How do I Get Better at Math?

In My Humble Opinion
1

I’m a college sophomore who’s had very little math - two semesters of high school algebra, one semester of useless college algebra (or: “How To Use a Few TI83 Functions”), and a little self-taught plane geometry/trigonometry.

Math really does interest me, it’s just that I’m terrible at it. I’m taking an elementary calculus course right now that’s causing me some small trouble - partly because I haven’t had much math, and partly because the course is not taught to the common denominator (and has a very, very high dropout rate).

If I wanted to continue learning about calculus and higher maths, what should I know and how should I find it out? Can anybody recommend books, especially to flesh out algebra skillz? Things like absolute value, powers and roots are just … confoosink me.

2

I can’t reccomend any US books (UK doper here), but I find that the UK A-Level (age 18) introductory calculus revision guides are superb. If you can find a ‘Dictionary of Mathematics’ anywhere in the US (sorry about the non-US help) they are EXTREMELY useful, especially for derivative and integral tables.

As for getting better at maths in general, I’m afraid there’s nothing for it but hard work! You need to find a book with HUNDREDS of calculus problems in it and work through it, there really is no other way, sorry. Once you’ve mastered integrating/differentiating polynomials, trig functions, products of functions, etc., you’ll find the rest becomes easier.

Link-

http://mathworld.wolfram.com/

Any specific problems, e-mail me (through my profile) and I’ll do my (final year of BSc Maths + Stats with Physics) best to help!

3

As with most fields of study the more complex buids on the simpler concepts. In math this is especially true. Before you can tackle calculus and the like effectively you need to have a good handle on the earlier bits such as algebra. If I were you I would go back and polish my algebra skills to a shine. If you don’t have your old textbooks handy just go to Amazon or a local bookstore and get some algebra books to work through…lots out there to choose from.

4

When I first had to really use absolute value functions and greater than/less than equations in analysis I got all tripped up, too. I had breezed through math all throughout school until I hit pre-calc (math analysis we called it, but whatever, same dealie) and then WHAMMO it was time to apply everything I thought I had been learning all this time. But wasn’t.

I wish I remember what I did, because my quarter and final grades took a very nice path: F, D, mid-term:D, B, A, final: A. So I taught myself the math at some point in there. Went on to get a 98% in calc I and II the next year. Good stuff.

I do remember just working out the problems, 1-whatever was in the book and forget about the assignment. I mean, whatever the assignment was, it was in there somewhere, I just turned it all in. And I went back to work over problems from topics we had already covered and I screwed up. Just kept doing them, looking at the examples at first and trying to handle the other problems without looking at them as time went on.

IMHO, after algebra two and trig, math gets conceptual really quick. Sure, there are still “formulas” and such, but they aren’t just plug and play anymore, you have to be able to manipulate equations to get them to do anything, and you have to sort of understand why you’re manipulating them the way you do. And I found that when I did understand what I was doing, knowing any formulas was sort of a moot point. The equations started solving themselves.

So I never used any of those “teach yourself math” books that I’ve seen at borders. The math books I had worked well enough, but it was definitely a labor of love. And it also helped me understand how to read math books, too, which I later applied to teaching myself first order linear differential equations just for fun.

Yeah, I’m sick.

So, long story short, if you really do like math but just can’t seem to do it, maybe it is your methodology that’s all wrong. A teacher can only do so much, IMO. From there on out it is you that has to do the rest.

Has anyone else any experience with these “teach yourself calculus” books or anything? I’ve honestly never looked at them, but if they are anything like the other teach yourself books they seem to gloss over important points that only a textbook can really offer (though on its terms, ugh!).

5

College campuses usually have a used bookstore nearby. Check them out for old (and relatively inexpensive) textbooks. Similarly, a local Goodwill or donation-based store might have what you’re looking for.

You could also solicit the aid of a tutor. Your student services center may offer such a program. If not, you’re still free to advertise for and hire someone to help you.

You have the interest, and that’s what’ll get you through this funk. Good luck.

6

Find the highest level of math you’re comfortable with - if you’re having trouble with calculus, start with the most basic stuff, like simplfying linear functions - and then follow my Universal Math Learning Plan:

  1. Practice,

  2. Practice,

  3. Practice,

and

  1. Practice.

Get whatever books and resources you can with practice problems and do ALL of them.

