Best Way To Teach Oneself Math? 609
An anonymous reader writes "In high school I failed two out of three years of math classes and eventually dropped out of school completely. I earned my general equivalency diploma as soon as was legally possible and from there went on to college and beyond. That was many years ago and my most basic algebra, trigonometry, and geometry skills are slipping away at an alarming rate. I'm looking for a self-guided course covering the equivalent of 4 years of high school mathematics including calculus. My math skills are holding me back. How can I turn this around?"
3 ideas (Score:5, Informative)
Another option, if it fits into a persons schedule, would be to take classes through a community college. Costs are lower, classes are generally smaller than a university and schedules are often flexible for working adults.
Another thought I had is home schooling materials. I've never personally been involved in homeschooling, but as I understand it these kids can earn a highschool diploma at home. So why couldn't someone put themselves through such a program just to learn the information? I'm sure there are lots of resources out there for this, a quick google turned up this one. [homeschoolmath.net]
Re:3 ideas (Score:5, Informative)
ocw.mit.edu (Score:5, Informative)
Re:3 ideas (Score:2, Informative)
Go to the course catalog and figure out undergrad level classes in the area you want to improve / learn. They are really cool. You will see all the lecture notes, exercises and reading material. If you are really serious about learning, I would highly recommend buying course textbook and following the course schedule strictly. I did this in couple of areas like business strategy and game theory and it really helped me in acquiring the relevant skills in these areas.
All the Best!
Community college (Score:5, Informative)
Math skills... (Score:5, Informative)
Any sort of advanced math is very easy in which to develop bad habits. Advanced math "build", unlike other subjects in those same grades. If you didn't "get" Death of a Salesman, you still have a shot at understanding Moby Dick. However, if you did not "get" fractions or percentages, then you really can't go a lot further.
If your math skills (or, rather, lack thereof) are holding you back, think of the tutor as an investment.
On a side note, you would be surprised at the proof of "bad math skills" that can be seen in the corporate world. People rarely / never stop to do a reality check. "Can it be that 105% of the people required to take the training have taken it?" Ugh.
Re:3 ideas (Score:3, Informative)
Read this book (Score:2, Informative)
John Mighton, a math PhD and award winning playwright, founded a math tutoring program called Jump Math. It has been very successful with all kinds of student. In particular, it has worked for adult learners in jail. "The Myth of Ability" gives the basic philosophy of the program. Once you have read it, you will have the clues you need to direct your own math learning program.
Almost all the things we think about as intelligence are a result of pattern recognition. We really don't work by logic. Master level chess players, for instance, don't work out positions by logic. They can't work out moves much farther ahead than non-experts. What makes them experts is that they have studied thousands of games and they recognize situations when they see them. The way they got to be experts was by 'deliberate practice'. That's how you are going to learn math. http://www.nytimes.com/2006/05/07/magazine/07wwln_freak.html?_r=1&n=Top%2FFeatures%2FMagazine%2FColumns%2FFreakonomics&oref=slogin [nytimes.com]
Once you understand the underlying principles of how we learn and once you understand that the effort required will almost certainly lead to success, you will be much more likely to put forth the effort required.
My approach (Score:2, Informative)
Instead of looking for a curriculum, it sounds easier to find some relevant problems and work backwards. You mentioned that your lack of math is holding you back. Why not identify some specific cases of this, and learn enough math to overcome whatever issue made you feel this way? Doing this enough times will give you a solid background in math, I think.
In my own case, the reason I had to ramp up on math is that I was taking a pretty hardcore machine learning class during my masters. The course assumed a much deeper knowledge of linear algebra than I had. I literally had to do hours of research to understand many slides from the lectures which were really intended to be background and proofs, not the meat of the course. You can imagine that by the time the course ended (I got an A- which was a big deal for this class) I had a much stronger foundation in linear algebra and other math concepts than I did initially - even though I didn't set out to learn that stuff. Call it just-in-time learning. Now I am studying for the CFA (Level 1) and it also has some math, although nothing too hardcore. Still, the first volume contains a quantitative methods section which talks about statistics and the like. So again, even though my goal is to learn Finance, not math, I ended up refreshing a bit of math in the process.
Maybe this "just in time" learning isn't for everyone but it seems good to me in that it forces you to learn math that's the most relevant to your life, and it in a sense forces you to make sure you've learned it well, given that you'll be applying it immediately.
