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]
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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.
Re:Homeschoolers secret: Saxon Math (Score:4, Funny)
It seems to me you could benefit from english course as well. The word is memorable.***
Actually rememberable looks to be perfectly OK http://www.selfknowledge.com/80549.htm [selfknowledge.com] If you asked me the difference between rememberable and memorable, I'd say the former implies can't remember whereas the latter implies not worth remembering. e.g. The difference between the words rememberable and memorable is subtle and not very rememberable. Neither is it memorable.
Re:3 ideas (Score:5, Insightful)
I highly recommend this book: The Square Root of Two by David Flannery. It's an excellent book which gives some real good insight into how to think about math problems, and is a pretty fun read.
http://mathforum.org/dr.math/ [mathforum.org] is a great web site for helping with homework.
Also, don't get discouraged, Math Is Hard.
Re:3 ideas (Score:5, Interesting)
You know, I wince when people say that. Yes, math is hard, but then, music is hard. Creative writing is hard. Any subject is hard if you don't get it, and even if you do get it, any subject needs hard work to get good at it. Yes, math needs abstract thinking, and some folks are better at that than others, but then, some people are better at pitch and rhythm than others. Picking on math in this way is sowing the seeds of defeat.
One of the math books I have (I can't remember which one) starts with a riff about how most folks want to drop math as soon as they can, but then it lists a whole list of subjects (things like "how to avoid getting ripped off", "how to play the stock market", "how to save time and effort by taking shortcuts on common problems", "having fun with games and puzzles" and so on) and speculates that pretty much everyone would want to take a few of those options. The trick is, of course, that they're all math. I'm convinced that the reason most people hate math is because it's taught in an almost completely abstract way (because the teachers have to get through the syllabus in a limited number of class hours). Teach it the other way -- take real problems and show how math can solve them or generalise them, and I reckon a lot more of the students would go along for the ride.
A friend of mine used to teach remedial physics to a college class. He wasn't much older than the students, so he started the first class by pretending to be another student and mixing with the others as they came in. In the process he discovered that most of them were bikers who had to get the physics qualification to support a motor mechanics apprenticeship they were doing. After some consternation when they discovered he was really the teacher, he started by asking them how they would tune a 2-stroke engine; what effect the things they were doing would have on the engine, and how they would measure the effects. This led them through all sorts of physics, from friction and levers to gas laws and fluid flow. He got every student through the exam, because he made it relevant. The same can be done with math, and it makes it a whole lot easier.
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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
Re:3 ideas (Score:5, Insightful)
I think it's only too easy to just pick up a math book and tell yourself you're going to do the work, only to get frustrated and abandon it a few weeks later. By having an actual class that you have to make time to attend, you're making more of a commitment and are more likely to stay with it.
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Calculus is tougher, and the community college might be the best bet.
Re:3 ideas (Score:5, Insightful)
I concur, Good study guides and good courses will put you on the right track.
No matter what you do, realise the Mathematics is not a spectator sport. I continuously fall into the trap of reading about Mathematics than doing Mathematics. Do the exercises and do some more. One thing I did do which was invaluable was a bridging course that reviewed much of final year high school Mathematics with plenty of exercises and a great teacher. Recognise your wakness and go back and make sure you understand whatever is being assumed at the level you are having diffculty with and again, do those exercises. For example, if you are having trouble with trigonometry, review the ways of deducing angles for triangles and bisected parallel lines. Review Pythagoras's Theorem, fundamental algebra, etc.
Re:3 ideas (Score:5, Funny)
Not yet, but it sure would be more interesting than watching golf!
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A much more interesting, and more fun to play, game which involves lots of geometry and physics is Pool. Best of all, all it requires is a room and a table, with some balls and a stick, whereas golf requires an overpriced membership at some stupid club where hundreds of acres of prime real estate have been wasted on growing grass.
Re:3 ideas (Score:5, Insightful)
And remember that being good at maths is part aptitude, part attitude, and part doing it. Just like you won't become a good musician without having a minimum of talent, liking music and lots and lots of voluntary exercise, you won't master math as long as you dislike it and don't do more than you have been asked to do.
