January 15, 2013 10:05 AM Subscribe

I'm a 21 year old college senior liberal arts major who has managed to slide by in school (and life) without ever really learning math beyond a middle school/very early high school level. For no reason in particular, I've decided that I want to get serious about bettering myself in the math department. How can I teach myself the academic math skills I missed out on?

Throughout my academic career, math has always been a serious hang up for me. Even at the times when I at least vaguely grasped the concepts, it was my worst subject. I was a straight A student through high school, with the exception of math, in which I maintained a C average with some difficulty.

For reasons that don't bear explanation, I have managed to pass (barely) mathematics and physics classes with virtually no comprehension beyond a middle school level. My most recent math class, for example, was my Freshman "Intro to Math" course for liberal arts majors. It is far and away the most simple math course my university offers. I passed with a D-, and thought it an absolute miracle.

When I think about all of the years I wasted doing so poorly, knowing I never made even the slightest effort to improve, it makes me sick at heart. I want to learn mathematics. How can I? Internet and book-learning are options. Tutoring is not. Assume that I will be learning about these concepts more or less for the first time.

Here's what I do know:

These are all clear as day, and I can solve any number problem put before me:

Addition

Subtraction

Multiplication

Division

Very basic algebra

Here's what I don't know, but want to:

Algebra

Pre/Calculus

Physics

Percentages

Fractions- Fractions were where the shit really started to hit the fan in my education. Maybe sixth grade?

Probability- Draw a card/pick balls and replace/don't replace

Combinations- If you have X number of condiments, Y kind of meats, and Z types of fries, how many different meals can you have. That sort of thing

sin/cos/tan/logs

Geometry

Proofs

Functions

Trigonometry

Compound interest

General Economics math

Order of Operations

Permutations

I don't want to just punch things into a calculator. I want to understand how they work. I basically need a ground up math education. With time and patience can I teach myself? If so, please help me with the how! Thank you for your attention. I appreciate your responses in advance!
posted by Krazor to Education (19 answers total) 55 users marked this as a favorite

Throughout my academic career, math has always been a serious hang up for me. Even at the times when I at least vaguely grasped the concepts, it was my worst subject. I was a straight A student through high school, with the exception of math, in which I maintained a C average with some difficulty.

For reasons that don't bear explanation, I have managed to pass (barely) mathematics and physics classes with virtually no comprehension beyond a middle school level. My most recent math class, for example, was my Freshman "Intro to Math" course for liberal arts majors. It is far and away the most simple math course my university offers. I passed with a D-, and thought it an absolute miracle.

When I think about all of the years I wasted doing so poorly, knowing I never made even the slightest effort to improve, it makes me sick at heart. I want to learn mathematics. How can I? Internet and book-learning are options. Tutoring is not. Assume that I will be learning about these concepts more or less for the first time.

Here's what I do know:

These are all clear as day, and I can solve any number problem put before me:

Addition

Subtraction

Multiplication

Division

Very basic algebra

Here's what I don't know, but want to:

Algebra

Pre/Calculus

Physics

Percentages

Fractions- Fractions were where the shit really started to hit the fan in my education. Maybe sixth grade?

Probability- Draw a card/pick balls and replace/don't replace

Combinations- If you have X number of condiments, Y kind of meats, and Z types of fries, how many different meals can you have. That sort of thing

sin/cos/tan/logs

Geometry

Proofs

Functions

Trigonometry

Compound interest

General Economics math

Order of Operations

Permutations

I don't want to just punch things into a calculator. I want to understand how they work. I basically need a ground up math education. With time and patience can I teach myself? If so, please help me with the how! Thank you for your attention. I appreciate your responses in advance!

Try Coursera.Org.

There are a few courses you could try, namely Algebra and Pre-Calculus. The catalogue has a myriad other courses that may pique your interest as well.

posted by rozaine at 10:21 AM on January 15, 2013

There are a few courses you could try, namely Algebra and Pre-Calculus. The catalogue has a myriad other courses that may pique your interest as well.

posted by rozaine at 10:21 AM on January 15, 2013

I think it would be fun to teach a motivated older student. If your school has a college of education that prepares math teachers, it's possible you could get free tutoring by presenting it as "rehearsing your high school math lesson plans."

posted by Nomyte at 10:36 AM on January 15, 2013

posted by Nomyte at 10:36 AM on January 15, 2013

Khan Academy offers free video lessons on all sorts of math topics. They look like some excellent teaching to me (I have a bachelor's degree in physics and am finishing up an engineering Ph.D, so I've both learned and taught these topics).