Also, MIT has some online courses that you should check out. I know you talked about highschool level stuff but why not be even more ambitious? For example, there's a series of video lectures with dr. Gilbert Strange about Linear Algebra. I don't think the course requires too much other background (and again, if he talks about a concept that you don't know, this is a great opportunity for additional just-in-time learning).
The main thing I am trying to say is that you should set a goal for yourself that's narrower than "learning everything". Define a concrete problem and solve it. For example, your problem could be as simple as watching all of the lectures mentioned above, or reading some calculus text. Instead of spending years learning everything everyone tells you that you need to know before you can do calc, just do the reading and then branch out into understanding pre-requisites as you encounter them in the text. I think this is a much more structured and motivating way to do it.
Good luck!
Re:College Bookstore (Score:3, Informative)
An alternative would be review guides such as those for AP tests. Those are far cheaper, though they may or may not explain the concepts. If it's review you seek, then a college textbook is overkill.
Re:should have included (Score:4, Informative)
Free math lessons on YouTube (Score:2, Informative)
I've found a number of helpful math lessons on youtube recently. Some are actually pretty good. Just search for algebra [youtube.com] or whatever you're looking to learn. Last week I got refreshed on statistics [youtube.com].
Obviously there's a signal-to-noise ratio problem, just skip over the noise.
Question (Score:3, Informative)
For Self Teaching- don't do it. Your main problem is finding out what learning mechanism works best for you and then finding a compatible mentor. Don't go to a local college and merely buy the textbooks there, you will get through the first chapter then realize you wasted $100 on a book you have no idea how to read.
Also, you need to decide how far in math you need to go. For calculus not all books are created equal. Find a simple book that has easy to understand examples but does not go too far. Make sure it has a few chapters on limits only- you need to know these to know calculus. On the other hand, you likely do not need to know how to check if an integral is converging or diverging, knowing how to do Taylor series, Laplace Transform, Invariant coordinate systems, etc. The book you select should have basic differential and integral calculus but nothing too advanced. Take baby steps. If you can work your way (with someone) through these things you will have a better chance to succeed and know what types of math you need to specialize in and how much.
Also, tell us what types of problems you are running in to or else we can't pin down a specific way to help you. What types of applications are you doing and what do you need to find out? You may only need differential and some basic integral calculus do to the work you need.
That's my advice for self-teaching, but I would suggest going to a community college or finding a mentor who will (maybe for a small fee) teach you the math.
Finally, if you do not understand the math you will not be able to use it in your job. Make sure you don't waste your time going down the wrong path. It's essential to have someone to ask and review your work so that you find out you are not doing things backwards and upside-down.
Learning math is similar to learning a language, although the constructs are vastly different between the two. It doesn't happen through osmosis and it's hard to get a good understanding of the "pronounciation" unless you have someone you can go to. Again, seriously consider taking some precalculus classes at a Community College then going on to calc. Without the foundation for the more advanced stuff you will get nowhere. De toute façon, on chance!
Homeschoolers secret: Saxon Math (Score:5, Informative)
http://www.saxonpub.com/ [saxonpub.com] .
they've changed their URL, but it redirects pronto, and the new one isn't rememberable. .
Diff between these and the normal ones?
One concept, one lesson.
Big concept? broken into several components, and distributed over several lessons.
Syncopated plan: one gets the chance to get a knowing into long-term-memory/function before one hits the next lesson that relies on it.
having tried many, and lost my math in some brain-damage I got in my teens, this is THE required one.
Find the book you need,
by doing a placement-test,
then get the ISB# for that recommended book,
then find a second-hand copy on http://www.abebooks.com/ [abebooks.com] for cheap.
Sullivan's "Algebra & Trigonometry" (Score:3, Informative)
Re:College Bookstore (Score:3, Informative)
Get a GMAT Test math prep book (Score:5, Informative)
GMAT math covers basic athrimetic, geometry, algebra, combinatorics, probability, word problems and data sufficiency. I haven't done long division
by hand in probably 15 years so I found the steps to be quite helpful.
One plus of using the gmat math as a stepping stone is that if you ever want to take the test yourself then you will be pretty well prepared for it.
Another plus is that there is a ton of free material out there for gmat math preparation - study guides, practice tests, quizzes, etc. that can all be downloaded for free.