If you can find a tutor for a few sessions to get you started that’s great, but the real key is practice. Do hundreds of problems.

I have a stack of practice problems I’ve drawn up for Mrs. RickJay, who’s strugglign thru the same thing. E-mail me if you want some.

7

Although this isn’t exactly the kind of advice you asked for, and although it contradicts erislover somewhat, I’d like to say this: use all of the resources available to you in the courses you’re taking now. And by “resources”, I mean “people”. Didn’t understand the homework? Find the TA, pin him down, and ask questions until you do. Still don’t quite follow the technique that was just explained in the lectures? Look up the professor’s office hours, show up during those office hours, and don’t leave the office until you do understand the technique (or until the professor turns out the lights and flees). Can’t show up during the office hours because of a scheduling conflict? Contact the prof and make an appointment for a better time. Don’t worry about being an inconvenience to them; it’s the job of the instructors to help you understand the material, so make them do their jobs.

I know that sounds incredibly obvious…heck, you’re quite possibly doing all of that already…but I just spent the last four months as an instructor for a second-year calculus course, and despite the fact that some students clearly had a very weak understanding of the material, I still spent 95% percent of my office hours twiddling my thumbs and I received requests for appointments outside my office hours maybe three times in total. (And I got fairly decent reviews from my students, so I’m hopefully not too presumtuous when I say that I wasn’t the reason for the poor attendance :slight_smile: )

In the worst-case scenario, when your prof and TA’s are fargin’ bastiches and not worth the skin they’re wrapped in, find a bright upper-year student who’s already passed the course and ask them for help. Bribe them if you have to. Beer would probably work well here.

Camping on people’s doors like this is a bit of work, but if you enjoy the material (and it sounds like you do) then it should be worth the effort. And it sure beats frustration.

8

Thanks for the help so far. I’ve used a book - Geometry and Trigonometry for Calculus, Peter H. Selby - to teach myself a bit from those subjects. While it seems pretty user-friendly, I really haven’t had a chance yet to do anything with what I’ve learned.

Perhaps one of you could help with something I don’t understand.

[-abs(-3 + x) - -abs(-3)] / x = 1

[-abs(3 + x) - -abs(3)] / x = -1

Why does the first expression seem to simplify into x / x , and the second into -x / x? Does the negative three make the positive x negative, somehow, before taking the absolute value? I just don’t understand this.

9

I had a methodology that worked great for me albeit I stumbled upon it by accident.

I only got as far as algebra in high school. I wasn’t destined for any math heavy jobs and already knew it so I wasn’t concerned. Once in college I took an Astronomy class to get rid of a science requirement and because I like Astronomy. Unfortunately they started throwing math at me in the pre-calc to calculus range and I had NEVER seen that stuff before!

I was having a helluva time so I decided to cheat. I had an extremely advanced calculator (for the time) that could be programmed using Basic programming language (it had a tiny keyboard and all). This was before professors were wise to such devices as such things were still quite new and rare (the handheld variety at least).

I proceeded to program my calculator for all the upcoming problems that were to be on the next test. Of course I didn’t know the details of the problems so I had to program my machine to solve for any variable in a variety of different equations. Worked great…very cool.

Along comes the test and to my surprise I knew the material so well that I didn’t even run my program as it was faster to manually enter the stuff as a normal calculator (which was allowed to be used for the test). My program worked great but it was admittedly clunky and not too speedy. I finished so fast that I was the first to turn in my test. I actually sat there as I figured I couldn’t possibly have done it that fast and reviewed the test twice…I was still first in. Got a 98% on that test!

It turns out in my attempt to cheat I had taught myself all I needed to know for that test. By trying to program my calculator to solve for all variables I had to understand what it was I was programming and thus unintentionally taught myself the material REALLY well…surprised the hell out of me but I was overall pleased at the final result.

I’m not syaing programming calculators (or computers) is right for you (and certainly not cheating) but cast about for whatever it is that helps you work the problems. Maybe some ‘practical’ math books that apply what is being taught to some real-world problem. I don’t know…whatever works for you but you might think about it.