(Frustratingly, the site is down right this second as I post. As far as I know that's not a regular happening; hopefully it'll be back up by the time you check these responses!)

posted by snowmentality at 10:36 AM on January 15, 2013 [1 favorite]

(Frustratingly, the site is down right this second as I post. As far as I know that's not a regular happening; hopefully it'll be back up by the time you check these responses!)

posted by snowmentality at 10:36 AM on January 15, 2013 [1 favorite]

This is totally doable with some time, effort, and perhaps a bit of outside "human" help!

Many of those topics are on Betterexplained.

Intro level macro and micro classes typically are algebra based, while higher (undergrad) levels are more calculus based.

Math applets (ex) are your friend.

IMO a conceptual understanding at this level of math is very important, but so is a lot of practice with these types of problems.

Among other explanations, fractions are just another way to write division.

MEP math is a better elementary than middle/ secondary school resource. However, if you are missing the connections between division, fractions, and percents then it is possible you are not as fluent/ comfortable with number than you could be.

Memail me. I had a similar experience (re)learning math as an adult. I'd be happy to share my personal experience doing this and be someone to bounce ideas off of.

posted by oceano at 10:53 AM on January 15, 2013

Many of those topics are on Betterexplained.

Intro level macro and micro classes typically are algebra based, while higher (undergrad) levels are more calculus based.

Math applets (ex) are your friend.

IMO a conceptual understanding at this level of math is very important, but so is a lot of practice with these types of problems.

Among other explanations, fractions are just another way to write division.

MEP math is a better elementary than middle/ secondary school resource. However, if you are missing the connections between division, fractions, and percents then it is possible you are not as fluent/ comfortable with number than you could be.

Memail me. I had a similar experience (re)learning math as an adult. I'd be happy to share my personal experience doing this and be someone to bounce ideas off of.

posted by oceano at 10:53 AM on January 15, 2013

The list of what you want to know is quite a mixture of stuff. I'd start off with fractions and percentages first, because these appear everywhere and you can't really do any sort of math without understanding them. Order of operations too, although that's a simple, mechanical thing.

Algebra and pre-calculus go together. Pre-calculus, from what I recall, is "Algebra 2.0 - This Time Pay Attention". Calculus is applied algebra. You don't fail calculus, you fail algebra while taking calculus. Compound interest can't really be understood without algebra, so that comes next.

I find an ability to estimate probabilities to be incredibly useful, as well as the ability to work with numbers and get back-of-the-envelope answers. Estimating sales tax without a calculator, for example. What is a marginal tax rate and what happens to me when it goes up?

Proofs, combinations, and permutations can be interesting, but I don't know what I'd do with them. Leave them until last.

Physics is an enormous subject. You are going to have to break that down a little.

posted by It's Never Lurgi at 11:02 AM on January 15, 2013 [1 favorite]

Algebra and pre-calculus go together. Pre-calculus, from what I recall, is "Algebra 2.0 - This Time Pay Attention". Calculus is applied algebra. You don't fail calculus, you fail algebra while taking calculus. Compound interest can't really be understood without algebra, so that comes next.

I find an ability to estimate probabilities to be incredibly useful, as well as the ability to work with numbers and get back-of-the-envelope answers. Estimating sales tax without a calculator, for example. What is a marginal tax rate and what happens to me when it goes up?

Proofs, combinations, and permutations can be interesting, but I don't know what I'd do with them. Leave them until last.

Physics is an enormous subject. You are going to have to break that down a little.

posted by It's Never Lurgi at 11:02 AM on January 15, 2013 [1 favorite]

Read the new book *Measurement* by Paul Lockhart, if you want to get a feel for proof-based mathematics. He does a lot of analytical geometry and calculus in there, so the topics are up your alley also.

posted by King Bee at 11:04 AM on January 15, 2013

posted by King Bee at 11:04 AM on January 15, 2013

The Wiley math self-teaching guides are pretty solid. I have personally used and gotten value from "All the Math You'll Ever Need," "Practical Algebra," "Geometry and Trigonometry for Calculus," and "Quick Calculus."

They're clearly-written tutorials that will give you something of a math base to build from.

posted by zjacreman at 11:19 AM on January 15, 2013 [1 favorite]

They're clearly-written tutorials that will give you something of a math base to build from.

posted by zjacreman at 11:19 AM on January 15, 2013 [1 favorite]

Math is a lot of fun, but it's taught really poorly in most schools. Lockhart's Lament [pdf] is a really interesting musing on this subject. GH Hardy's *A Mathematician's Lament* is also good, and might help you start to see the why of math.

Some mathy logic puzzle books would probably help spark your interest and get your mind thinking in that proofy playful mode, too -- I'm a big fan of Raymond Smullyan's*To Mock a Mockingbird* (now out of print? dang) but virtually anything by Smullyan or Martin Gardner would work. Might also want to watch some of Vi Hart's videos.

It also might help to take a break from the algebra/calculus continuum (ha) and look at something else. I really liked this introduction to graph theory, and it's intended to be accessible to the "mathematically traumatized".