Re:Nothing fancy. (Score:3, Informative)
If teaching yourself (Score:5, Informative)
That said, I do maths at Uni and still occasionally forget some of the specifics about the basics. For that reason, I still have all of my high-school text books and even a few second-third-forth hand. One of them is particually good at one thing, another is concise at another. So, my suggestion is to go to second hand book stores and garage sales and pick up a couple of these. Few people want these after school and if the textbook was fazed out, they wouldn't of been able to sell it. As a result, you can often pick these up for $5-$10, especially if you aren't worried about it being brand new.
Teach Yourself Math (Score:2, Informative)
Get the solutions manual for each book.
Work through the textbook. I really mean work, so write down and think through all of the examples in each chapter. Then, do 'enough' problems at the end of the chapter. Check your answers with the answers in the solutions manual. If you didn't get it right, do it again. If you still didn't get it right, then read through the solution provided. If you STILL can't get it, ask someone, possibly on a forum online or in person.
It worked for me--6 years ago I was a B- high school math student and now I'm taking graduate level math courses.
A good Trig book... (Score:2, Informative)
I'll admit it isn't the most visually appealing book or the easiest thing to read, but if you spend a few hours really working to understand the contents of a chapter, it's totally worth it, because in the end you'll have a very very deep understanding.
Also, the Blitzer: Precalculus book is very good. Great if you need to refresh your algebra skills. It also has a great Trig section.
For calculus, I would suggest, "The Complete Idiots Guide to: Calculus" (to get started), it was surprisingly good. And most of all, Calculus: An Intuitive and Physical Approach. That last book is practically my bible.
Anyways, good luck, you learn your math, and I'll struggle to get my stupid high school to let me take an interesting math class I won't be bored in.
N = 8 * 10^8 * x-3/2 (Score:2, Informative)
N = 8 * 10^8 * x-3/2
doesn't seem right. That's
N = 800000000*x - 1.5
and N increases with x, which is inconsistent with the problem statement.
How To Ace Calculus - good book (Score:3, Informative)
P.S. One of my favorite parts is how the authors will say stuff like "your teacher really means this, but the other way makes them sound more important"
The low-brow, DIRTY way to quickly learn the math (Score:5, Informative)
What I recommend here is the "low-brow" way. The easy, the "dirty" way that purists and snobs will turn up their nose at. This is equivalent to the advice of those people who give children comic books to encourage them to read. The method works, right? This will work for you too, and you'll enjoy it as much as comic books.
The key, essential text, is a book written a long time ago, called "Mathematics for the Million". It is still in print, and is excellent. It takes you from early chapters on counting from one to five, and works up through simple geometry through to algebra, logarithms, trigonometry, spherical trigonometry, calculus, and ends off with combinators and linear algebra. It is written in a great style, easy to read, but packed with information. It has lots of interesting stories and applications of the math, but not any fluff. This is the key text. It is 800 pages long, and worth every page. The price is astoundingly cheap. A chap on a desert island could rebuild much of civilization if he had this book with him. If I was on a desert island, this book would come second on my list, right after the Bible. With each chapter, it puts the mathematical developement in historical context, showing how real people developed the math out of the math that went before it, which will be fresh in your mind from the chapters you already read.
After that, you may want to work through these books: "Algebra The Easy Way", "Trigonometry The Easy Way", and "Calculus The Easy Way". In the "Easy Way" series of books, each concept is introduced in the context of a story and a practical application, as a group of people "discover" these fields of mathematics for themselves, to solve their problems. It is set in a fantasy setting with kings, queens, dragons, etc.
Finally, for inspiration, and "fun", I recommend all of the mathematics books by Martin Gardner, Ian Stewart, and A.K. Dewdney. All three of these men ran a very successful mathematical amusements and puzzles column in Scientific American. Their books are compilations of their columns. They make math interesting, showing interesting relationships between the different bits of math that we are told are "important". And they show interesting applications, puzzles, and pictures resulting from the mathematics. One Martin Gardner column that really stuck with me was the one on the "super ellipse". It has the interesting property that it looks like it should tip over, but it actually keeps itself balanced, and resists being tipped over.
As an earlier commenter said, you can't just read about math. You have to do it. You have to practice. If you are willing to practice though, the books I listed above will get you where you want to be, with a minimum of head-scratching.
Good Luck!
