch at 11:57 PM on January 17, 2005

Third for "practice". Maths is a conceptual language. You can't learn it by listening (reading) alone.

Math in the real world (ie physics, engineering, etc) is entirely impromptu -- one merely needs to know what is out there.

I can think of several Professional Mechanical, Electrical and Nuclear engineers I've worked with who might debate that with you. Stress Analysis springs to mind as just one discipline where none of us need the pros to be 'impromptu' about the calculus in their modeling.
posted by normy at 1:53 AM on January 18, 2005

Math in the real world (ie physics, engineering, etc) is entirely impromptu -- one merely needs to know what is out there.

What normy said. I'm sure string theorists wrestling with the complexities of Calabi-Yau manifolds and n-categories will be rather pleased to learn they can cease with their efforts.
posted by Goedel at 5:50 AM on January 18, 2005

Hm, in my experience people who sit down to "learn maths" end up doing about as well as people who sit down to "learn computers" — ie, usually not at all, unless they have some more specific goal in mind.

My recommendation? Pick up Martin Gardner's The Armchair Universe (or something similar), get interested in some of the problems, and then pick up a textbook on linear algebra, or calculus, or complex analysis, and pick out the bits you need to know to work on the interesting problems. (And learning one bit will maybe make you interested in something nearby, and you can just follow your nose.)

You might also enjoy something like Dover's USSR Olympiad Problem Book, which has oodles of interesting problems, with solutions... and when you don't understand the solution it's time to hit a textbook and learn about the necessary bits.

Get a copy of Gyorgy Polya's How To Solve It, too.

(I was totally driven by wanting to make cool computer graphics, so I gobbled up stuff about parametric curves and vectors and cross products and dot products and partial derivatives and so on. Taken on their own? Mostly pretty boring stuff. But when they make something else go, it's awesome & addictive.)

It depends on personality, I'm sure, but consider a non-linear approach, instead of just sitting down with a text and going chapter 1 - problems 1 - chapter 2 - problems 2 - etc.
posted by Wolfdog at 6:43 AM on January 18, 2005 [2 favorites]

Here's a long list of free on-line match books.
posted by Zed_Lopez at 11:15 AM on January 18, 2005

After you get the hang of calculus, and before you move on to more advanced maths, you should take a look at Apostol's Calculus (or Spivak, which someone mentioned before).

Based on my experience, having a solid calculus background is extremely helpful in understanding the more advanced stuff like differential equations, analysis, or algebra.
posted by scalespace at 6:14 PM on January 18, 2005

Response by poster: Thanks to everyone who provided information, advice and links. Lots of good stuff to follow up on!
posted by Ritchie at 4:44 AM on January 19, 2005

I have to add Mary L. Boas's Mathematical Methods of the Physical Sciences. It is awesome. I wouldn't recommend it as a starter calculus book, but though it's not example-heavy it is excellent for gaining a deeper knowledge of calculus and some higher calculus, as well as differential equations. It is excellent if you want a more application-based approach. And the organization is so very, very nice!

Know what you're doing before tackling Apostol; it's extremely in-depth, theory-heavy, and woefully short of examples, so you can quickly get lost in the notation and difficult wording if you're not careful. But man, once you know what's going on you really know what's going on after going through that thing.
posted by Anonymous at 7:54 PM on January 19, 2005

normy, Goedel: One needs to know as much math as one needs. You may very well know people who have calc inside and out. That's good; we should teach our kids that (we do for some). But math is a tool, you only really need it when you hit "that problem".

Math, all of it, should be known, but the details are only important when your problem demands it. String theorists have to pick up some math. My field has to pick up some math (etc physics). But I know the intimate details of more maths than your average person can even name. Math is a tool, you'll get it as you need it, or you will fail.

Math is something you make up to get the job done; almost always, your math is something someone has already done. That's when you learn it. Knowing it all only helps to reduce wasted effort a bit.
posted by theatrical matriarch at 12:39 AM on February 7, 2005