*Proofs [...] can be interesting, but I don't know what I'd do with them. Leave them until last. *

I strongly disagree. I didn't start understanding math until I started doing proofs. Everything before that felt like swimming in a disconnected sea of tricks and techniques.

posted by wayland at 11:45 AM on January 15, 2013 [1 favorite]

Some mathy logic puzzle books would probably help spark your interest and get your mind thinking in that proofy playful mode, too -- I'm a big fan of Raymond Smullyan's

It also might help to take a break from the algebra/calculus continuum (ha) and look at something else. I really liked this introduction to graph theory, and it's intended to be accessible to the "mathematically traumatized".

I strongly disagree. I didn't start understanding math until I started doing proofs. Everything before that felt like swimming in a disconnected sea of tricks and techniques.

posted by wayland at 11:45 AM on January 15, 2013 [1 favorite]

You've received a bunch of good suggestions already. But let me suggest one thing to start you off: find *The Feynman Lectures on Physics, Volume 1* - your nearest library can help [*] - and open it up to Chapter 22, "*Algebra*".

The Feynman lectures are famous in the community for reinventing physics from the ground up. In this chapter, Feynman does the same for algebra: he starts with definitions of integers, zero, and addition, and while taking 10 square roots of 10, he discovers (invents?) logarithms, irrational numbers, complex numbers...

The lecture ends with a formula that Feynman calls "an amazing jewel" - we write it as e^(i*pi)+1=0, a simple equation that connects 0, 1, e (2.71828182846...), pi (3.1415926...), and i (sqrt(-1)), linking algebra and geometry in a wonderfully, breathtakingly deep way.

I'm blathering - but seriously, if you've never done any math, try this chapter from the Lectures. At the very least, you'll have a better appreciation for the richness of the territory to be covered.

[*] If you google Feynman Lectures Algebra, there are several PDF matches too...

posted by RedOrGreen at 12:17 PM on January 15, 2013 [6 favorites]

The Feynman lectures are famous in the community for reinventing physics from the ground up. In this chapter, Feynman does the same for algebra: he starts with definitions of integers, zero, and addition, and while taking 10 square roots of 10, he discovers (invents?) logarithms, irrational numbers, complex numbers...

The lecture ends with a formula that Feynman calls "an amazing jewel" - we write it as e^(i*pi)+1=0, a simple equation that connects 0, 1, e (2.71828182846...), pi (3.1415926...), and i (sqrt(-1)), linking algebra and geometry in a wonderfully, breathtakingly deep way.

I'm blathering - but seriously, if you've never done any math, try this chapter from the Lectures. At the very least, you'll have a better appreciation for the richness of the territory to be covered.

[*] If you google Feynman Lectures Algebra, there are several PDF matches too...

posted by RedOrGreen at 12:17 PM on January 15, 2013 [6 favorites]

Yay, Math! I'm so happy to see people making the effort to learn more about math. Good for you for doing this! Please feel free to MeMail me if you have any questions. I've taught & tutored math to children and adults.

**General suggestions**

1. Do as much math as you can. Once you've read about a topic, try it. Try all of the practice problems as you can and check your work.

2. Learn to speak mathematics as well as do it. Learning to read exercises aloud can be very helpful in understanding math and it is great for communicating about math.

3. Try to do more than "practice this skill" exercises. Do problems that require you to combine your skills and to look at ideas in new ways. Math brain teasers and things like the American Mathematics Competition questions are likely a good place to start.

**Suggested ordering** for what you've mentioned you'd like to learn. It's by no means an order than must be followed, but one that I would tend to teach:

*Order of Operations* - this will likely be relatively quick and there are plenty of games for practice on the internet. Write down each step every time.

*Fractions/percentages(/decimals)* - These are all related. Purple Math and Khan Academy will likely be a big help. I believe freerice.com has a section devoted to fraction practice.

*Algebra/Functions/log* - Very large topic. I'd start at PurpleMath.com to help you out.

*Probability/Combinatorics* - Once you understand fractions, I think you can explore these. Further math knowledge helps, but you can start delving into these once you get fractions.

*Compound interest* - Once you understand exponents, I think you can start getting into compound interest.

*Proofs* - I'd start with discrete mathematics, then once you've got some geometry, try geometric proofs. Geometric constructions (as done in HS geometry with a straight edge and compass) can be fantastic in both helping develop mathematical thinking and in drawing some wonderful images.

*Geometry* - You can certainly learn some of this before algebra, but some algebra helps. Once you get further knowledge, you can also double back to get into things like the math behind computer graphics (geometry, trig, matrix algebra) and computational geometry.