If there's something in math you don't understand, take one step back and play with what precedes it, over and over again, until you truly master it, and it leads you into what you don't understand. Then you'll get the "a-ha!" experience, and everything will become much easier. In math, you must understand all the foundations before you can proceed to the next level. You can't pick that up later, or you'll end up just going through the motions with no understanding, and you will become lost and unable to apply your skills if a similar but not identical problem comes along.
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Internet-Age Approach (Score:4, Interesting)
Buy the same textbooks that the students at those universities use. For the pre-calculus mathematics, UC-Berkeley would be your best bet. MIT caters to only students who have already taken calculus in high school.
My best advice is to try a two-track approach: non-discrete mathematics and discrete mathematics. Traditionally high schools teach only non-discrete mathematics: e.g., trigonometry and calculus. Since you are studying the material on your own, you could improve upon the standard curriculum. Read a good book on discrete mathematics first. It will build your intuition of mathematics. Then, study the standard topics in non-discrete mathematics.
Discrete mathematics and non-discrete mathematics are quite different, but the reasoning in discrete mathematics will hone your skill in handling mathematical proofs, which are central to both branches of mathematics.
For a real challenge, after you finish your studies, try to determine whether P = NP.
Re:Internet-Age Approach (Score:4, Insightful)
Buy the same textbooks that the students at those universities use. For the pre-calculus mathematics, UC-Berkeley would be your best bet. MIT caters to only students who have already taken calculus in high school.
Why would that make them good resources for someone who wants a remedial education? If you want to catch up on barely-remembered stuff from high school in your spare time you don't go for a course that expects the best and brightest and will try to weed a quarter of them out early on. I'd be wary of the textbook choices, too. Professors don't always pick the textbooks that are easiest to learn from. This goes double if the professor writes their own textbook -- I have a signal analysis book by an MIT prof that's written in a deliberately dense and formal style. Amazon.com reviews are much more helpful for textbook selection, IMHO. Going to a local library and checking out a couple is also a good idea.
Re:Internet-Age Approach (Score:5, Interesting)
The materials mentioned are quite good, but never forget that math is learned by working problems. My advice: go to your nearest college bookstore and buy the text book for whatever course is appropriate for your level. Read it, in order and work the problems. I also recommend creating your own "lecture notes", with the book closed, for what you just learned. Do not ever skip move to the next section until you you absolutely understand it cold. Memorize nothing (other than defintions and terminology). Math is very natural to do self paced like this, and there's a good chance you'll enjoy it more this way. Just don't get impatient.
Re:Internet-Age Approach (Score:4, Informative)
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Study ... (Score:2, Funny)
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Then stay the bloody hell away from my circles Mr Pi=3 thicky.
Re:Study ... (Score:5, Funny)
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College Bookstore (Score:4, Interesting)
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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.
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Whatever, a college textbook is probably the cheapest thing you can use. Buy the 3-year-old previous edition off half.com or something for like 8 bucks.
How much has math changed in three years? It's not like the problems matter since no one is grading them. I mean, 10th edition, 11th edition, they're practically the same damn thing but one costs $139 and one costs $9.
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Re:College Bookstore (Score:5, Interesting)
Seems like every math class in america should have a playstation 2 with "Calculus: The Beginning" stuck in it. Cheaper then the calculators and computers per student and the student can play it at home if they want. What's not to like?
In the larger case though, i would just like to have such a thing as an entertainment option to, like the submitter said, keep a sharp edge on the skills.
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Practice (Score:5, Insightful)
Derive newton's method.
Find the formula for the circle that passes through any three arbitrary points
Derive all the trigonometric identity functions
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Re:Practice (Score:5, Funny)
well (Score:5, Insightful)
Re:well (Score:5, Interesting)
I'm not currently a professional teacher, but I have been one, at a Big Technical University that you have heard of, for four years. My skin crawls when I hear people demeaning a linear pedagogic approach because, frankly, and you can take this as an expert opinion by someone who has won awards for teaching, there is no better way. Period. People learn depth-first by cycling down from coarser details to finer ones. They learn in steps. To quote Prof. Patrick Winston of AI fame, you only learn that which you almost already know. Trying to teach in fuzzy alternate ways, teaching by trickery, emphasizing word problems or case study, teaching two or three paths at the same time, all of that stuff does not work for technical and mathematical subjects, pure and simple.
