# I still KNOW the quadratic equation, just not what it means

October 19, 2011 8:37 AM Subscribe

I have forgotten basically all of math, and I want to learn it again from the ground up.

While attempting to prep for the GRE, I realized that I have really lost my entire math background. I was extremely frustrated by trying to do the exercises in my GRE book, because I've forgotten even the little things from, like, 7th grade algebra that I used to take for granted I knew.

The thing is, I actually used to be pretty good at math- I did two years of AP Calculus in high school and did, well, ok at it- but I then placed out of college math with my AP scores and never did math again. Now it's been five or six years and I can't so much as add fractions or remember what the purpose of the quadratic equation is. I couldn't even remember the formula for the diameter of a circle until I looked it up, for cripe's sake.

This isn't just about prepping for the GRE. As I was struggling with my GRE book, I realized that I actually LIKED math, and I'm sad that I've forgotten it. It's like I forgot a language I used to know, or something. (I

SO. I would like to completely reboot my math knowledge, starting with the absolute most basic stuff (like, arithmetic basic) and moving up at my own pace until I can do at least basic calculus again. Ideally I would have access to LOTS of problems with available answers, so that I could spend as much time as I needed on a particular topic. I expect I'll advance through the basic stuff pretty speedily, and then take my time with the more advanced stuff.

What is the best resource or resources for this? And have any of you guys ever tried to do this before, after such a gap? How was it?

While attempting to prep for the GRE, I realized that I have really lost my entire math background. I was extremely frustrated by trying to do the exercises in my GRE book, because I've forgotten even the little things from, like, 7th grade algebra that I used to take for granted I knew.

The thing is, I actually used to be pretty good at math- I did two years of AP Calculus in high school and did, well, ok at it- but I then placed out of college math with my AP scores and never did math again. Now it's been five or six years and I can't so much as add fractions or remember what the purpose of the quadratic equation is. I couldn't even remember the formula for the diameter of a circle until I looked it up, for cripe's sake.

This isn't just about prepping for the GRE. As I was struggling with my GRE book, I realized that I actually LIKED math, and I'm sad that I've forgotten it. It's like I forgot a language I used to know, or something. (I

*thought*I didn't like it while I was in school, but that was mostly because I had an hour of math class and an hour of math homework every single day, which burned me out.)

SO. I would like to completely reboot my math knowledge, starting with the absolute most basic stuff (like, arithmetic basic) and moving up at my own pace until I can do at least basic calculus again. Ideally I would have access to LOTS of problems with available answers, so that I could spend as much time as I needed on a particular topic. I expect I'll advance through the basic stuff pretty speedily, and then take my time with the more advanced stuff.

What is the best resource or resources for this? And have any of you guys ever tried to do this before, after such a gap? How was it?

For the purpose of the GRE, focus on nothing more than geometry.

posted by k8t at 8:40 AM on October 19, 2011

posted by k8t at 8:40 AM on October 19, 2011

*It might be fun to start with Euclid.*

It might not be. Euclid isn't exactly readable.

posted by madcaptenor at 8:49 AM on October 19, 2011 [3 favorites]

*This isn't just about prepping for the GRE.*

Don't think you can kill two birds with one stone here. Trying to learn math from scratch probably isn't going to help a lot with the GRE (counterintuitive as that may seem.) As horrible as it sounds, you're best off studying GRE math problems if you want to do well on the GRE.

posted by ennui.bz at 8:56 AM on October 19, 2011

That's funny because I just started doing the exact same thing. I used to do multivariable calculus for breakfast and now I have trouble adding numbers.

Another vote for Khan Academy, I just started going through the videos and they are well done.

UH has posted reference materials, the Fundamentals of Math textbook is free to download as a pdf.

A couple other universities with free online masterial:

MIT

Berkeley

I have a wonderful history of math and its development book at home, though I can't remember the name. I'll try to post it later but if I forget feel free to MeMail me.

posted by beowulf573 at 8:57 AM on October 19, 2011 [6 favorites]

Another vote for Khan Academy, I just started going through the videos and they are well done.

UH has posted reference materials, the Fundamentals of Math textbook is free to download as a pdf.

A couple other universities with free online masterial:

MIT

Berkeley

I have a wonderful history of math and its development book at home, though I can't remember the name. I'll try to post it later but if I forget feel free to MeMail me.

posted by beowulf573 at 8:57 AM on October 19, 2011 [6 favorites]

Nthing Khan. It is awesome.

posted by roomthreeseventeen at 9:00 AM on October 19, 2011

posted by roomthreeseventeen at 9:00 AM on October 19, 2011

Is your book not walking you through the problems? Maybe get another book. I grew up hating math and through studying for the GRE actually came to enjoy it. When we got to math-related classes in grad school, I really enjoyed it.