10

You mentioned Calculus.

Nowadays, most textbooks are programmed instruction, more or less.

Ch 1 Limit
Ch 2 Continuity
Ch 3 Differentiation
Ch 4 Application of Derivatives
Ch 5 Basic Integration
…

Now, this is kinda expected since that is the accepted order in teaching calculus (one exception is Apostol).

But, if you’re looking for books that speak in layman terms or have a lucid way of explaining, look at Thompson/Gardner or Spivak

Although, this might be getting ahead.

11

I agree with Tuco for I am in the same boat as the OP, and was thinking of opening a thread on this myself. I had to drop out of my calculus class because I was attempting the class during a compressed summer session. With four nights weekly of class I had too little time to study for the exams, and as Tuco says, practice. The funny thing was, I seemed to be able to follow the lectures completely, so that I expected to be able to sit down and crank out 10 correct test answers with no trouble. And not having had Trig before didn’t seem to be too much of a hurdle, since it was pretty much the case that if you could just memorize the 30-60-90 triangle, you were set.

As things turned out, my first test was so-so, my second test was worse, and I never went back to see how my third test turned out.

At that time my project at my job kicked into high gear so I realized I had to give up the calculus for now. But I do plan to try again when I have a chance, during a regular semester.

12

For starters, neither of those two equations are true for all x, only for some x. So you’re right to be concerned!

Remember the definition: abs(y) is equal to y if y >= 0, and is equal to -y if y < 0. So if you want to simplify an expression that contains abs(-3+x) (for example), it will simplify differently if -3+x >=0 than it will if -3+x < 0. You have to treat those two possibilities as different cases. Hope that helps…

13

erislover, I think I speak on behalf of everyone everywhere who has ever taught a course when I say that if all students were that dedicated, our job would be a lot easier. And I’ll also agree with Math Geek’s comments about using all resources. It’s not unlikely that your professors and TAs are literally sitting around bored, waiting for people to come to office hours. They’ll be glad to see you.

And Whack-a-Mole:

Now that professors are wise to such devices, the usual reaction is to just allow them. As one of my physics professors put it, in the real world, nobody’s going to lock you in a room without your books and make you do physics. Likewise, nobody’s going to lock you in a room without your calculator and make you do math. It’s a tool: Why not allow it?

14

You can allow it, but don’t create a calculator culture.

Use calculators for solving unmanageable equations, but not to solve something that can be done just as easily on paper. The aim is to impart some basic calculation and data & time management skills. The overabundance and usage of calculators means that even for trivial equations, I’ve seen some classmates use calculators.

15

This was exactly my take on the issue when any number of math teachers I had forbade electronic calculating devices. Come hell or high water they were determined to have me memorize the multiplication tables!

Anyway, calculators are fair enough on a math test…especially more advanced math such as calculus and beyond…plenty to concern the student beyond the basic arithmetic portion of their problem. However, do professors today consider that such devices can act as crib sheets? No need to write on the bottom of your shoe or up your forearm when you can input a veritable library in your PDA. Heck…I could even have my PDA attached wirelessly to the web and seek answers that way or communicate with a math grad student via instant messenger for help. The possibilities for cheating these days are astounding.

16

There are plenty of online resources, of course. In my opinion the best is Drexel’s Mathforum ( http://www.mathforum.org ). Especially Ask Dr. Math, (their FAQ alone covers 90% of the recurring math questions seen on the SDMB). You can get help with specific problems and they have links to other good sites, too.

17

Since you’re looking for advice, I’ll move this thread to IMHO.

18

Work lots of problems and proofs.

Try to put some time in on your course work every day. I found mathematics is best digested in small chunck because you really have to think about stuff.

Good luck.

19

Sorry to go off topic, but I had an Organic Chem teacher who actually encouraged people to create cheat sheets. If you got caught using one you were dead, but if you turned it in before the test he would grade it on its completeness and size and award extra points (max 5) to your test score. He said it was for the exact same reason that you said: in the course of creating the cheat sheet, condensing it, revising it, writing and re-writing it (they had to be done by hand), you actually learned the material.

20

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