For the basic mathematics that the original post is inquiring about, the concepts are reasonably simple and straightforward. What they require, however, is what often appears to be mind-numbing repetition. It's work. While I applaud this fellow's current initiative, the effort should have been put in when he was a teenager because it's a lot easier then. It sounds like he's understood the mistake and is currently, as an adult, trying to correct that, which is definitely commendable. Unless he's the sort of person who developed phenomenal self-discipline later in life, however, the best bet is to get to a classroom. There are any of a large number of adult education services in every city I've been to. Often local high schools will have evening adult-ed classes as well. Or, as another poster suggested, the local community college can be a good resource. But basic mathematics requires a lot of rote work. It can be a joy to know that you've learned everything that was used to get mankind to the moon, a tremendous joy in fact, but it takes work.
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Re:well (Score:5, Insightful)
I'll add a couple of things (Score:4, Insightful)
Don't shy away from calculators, embrace them. I know too many people who try and learn higher level math (and too many teachers) who don't want to use calculators because they don't want to rely on them. Ok, there's something to that, but because of the immense amount of calculation involved, you will really cripple your learning without one. You need a calculator to quickly take care of the simple stuff so you can use that to solve more advanced problems. Also, programming a calculator to do something is a good way to learn it. In general, if you understand a concept well enough to write a program for it, you've got a fairly solid understanding of it. Don't just put everything in the calculator to get the final answer, but do use it to simplify things you already understand. For example if you can do division, there's no reason to do long division every time you need an answer, just let the calculator handle it and work on the problem.
Make sure to get applications for the math explained to you. At the level you are talking about, I think essentially everything has a real world application. Make sure this is taught to you. It can really help your understanding to get some real world examples. I always had a really hard time with imaginary numbers in high school because I couldn't understand them (or why you'd need them if they were imaginary). Wasn't till many years later I learned what they actually are, and that they aren't imaginary at all.
Now, all that said, you need to ask yourself why it is you think math is holding you back. What is it that a higher level of math understanding is preventing? I ask this for two reasons:
1) You need to focus on what to learn. Many people think there's a certain, immutable, order you need to learn math in, or that you must know certain fields for no good reason. That's not the case. While math builds on more basic concepts, you do reach a point where you can learn only certain parts. If you are talking about math related to programming, then calc really isn't so useful, that's more linear algebra. Figure out what you need to focus your studies on. Not saying you can't learn more for fun, however if the point is to improve in something you need, make sure you learn the right things.
2) In most fields you need way less math than you think. I took through calc 2 in university and I use basically nothing past what I learned in 6th grade (algebra) in my life. There just isn't a lot in the world that requires more than basic math. If you aren't in a field that does, or don't want to move in to one of those fields, I don't know you'll find it that useful. My math skills have dropped way off through disuse. To the extent I use higher math at all it is usually solving a problem just for fun, one I could easily look up a solution to.
Please don't misunderstand, I'm not trying to discourage you from learning, I just want you to consider why so it is as successful as possible. I'd hate for you to struggle through learning new math, only to find that it does you no good at all.
Because one thing to remember is that it really isn't going to be any easier. If you take the advice of others and get a good teacher, that'll help a lot, there are plenty of lousy highschool math teachers, however you probably just don't have much of an affinity for math. Like most things, there are just some people that get it, some that don't, and a whole range in between. Unless your failure the first time was related to drugs, teenage rebellion, inattention, or something like that you'll probably still find it hard. Nothing wrong with that, I just don't want to see you getting frustrated for no reason.
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ocw.mit.edu (Score:5, Informative)
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Nothing fancy. (Score:5, Insightful)
Set aside 30 minutes a night.
Work the problems out with pen and paper.
Where necessary, remember formulas however best suits you.
Avoid technological fixes.
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The need to stop cheating on homework is a paltry excuse for totally screwing those of us trying to learn.
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Work through some high school exercise books (Score:2)
In some ways mathematics is a frame of mind you need to train your mind to think mathematically.
In Australia the last 3 years of high school are years 10,11 and 12. Pick up the equivalent of a year 10 maths/exercise book. There will bechapters explaining some stuff and then it will have lots of exercises to exercise your mind. Answers will be in the back.