Separate GRE study from math study. For the latter, I'd look into offerings at your local community college.

posted by amanda at 9:00 AM on October 19, 2011

Separate GRE study from math study. For the latter, I'd look into offerings at your local community college.

posted by amanda at 9:00 AM on October 19, 2011

Oh, I should also mention that grad school is a long way away for me. I was thinking of taking the GRE just because I'm (sort of) fresh out of school, but I doubt I'll even apply to grad schools for at least another couple years. This really is mostly about relearning math for the sake of it.

posted by showbiz_liz at 9:10 AM on October 19, 2011

posted by showbiz_liz at 9:10 AM on October 19, 2011

I know it's already mentioned in 4/5 of the answers (look, a non-cooking application of fractions in real life!), but since your story sounded exactly like my experience recently (without the GRE as the origin), I've got to come in here to suggest again that the Khan Academy is where you want to start.

I'm guessing that my time away from the math trenches was longer than yours (gifted math/science program in high school, took a Calc class to get an easy credit in college, but that all ended in '94) and I found the videos/exercises at Khan Academy exactly the place to start -- both the algebra/geometry questions/exercises as review/re-learning and the Calc videos to jog my memory helped out and after a couple of months just messing around with that, I think I'm already back to knowing more about math than I did previously. The MIT and Berkeley stuff, which I must have seen recommended here as well, is also helpful, but I think you'll find there's tons of stuff on the web to learn once you get the fundamentals back under your belt.

Good luck. (I'm always glad to find the non-mathematician who thinks math can be fun; after being told forever that it was something I should do because I was good at it, I rebelled to the English department as a kid, and though there's no regrets with that, I'm glad to have rediscovered that part of my brain. I always did better in my writing workshops when I was also taking a Computer Science class that term, and I can't believe it's taken me 15 years to realize that's one of those "liberal arts college lessons" I could apply to the rest of my life.)

posted by MCMikeNamara at 9:15 AM on October 19, 2011

*And have any of you guys ever tried to do this before, after such a gap? How was it?*I'm guessing that my time away from the math trenches was longer than yours (gifted math/science program in high school, took a Calc class to get an easy credit in college, but that all ended in '94) and I found the videos/exercises at Khan Academy exactly the place to start -- both the algebra/geometry questions/exercises as review/re-learning and the Calc videos to jog my memory helped out and after a couple of months just messing around with that, I think I'm already back to knowing more about math than I did previously. The MIT and Berkeley stuff, which I must have seen recommended here as well, is also helpful, but I think you'll find there's tons of stuff on the web to learn once you get the fundamentals back under your belt.

Good luck. (I'm always glad to find the non-mathematician who thinks math can be fun; after being told forever that it was something I should do because I was good at it, I rebelled to the English department as a kid, and though there's no regrets with that, I'm glad to have rediscovered that part of my brain. I always did better in my writing workshops when I was also taking a Computer Science class that term, and I can't believe it's taken me 15 years to realize that's one of those "liberal arts college lessons" I could apply to the rest of my life.)

posted by MCMikeNamara at 9:15 AM on October 19, 2011

At the beginning of 2010, Steven Strogatz, a professor of applied mathematics at Cornell, wrote a weekly column in 15 installments for the New York Times that I thought was really wonderful. It went back through the basics of math and discussed concepts in ways I'd never thought of before, so it might be a good starting place for you:

1. From Fish to Infinity

2. Rock Groups

3. The Enemy of My Enemy

4. Divisions and Its Discontents

5. The Joy of X

6. Finding Your Roots

7. Think Globally

8. Power Tools

9. Take It to the Limit

10. Change We Can Believe In

11. It Slices, It Dices

12. Chances Are

13. Group Think

14. The Hilbert Hotel

Also, at the end of each of the columns, he provided some great resources to explore that week's topic some more.

posted by shiu mai baby at 9:19 AM on October 19, 2011 [61 favorites]

1. From Fish to Infinity

2. Rock Groups

3. The Enemy of My Enemy

4. Divisions and Its Discontents

5. The Joy of X

6. Finding Your Roots

7. Think Globally

8. Power Tools

9. Take It to the Limit

10. Change We Can Believe In

11. It Slices, It Dices

12. Chances Are

13. Group Think

14. The Hilbert Hotel

Also, at the end of each of the columns, he provided some great resources to explore that week's topic some more.

posted by shiu mai baby at 9:19 AM on October 19, 2011 [61 favorites]

Oh, FFS, it's 14 installments. Obviously. Hilarious irony, how I adore thee.

posted by shiu mai baby at 9:20 AM on October 19, 2011 [3 favorites]

posted by shiu mai baby at 9:20 AM on October 19, 2011 [3 favorites]

The good thing is that you don't have to learn it again from the ground up. You need to reacquaint yourself with it.