*Trigonometry (incl sin/cos/tan)* - Once you have some algebra and understand the Pythagorean theorem, you can jump into trig. Here's an interesting short course online: http://www.clarku.edu/~djoyce/trig/

*Pre/Calculus* - Review of algebra, going into calc

*Physics* - Once you have algebra, you can start basic physics. Some physics courses are split into algebra-based physic courses and calculus-based physics courses.

*General Economics math* - I believe that you can start with algebra knowledge, but haven't taken economics in a long time.

**Resources**

PurpleMath.com - practical algebra lessons

Math.com - Free lessons on a variety of topics

KhanAcademy - seems to be very good at teaching skills, but not always the reasoning behind skills (this may have changed, I'll have to check further)

The Art of Problem Solving - The free videos and the AMC 8/10 info are probably the most useful to you right now.

posted by wiskunde at 12:55 PM on January 15, 2013 [5 favorites]

1. Do as much math as you can. Once you've read about a topic, try it. Try all of the practice problems as you can and check your work.

2. Learn to speak mathematics as well as do it. Learning to read exercises aloud can be very helpful in understanding math and it is great for communicating about math.

3. Try to do more than "practice this skill" exercises. Do problems that require you to combine your skills and to look at ideas in new ways. Math brain teasers and things like the American Mathematics Competition questions are likely a good place to start.

PurpleMath.com - practical algebra lessons

Math.com - Free lessons on a variety of topics

KhanAcademy - seems to be very good at teaching skills, but not always the reasoning behind skills (this may have changed, I'll have to check further)

The Art of Problem Solving - The free videos and the AMC 8/10 info are probably the most useful to you right now.

posted by wiskunde at 12:55 PM on January 15, 2013 [5 favorites]

A couple more ideas for you:

Pauk's Online Math Notes - These are probably a good supplement to something like Khan Academy. He starts with Algebra and goes through Calculus and Differential Equations. The notes have basic info and work through a few examples.

Once you have some algebra skills under your belt, I'd suggest taking a look at Polya's*How to Solve It*. I'd get it from the library, not purchase it, but it is excellent for structuring and thinking about problem solving.

Also, Common Errors in College Math - The Algebra Errors info might help. The page itself can be a bit much at once, but each section taken separately can be very helpful.

posted by wiskunde at 1:48 PM on January 15, 2013 [2 favorites]

Pauk's Online Math Notes - These are probably a good supplement to something like Khan Academy. He starts with Algebra and goes through Calculus and Differential Equations. The notes have basic info and work through a few examples.

Once you have some algebra skills under your belt, I'd suggest taking a look at Polya's

Also, Common Errors in College Math - The Algebra Errors info might help. The page itself can be a bit much at once, but each section taken separately can be very helpful.

posted by wiskunde at 1:48 PM on January 15, 2013 [2 favorites]

nthing khanacademy.org

posted by michellenoel at 2:19 PM on January 15, 2013

posted by michellenoel at 2:19 PM on January 15, 2013

This is me. I did this! You can too!

What made it all click for me was working through a GRE study guide. In the back it had a math summary/glossary type section of key terms and formulas. I memorized it, and it's been amazing. My GRE math score ended up not just being higher than my verbal (!), but objectively high. I got C's in honors math classes until I failed* Trig at community college one summer and just quit taking math altogether. Got a degree in fine art.

*I do mean fail. Not a C- or D, but an actual F. I was otherwise an "A" student...

Good luck!

posted by jrobin276 at 2:57 PM on January 15, 2013

What made it all click for me was working through a GRE study guide. In the back it had a math summary/glossary type section of key terms and formulas. I memorized it, and it's been amazing. My GRE math score ended up not just being higher than my verbal (!), but objectively high. I got C's in honors math classes until I failed* Trig at community college one summer and just quit taking math altogether. Got a degree in fine art.

*I do mean fail. Not a C- or D, but an actual F. I was otherwise an "A" student...

Good luck!

posted by jrobin276 at 2:57 PM on January 15, 2013

Keith Devlin's Coursera Course, Introduction to Mathematical Thinking might be useful to you. He's got an explanatory video on the page for the course, and here are some interviews.

posted by at at 10:04 PM on January 15, 2013 [1 favorite]

posted by at at 10:04 PM on January 15, 2013 [1 favorite]

... You are all honestly the best people. I really appreciate all of the help! I can't wait to get started, so I'm going to dive right in today! Thank you so, so much!

posted by Krazor at 11:08 AM on January 16, 2013

posted by Krazor at 11:08 AM on January 16, 2013

Err, I totally meant "GH Hardy's *A Mathematician's ***Apology**". Sorry for the confusions!

posted by wayland at 7:26 AM on January 27, 2013

posted by wayland at 7:26 AM on January 27, 2013

This thread is closed to new comments.

posted by wyzewoman at 10:18 AM on January 15, 2013