At year 11 and 12 level you are looking at what we call "Mathematics II". The yr 10 book will have given you the basics of differentials and Integrals, t
Get a Pre-calculus textbook (Score:2)
There are no two ways around it. You can learn or pretend you learned the material, but if you never have to apply it (doing problems) you'll never know. Community College courses like some suggested I offer hesitantly - I never liked classes as I have to keep to their schedule - in going there, etcetera. I l
Community college (Score:5, Informative)
Repetition of simple problems (Score:4, Interesting)
The thing is, when you're learning math you want to focus your efforts on the subject at hand - not the other simple math that accompanies it. For example, when a prof is going over a question on the board you don't want to waste time with the simple stuff. It takes away from what you should really be learning.
So I guess my suggestion is this - make sure you know the basic stuff really well. You will always have to use it and without it you will always be at a disadvantage.
Willy
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.
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I'm in a similar situation... (Score:3, Insightful)
MBA (Score:3)
Thank you, you've gone a long way towards explaining what kind of people get MBA's.
The skills go quickly (Score:4, Insightful)
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A view from the other side... (Score:4, Insightful)
That being said, and the understanding that you don't want to pour in the money required to get a good teacher (craigslist looking for a math tutor is a place to start. If you start off with one and it doesn't feel like a good emotional fit, then get a different one. A good tutor will try to get a solid grasp of where you are now, and then start taking steps to get you moving forward from where you are. A great tutor will help you when you're stuck, but also give you specific resources that you can use to work on exactly what you need to be working on right now in your time away from the tutor), here's my advice.
First off, understand what exactly it is you are trying to do. You are trying to build abstract thought paths in your brain. This is hard to do. Many of the math problems you were presented with in high school were an attempt to get you to make the leap from specific application of concepts in lots of different ways to the abstract concept itself. In algebra, you do tons of factoring and other ways of solving the quadratic equation. The point of all those problems was that you would, through many problems approaching the concepts from different angles, fundamentally understand what parabolas are all about. Accurate quadratic thinking is much much harder than linear thinking. When you see a line, you know it's a line, but when you see a curve, it might be quadratic, cubic, exponential, logarithmic, or any of a host of variations.
So, do a bunch of problems to build your skills and gain fluency with the concepts. Then try to figure out exactly what it is that's really going on. There's often some really obvious reason that something works the way it does, if you can find it. For instance, the whole FOIL method for multiplying binomials like this: (x+3)(x+2). If you draw a rectangle, and put the x+2 on top and the x+3 going down the side, and break the rectangle into an x part and a 2 part vertically, and an x part and a 3 part going horizontally, then you'll get 4 rectangles that all add up to make the original rectangle. Their areas are x^2, 2x for the first row and 3x, 6 for the second row. Those are, respectively, the First, Outer, Inner, and Last products of the FOIL method. If you draw the picture, it's really obvious, and you'll wonder why you struggled with it for so long (if you did). A good tutor can help make it all easy for you by showing you the really obvious reasons why things work the way they do.
Good luck
What do you need math for? (Score:2, Insightful)
That's the key question. What tasks are you doing regularly that your past failures to learn high school math are stopping your from?
I use some form or another of "math" regularly, but I'll tell you one thing: most of high-school math isn't very useful for me. I've never needed calculus, and barely ever needed geometry. Algebra is ocassionally useful, but the very basic bits of it are good enough (I remember that there is such a thing as the quadratic equation and factorization of polynomials, but I've
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
Buy a good calculus book (Score:2)
It helps a lot if you have a reason to use it.
If you don't have the discipline to do this, take a class.
(Well, it's always worked for me....)
Work problems (Score:2)
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
college (Score:2)
Conceptual (Score:2)
Possibly the most important point is to truly understand the concepts. Mathematics in some sense are self-evident - 2+2 will always equal 4, and the derivative of 2x (with respect to x) will always be 2. More complex ideas in math are equally self-evident, but are much harder to understand. As a result, a lot of math classes focus on memorization without understanding the ideas.
Buy a textbook and do the problems. But also be sure to read what the textbook is trying to say - why does the math work the w
maximize your curiousity (Score:5, Interesting)
Sometimes you'll find something that requires previous concepts that you don't yet have. This is fine, because now you can go look up those concepts with a sense of purpose. This will help you to your larger goal of the more interesting thing that you flipped to in the book. I did this when i picked up a book on fractals...lots of bright pictures, it seemed interesting. In there, they talked about integrals, which i hadn't learned yet, so i set out to find out what those were.