It is too huge a field to be good at it all. Even a thorough topical survey could take you the better part of your remaining life.

It's just a specialized vocabulary, notations, and processes.

Do you want to teach yourself? Do you have a friend with some expertise who likes to share? Surely there's an engineer, chemist, programmer, math teacher, financial quant in your posse? A mentor is an awfully useful thing to have around. Much better than a recommended reading list, IMO.

Do you just want not to feel mathematically ignorant? If so, because the field is so huge, get ready for a lifelong fight. Feeling inept comes with the territory and never really goes away. Hell, even when I manage to reason something out and get the right answer, I often ascribe it to blind luck, just out of habit.

One thing... if you attain ANY competence in ANY portion of math, you'll find yourself in a minority among your cohort. Innumeracy is epidemic.

posted by FauxScot at 9:40 AM on October 19, 2011 [1 favorite]

It is too huge a field to be good at it all. Even a thorough topical survey could take you the better part of your remaining life.

It's just a specialized vocabulary, notations, and processes.

Do you want to teach yourself? Do you have a friend with some expertise who likes to share? Surely there's an engineer, chemist, programmer, math teacher, financial quant in your posse? A mentor is an awfully useful thing to have around. Much better than a recommended reading list, IMO.

Do you just want not to feel mathematically ignorant? If so, because the field is so huge, get ready for a lifelong fight. Feeling inept comes with the territory and never really goes away. Hell, even when I manage to reason something out and get the right answer, I often ascribe it to blind luck, just out of habit.

One thing... if you attain ANY competence in ANY portion of math, you'll find yourself in a minority among your cohort. Innumeracy is epidemic.

posted by FauxScot at 9:40 AM on October 19, 2011 [1 favorite]

Get a college algebra textbook. If your local library doesn't have one, you can easily find older versions of textbooks on Amazon for $5 or less. Start on page 1, don't assume that you understand something unless you prove it to yourself by doing the exercises, and by the end of the book you'll know algebra.

Then buy a precalculus textbook. Then buy a calculus textbook.

The videos that other people are recommending are good, but they can easily make you feel like you've attained a higher level of understanding than you actually have. Even the teachers that made those videos still have their students use textbooks.

posted by Soilcreep at 10:03 AM on October 19, 2011 [3 favorites]

Then buy a precalculus textbook. Then buy a calculus textbook.

The videos that other people are recommending are good, but they can easily make you feel like you've attained a higher level of understanding than you actually have. Even the teachers that made those videos still have their students use textbooks.

posted by Soilcreep at 10:03 AM on October 19, 2011 [3 favorites]

I did this.

When I took calculus I after 8 years without math, my math skills had seriously atrophied. I had to reteach myself, starting at algebra and working my way back up. To do this, I worked through an algebra book. I passed the course, and then went another two years without math before deciding to go to graduate school. I did the whole thing again while preparing for the GRE. I began by working GRE problems until I understood the areas I needed to work on, and then went back and worked on those areas. The whole process took about 6 months. I ended up getting a perfect math score, so it's totally possible to do very well and catch yourself back up despite a spotty math background.

posted by zug at 10:08 AM on October 19, 2011 [3 favorites]

When I took calculus I after 8 years without math, my math skills had seriously atrophied. I had to reteach myself, starting at algebra and working my way back up. To do this, I worked through an algebra book. I passed the course, and then went another two years without math before deciding to go to graduate school. I did the whole thing again while preparing for the GRE. I began by working GRE problems until I understood the areas I needed to work on, and then went back and worked on those areas. The whole process took about 6 months. I ended up getting a perfect math score, so it's totally possible to do very well and catch yourself back up despite a spotty math background.

posted by zug at 10:08 AM on October 19, 2011 [3 favorites]

I went about this half-assedly recently but can strongly recommend Forgotten Algebra. I took this book and my sticker-covered math notebook with me on vacation to Florida and did math in the hotel room and on the plane, because math is FUN!!! The author also wrote Forgotten Calculus which looks to be equally highly reviewed.

posted by jabes at 10:47 AM on October 19, 2011 [4 favorites]

posted by jabes at 10:47 AM on October 19, 2011 [4 favorites]

I was in your situation a few years ago and found this book extremely helpful as a first step.

posted by pete_22 at 10:48 AM on October 19, 2011

posted by pete_22 at 10:48 AM on October 19, 2011

If your life is busy and you find the auto didactic route to be arduous and tough to maintain, consider an affordable course at your local community college. It's amazing what structure can do for reaching goals.