Re:Internet-Age Approach (Score:4, Informative)
A Self-guided Path (Score:2, Informative)
Google: On the study and difficulties of mathematics by Augustus De Morgan... you can download it for free from google!
after reading that title I suggest reading De Morgan's Trigonometry and double algebra title also available for free from google
Followed with elements of algebra also by Augustus De Morgan
followed with elements of trigonometry by De Morgan
I would also supplement this study with project MATHEMATICS! by Tom apostol
Then work through Tom Apostol's Calculus ( M.I.T. uses this text for their theory calculus courses) you can find this ebook
floating around on most bit torrent sites.
I would also suggest you have a look at Dover Publications, they have great reprints of math classics including some by De Morgon.
Truly, once you get the basics firmly in your head, the more advanced topics come much more readily.
I hope this short list can help others as much as it has help me in the self-study of mathematics.
Open University (Score:2, Informative)
Course details are: http://www3.open.ac.uk/courses/bin/p12.dll?C01MU120 [open.ac.uk]
It will cost you around $600 if you can afford that, but is far more effective in my view. You get a tutor and set texts all online, plus messageboards for the other students and tutorials if you are in the right country.
Re:Internet-Age Approach (Score:3, Informative)
Re:Homeschoolers secret: Saxon Math (Score:2, Informative)
I was homeschooled, and my math skills are also not the best. Probably because it just doesn't seem like there was anything USEFUL that I could do with the Math I was learning.
But I will say this about saxon math; It was the only math circitulum that I Cried over. Yes, that's right. I bawled my eyes out because I didn't understand it. Saxon Math is the most terrible math that I have ever used. I started using a ciriculum called "Making Math Meaningful" it was so much better then Saxon. IT actually MADE SENSE! I actually learned math.
If you are trying to self teach, don't use Saxon math. It is designed for a teacher to assign homework out of. Nothing more. It is a terrible way to learn math on your own. Maybe I'm a little bias, but I know what I experienced, and it was horrifing.
I am OP, thank you for all of the replies. (Score:5, Informative)
Perhaps I should have replied earlier to this topic to give a little more background on my situation, some details were omitted by myself or Slashdot editors. But I'm actually glad I didn't get too specific because of the breadth of answers I have received. Many others will benefit from them, so I thank you for your indulgence.
Some of you wanted to know more background, well here it is for the interested.
I moved around a lot as a child, five different school systems up to junior high. Mismatched curriculum was always a problem, each school I'd start at was more advanced than the last, but my real problems didn't begin until I stopped moving. I went to a very reputable New York high school in the mid-80s. In my latter years there I was diagnosed (perhaps incorrectly) with some vague, undefined "learning disability". They'd no doubt label it ADHD today. I do seem to have dyslexia, but personality conflicts with my teachers had a bigger impact on my learning. Their anger and frustration with my obvious ability versus my lack of performance had a very negative effect on me. It didn't matter that I had an IQ of 136 or that I scored 1390 on my SATs, my grades were always terrible because I resented having to do what I thought was pointless busy work (something I regret today). By my twelfth year I was cutting classes everyday to spend my time in the library, learning what I wanted to learn about science, mathematics, and computers. If I am interested in a subject, and have the proper material, I usually have little difficulty learning and excelling in it.
My specific problems in mathematics classes were varied. Part of it was not being presented with practical applications. Most of it was not doing the home work, which severely penalized my grades and crippled my overall retention. Although I did well on tests, I wasn't learning. Having a literal nervous breakdown during my analytic geometry finals didn't help anything. All that said, I LOVE mathematics. I love its purity, its elegance, its logic, and its lack of ambiguity.
Fast forward to today, I'm a clever and skilled programmer, graphics designer, and game developer, 26 years as a hobbyist, 10 as a professional, with no formal education in those fields. As I expand my skill set in game programming, I'm finding more and more that I don't possess enough basic mathematics ability to truly understand topics like kinematics, physics, artificial intelligence, and statistics, even if I almost blindly employ them everyday. The practical applications I craved as a child are squarely in my lap, and I'm so rusty now that I couldn't tell you the difference between a derivative and a determinant. I may know more about fractals and ray tracers than any of my friends, but I couldn't possibly explain them or think about them critically because I don't speak the language. I liken it to being able to play jazz, but not being able to read music or talk about music theory in a meaningful way. This needs to change, my lack of mathematics skills are holding me back.
So there you have it, in too many words or less. Thanks again to all the respondents, and to Slashdot for posting this topic.