As for practical tips when you're learning one particular concept, reading textbooks is sorta like reading manpages in unix. it takes a certain mindset, and you usually want to pick out the relevant pieces from the page the first time around and then go back for specifics later. Textbooks are usually written very precisely and they sometimes have a lot of formal jargon or formulae that aren't useful the first time you read it, but can be helpful when you go back to get more details. So read it with that in mind. The first time through, don't expect to understand everything there. Just skip past the parts that are too hard and continue on, trying to get the general idea.
Next, do some of the easiest questions at the end of that section or chapter. Sometimes those questions may seem too easy, like you can just look at them and you think you know how to do it already. I suggest doing some anyway rather than skipping them. There's a difference between knowing the concept enough to recognize it in the questions, and actually knowing it well enough to do the questions quickly and correctly. Doing more questions is always good practice even when they seem easy at first glance.
When you've done several of the easy questions, you start to get more of an intuitive feel for the concept. Go on to the medium questions, and now you'll probably better understand the parts of the text that were difficult to understand on the first time you read the section. I suggest that you try hard to really understand the concepts in one chapter before you go onto the next one. If you have a solid grounding in the beginning, then the later stuff will be much easier and it'll be easier to get that intuitive understanding that lets you see the direction to the answer right from the start.
If you have several textbooks to choose from each time, then as you work your way through bits of each of them, you'll start to see the connections between different areas of math. This is something that most people don't get in their normal classes because they tend to focus too closely on one topic. If you wander through several topics following your curiousity, i think you'll get a better broad understanding of the connections, and it'll help you personally keep your motivation up so that you can continue to do it. remember to have fun with it. if it turns into a chore, then you'll stop doing it before you reach your goals.
have fun!
Write little programs to solve problems (Score:2)
Assuming you know a computer language, writing a computer program is a great way to do both of these things, since programming can be looked at as teaching the computer how to solve problems.
Start writing a program that is likely to involve the kind of math you want to learn, and since the development of your app will be dead in the
a live-person (Score:2)
community college (Score:2)
Fear (Score:2, Funny)
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!
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Ça veut dire "Bon chance!" Je suis désolé.
Sullivan's "Algebra & Trigonometry" (Score:3, Informative)
Good books (Score:2)
"What Is Mathematics? An Elementary Approach to Ideas and Methods," by Courant is a good but terse introduction.
"Mathematics: From the Birth of Numbers," by Gullberg is a really fun book that explains all facets of mathematics. It's not as rigorous as
Do what I did (Score:3, Insightful)
That way, you can afford to hire an accountant...
In all seriousness, I was a geek in high school and did well in every subject except math. I aced AP Computer Science and, yes, received full credit. I aced Geometry without any real effort - it made sense to me, and I could apply it to a real object. But when it came to algebra or any form of math I could not immediately apply to something that mattered to me I simply could not get my head around it. I just didn't care unless I could actually use it.
I realized this was a weakness of mine, and shifted away from computer work to other areas. If math is your weakness, but you have strengths in other areas, you may want to consider doing the same. I'm sure I could be good at math if I really put my mind to it, but I just don't find it enjoyable - why kill myself when I can make a living at something I enjoy more?
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.
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.
Guarnateed math learning! (Score:3, Interesting)
OK, Arithmetic: "The Trachtenberg Speed System of Basic Mathematics" by Ann Cutler and Rudolph McShane. This will teach you to do Addition, Subtraction, Multiplication, Division and Square Roots, much of it in your head. Learn to use an Abacus/Soroban. It helps to bring arithmetic into focus. there are a couple of computer-based practice utilities on the net to help you memorize the rules and gain quickness in TSS.
Algebra: "Programmed Reviews of Mathematics" by Flexer and Flexer. Six small books with a good introduction to the basics of many Math concepts.
"Algebra", "Functions and Relations", and "Trigonometry and Analytic Geometry": "Pre-calculus Mathematics" Vols I, II, III by Vernon Howe.
Calculus: "Quick Calculus" (Wiley Self-Study Guide) by Kleppner and Ramsey, and also "Calculator Calculus" by McCarty.