posted by stroke_count at 11:21 AM on October 19, 2011

posted by stroke_count at 11:21 AM on October 19, 2011

Again, Khan Academy. I'm an attorney that, like MANY others, got into law because my liberal arts background wasn't going to get me paid otherwise. I've long been kind of ashamed of my lack of math skills, and have been doing Khan Academy stuff for the past 3 months or so with the ultimate goal of taking the Fundamentals of Engineering exam followed by (and in order to take) the Patent Bar exam. I'm up into Trigonometry now, and I'm absolutely addicted to the site. Can I brag that I have nearly 1 million "energy points"?

posted by holterbarbour at 4:24 PM on October 19, 2011 [5 favorites]

posted by holterbarbour at 4:24 PM on October 19, 2011 [5 favorites]

*It might be fun to start with Euclid.*

It might not be. Euclid isn't exactly readable.

It might not be. Euclid isn't exactly readable.

I totally disagree with this. Euclid is actually awesome to work through if you start from the beginning and work through each and every proof.

However, I doubt that will meet your needs, OP, as well as Khan Academy.

posted by pupstocks at 5:36 PM on October 19, 2011

For a great overview of the history and development of math, I recommend Mathematics: From the Birth of Numbers.

posted by beowulf573 at 8:02 PM on October 19, 2011 [2 favorites]

posted by beowulf573 at 8:02 PM on October 19, 2011 [2 favorites]

I'm also embarrassed at my lack of math skills, and I'm currently working through college textbooks that I bought on Amazon for a penny. Started with College Albgebra, moved on to trig, and plan to continue with basic calculus.

I would like to point out that if you choose to get textbooks, try and find ones that have companion student-solutions manuals for the odd problems. This gives you more feedback then just the pure answers printed in the back of the textbook, and also helps you determine where you took a wrong turn when solving the problem.

posted by crLLC at 7:38 AM on October 20, 2011 [2 favorites]

I would like to point out that if you choose to get textbooks, try and find ones that have companion student-solutions manuals for the odd problems. This gives you more feedback then just the pure answers printed in the back of the textbook, and also helps you determine where you took a wrong turn when solving the problem.

posted by crLLC at 7:38 AM on October 20, 2011 [2 favorites]

*Ideally I would have access to LOTS of problems with available answers, so that I could spend as much time as I needed on a particular topic.*

I really like Schaum's Outlines for this. They're pretty dry, but they do have tons of problems. The answers are given for all problems, and the worked solutions are provided for about half of the problems. My local library system carries a lot of Schaum's Outlines, so I don't even have to buy them.

They go all the way from Elementary Mathematics to really complex stuff. There's over 200 different math/chem/physics outlines available. A much smaller subset of these are available on the Kindle, and they're pretty cheap. Most less than $10.

posted by marsha56 at 4:03 PM on October 20, 2011

Let me recommend Precalculus Mathematics in a Nutshell. All content, no cruft. Avoid traditional textbooks, they're designed by committee to meet school district requirements, and therefore contain tons of repetitive filler.

posted by leotrotsky at 4:50 PM on October 24, 2011 [1 favorite]

posted by leotrotsky at 4:50 PM on October 24, 2011 [1 favorite]

*Oh, FFS, it's 14 installments.*

Thanks for this list of articles ("Steven Strogatz on the Elements of Math" series), shiu mai baby; they look good!

BTW, it actually is 15 installments. Square Dancing falls in between 6 & 7 of your list.

This page links to all 15.

posted by agog at 1:27 PM on October 26, 2011 [2 favorites]

This is late, but I am doing this right now myself. Goal is to test into Calculus at my local community college and eventually take Computer Science courses.

Started with a high school Algebra text that I downloaded onto my iPad. Done with that, and now doing Geometry videos on Khan. I also found a Trig and Precalculus textbook at a garage sale for 50 cents, so I just ordered the companion study guide and problem answer set books for it. I haven't been the most diligent about studying lately, (I blame the Occupy movement), butitnhas been incredibly satisfying on a personal level.

I find it good to establish a structure for studying. I have a lot of free Starbucks drink coupons, because format while there, I went there every night after work to study before heading home.

posted by spinifex23 at 10:50 AM on December 4, 2011

Started with a high school Algebra text that I downloaded onto my iPad. Done with that, and now doing Geometry videos on Khan. I also found a Trig and Precalculus textbook at a garage sale for 50 cents, so I just ordered the companion study guide and problem answer set books for it. I haven't been the most diligent about studying lately, (I blame the Occupy movement), butitnhas been incredibly satisfying on a personal level.

I find it good to establish a structure for studying. I have a lot of free Starbucks drink coupons, because format while there, I went there every night after work to study before heading home.

posted by spinifex23 at 10:50 AM on December 4, 2011

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posted by mskyle at 8:39 AM on October 19, 2011 [18 favorites]