Most of these books are older and you will need to look for them. Most of them are "programmed instruction books", which is not a popular Thing to publish these days. Programmed Instruction was developed by B. F. Skinner and Norman Crowder and has been used to teach almost any subject imaginable. The information is presented in "frames" with questions and answers, on the principle that people learn faster in short, successful segments than they do with larger difficult presentations. Programmed Instruction seems to have fallen out of favor about the time that B. F. Skinner was castigated and demonized for his rigid behavioral views. I have never known anyone to NOT learn from good programmed instruction, if they could read the material and understand it. You might want to check with your physician to make sure you don't have an issue like dyscalcula (similar to dyslexia) or some other learning disorder that needs to be overcome first. If so, that could explain much of your frustration and can be handled.
Good programmed instruction takes a long time to develop and test. Each frame should lead to 96%+ success for people taking the course. Many older books simply broke up their information in short segments and asked a question without actually testing the goal and result. I am least satisfied with the Wiley Self-Study guides, but they are usually adequate for learning.
Good luck!
I wanted to learn math -- so I started a blog (Score:3, Interesting)
To regain my mastery of mathematics, I decided to take a single math problem very seriously. I figured that I would try to
understand the solution by grounding all ideas down to postulates.
I figured that this was a great way to learn mathematics anew and really get advanced. I soon learned that there were wonderful
math resources on the web. Wikipedia is really great. There's also MathWorld.com [wolfram.com].,
PlanetMath [planetmath.org], MathForum.org, and
Cut-The-Knot.org [cut-the-knot.org].
Being pretty ambitious, I chose Fermat's Last Theorem and Andrew Wiles's solution as my jump off point. I started this adventure
in 2004. Since then, because the problem is so tough, I started blogging through the different threads of the problem and I find
myself recreating the history of mathematics from the perspective of number theory.
I am not sure that this approach would work for everyone but if you are a solid problem solver, it can really make advanced
mathematics more fun. If you are interested to see what I came up with, you can check out my blog a My math blog [blogspot.com].
I also started a general math blog [blogspot.com].
Best of luck in learning mathematics.
-Larry
Losing the touch (Score:3, Insightful)
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!
Comment removed (Score:3, Insightful)
Math is a mess. (Score:3, Interesting)
1.) Don't be intimidated.
2.) Stay curious. Find ways to get curious about certain fields of math.
These are from different posts, but I think they go good together.
The truth is, math is a mess. It's a historically grown mumbo-jumbo of countless variations in notation. The problem is that with programming languages - no matter how crazy they may be - they allways come with a reference manual to explain their syntax. In fact, that is the main element by which we judge the viability of a PL. With math on the other hand academia kind of expects us to understand what the Professor is writing on the blackboard without even addressing the issue of a solid reference in which I can look up the meaning of the sum-symbol or what a limes means and how it looks like. It's like music-notation. Somewhere back in the day - often a few hundred years ago - someone came up with a certain notation and since then that's the rule of thumb by which everybody sticks to sorta-kinda 50% of the time. If he feels like it. These notations are mostly literally bolted on to terms and expressions in the most chaotic and hideous way one can imagine. It's like trying to understand a Perl obfuscation contest without the manual.
This is IMHO the single biggest problem in grasping math. Especially for Computer Geeks who are used to strict syntax constraints.
I' currently studying the first semester of BS-CompSci and am glad for having finished my German GED just this summer, with all the accelerated math (barely made it with a D+ due to the time-constrained tests) still in my head. I can just about keep up with the lectures. We allready have quite a few students bickering about the lack of a symbol and notation reference.
Bottom line:
Math is a mess. It is a non-trivial science and takes work to understand, but it's a mess none-the-less. If one keeps that in mind without using it as a cheap excuse not to fully work out and understand the details then learning math is much less frustrating. That's how I feel about it anyway.
city college (Score:3, Interesting)
The other posts seem to have forgotten step 1 (Score:5, Insightful)
Step 1: Figure out what you want to know and why you want to know it.
You are probably living a rich, full life without knowing advanced group theory. So you are probably thinking about learning math for a specific reason, either for professional advancement or curiosity. If you are going to be successful, figure out what it is you really want to know or what it is that piques your curiosity. Are you frustrated because you want to save for retirement but don't know how to handle investment returns? Do you just want to not be embarrassed when you have to do simple addition and subtraction in front of your peers? Are there specific problems that crop up at work?
Once you've identified these issues, then refer to the advice from the other posts and put together a game plan.
The key is to pursue the things you're interested in. The approach is the same as, for example, you want to know more about cars. Finding out about auto mechanics is much easier and more interesting when your car is broken and you've got a specific problem to solve. Or if you have friends who are grease monkeys and you want to be able to talk to them on their own level.
Pick some problems in the books or classwork, but also just pick little problems that crop up in your life and try to work them out while you're on the bus, waiting in line, at the gym, whatever. And be sure to talk to other people who know more. Don't be embarrassed. If you don't meet someone in your class, join in online forums. Trust me, people who enjoy math really enjoy talking to other people about math. Like learning a foreign language, you can't learn it by reading a book. You have to do it and you are most efficient when you engage other people in your learning process.
I base this advice on experience: I stopped taking mathematics courses in my sophomore year in high school because I found it boring. (Unfortunately, the way high school math is typically taught, it usually is boring). Later, because there were things I was interested in, I took it up again in college and went on to earn a BA in mathematics, probably one of the best choices (both for my intellectual enrichment and my professional life) I've ever made in my life. I kept my focus by finding things that made me curious and following up on them and have never looked back.
SAT prep (Score:3, Interesting)
What worked for me (Score:4, Insightful)
1) Make use of other people. Unlike many other subjects, with math it can really help to have something explained by a live person. Make use of teachers, tutors, and fellow students.
2) Don't fall behind. Unlike many other subjects, cramming seldomly works with math. You can get hung-up on some concept and not be able to go any further. In math, you are always building on what you have already learned.
3) If one source doesn't work, use another, and another. If you read on books explaination, and it doesn't make sense for you, get another book and read that explaination. Read a few explainations.
4) Of course, do as many problems as you can.
5) If you having trouble, do your best to isolate exactly where the problem. That way you can explain to somebody else much better. Also, the process of isolating the difficulty will lead to the solution.
6) Sometimes it helps to know the history of certain areas of math.
Math some esoteric comments... (Score:3, Insightful)
You know I can remember thinking about mathematics and the legends behind the basic foundations in analysis, calculas and the like. (i.e. Euler and Newton and Kepler et al.)
I thought WOW I must be stupid, these guys just picked up Mathematics no problemo......
Well....not quite. I mean, make no doubt, Newton, Kepler and Euler all where very adept at Mathematics.
But, they also worked VERY....VERY very VERY hard at it.
Can you imagine the PAIN and SUFFERING, Kepler had to go through in building even the most basic elementals of planetary motion by doing the same calculation sometimes 100 times to prevent error?
Even then, he got the calculations wrong for the orbit of Mars and missed the eccentricity factor that would have been a shoe in while he was testing different shapes of orbits for Mars: namely an ellipse.
It would take Kepler WEEKS to perform these calculations, which now I can do in a fraction of a second on my laptop.
The labor required in those days to do mathematics was intense, and highly error prone.
Newton would lock himself away for DAYS barely eating anything performing every possible experiment, and when not satisfied with just experimentation, he wanted quantitative results from the experiment as well.
Has anyone, I mean anyone here gone for days barely eating anything working non stop on a mathematics problem for 18 hours at a time?
You know the "greats" in Mathematics worked at it with super human resolve and zeal, only if you would care to read about this HISTORY of mathematics you would find it as so.
Expect to put in at LEAST as much effort if you want to really join their ranks.
I would like to point out that with tools like: http://www.gnu.org/software/octave/ [gnu.org] you can bypass the pain and labor of mathematics and get to the core of the matter MUCH faster than Kepler or Newton ever could. So you could literally "cheat" out of the labor these guys had to put in, and put the machine to work doing the calculations to develop methods of computation much quicker to solve problems.
So, although no doubt, these men became literal geniuses, if you look at their lives and what governed their passions with regards to numerical studies, they put in huge amounts of time to the problems they wanted answers to. They earned the right to be called geniuses, it certainly wasn't given to them at birth.
Keep this in mind the next time you are stumped on any sort of mathematics problem. Also keep in mind that like the "greats" you have to be stick with it, and never give up!
-Hack
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.
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I would suggest the way to go about it is go back to school. You could find
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Once you learn how to get a best fit line, do percents, fractions, basic geometry, understand the concept of funct
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