1. Jul 23, 2004

### nerdygirl

Long story short: In college, I tried to major in the sciences, but couldn't cut it because of my weak math/logic background. I graduated with a liberal arts degree, but I promised myself that I would teach myself enough math and science to succeed in attaining a bachelor's degree in the sciences next time around. So, after a two month break, I've decided to start reviewing for precalculus again. Some background follows, skip to the last paragraph to get to the point.

Currently, the plan is to go all the way to graduate level real analysis because my fiancé is eventually going to get a Ph.D in math and specializing in real analysis. I want to know what he's studying, and what the hell he gets all excited about. I also want to master (at least) undergraduate level physics, because that's the science that gets me all excited. Technology gets me excited, too, but physics was my first love.

When I was a child, I did projects in basic physics, and I enjoyed that immensely. Unfortunately, my teachers, noting what a good writer I was, steered me into writing instead. While writing is a great skill that I take pride in, I do not get excited about it as much as I do about physics.

What do I plan to do with this? I'm not sure yet, but I have a few ideas. I'm going to get my master's degree in Library Science in a year or two, so maybe I can be a research librarian in the sciences.

Think back when you were a student . . . I predict that most of you taught yourselves quite a bit of what you know, at least at the beginning, and you were ahead of your peers because of that. What advice would you give to another self-taught wannabe in math and physics? I've already looked up advice on "how to read a math textbook." But sites, books, advice, and general experiences/anecdotes would be very appreciated.

2. Jul 23, 2004

### JohnDubYa

I think you need to concentrate on shoring up your math skills before anything.

I would be cautious about torturing yourself. If you are a weak mathematician, you will struggle to succeed in physics. So take math courses and see if you can develop a flair for the subject first.

3. Jul 23, 2004

### Jin314159

Speaking from my experience alone, I find it hard to teach yourself mathematics, especially in high level mathematics. Most math textbooks are rather concise, they will skip over implications and jump straight to conclusions, letting you figure out the steps in between.

I think the best way to learn math is through human interaction, either in a class room or through a tutor or friend. There are many different ways of understanding the same concepts in math. A book will generally present only one way. A person can present it in many different ways, hence deepening your understanding.

If you have a lot of trouble teaching yourself, maybe you should hire a tutor. If you're lucky enough to live around a big college campus, I'm sure you'll find plenty of starving math majors willing to help for as little as $15/hour. 4. Jul 24, 2004 ### Petrushka I agree with Jin. I found that as I took maths to higher levels, it became harder to teach myself the material but got on with it much better when it was taught to me by someone else. 5. Jul 24, 2004 ### nerdygirl I personally know two math graduate students, but neither of them are local, but I can still contact them with questions. I also know a couple of locals that are undergraduate math majors, so I can reach them as well. As a last resort, there's always the local math tutor for$20 an hour. But right now, the review material is going smoothly, because I'm reviewing the prerequisites for precalculus -- very easy stuff.

I always struggled in the math classroom because the teacher would tend to teach the faster people who caught on quickly in the classroom and left those of us with questions behind. My boyfriend told me that I asked questions that seemed simple to answer to me, but were actually quite difficult. Like, I'd end up asking questions that would take real analysis to adequately answer -- and I wouldn't understand the explanation because I wasn't equipped to handle real analysis! I have to accept that there are just some things that I have to assume are true until I get a real grasp on the why beyond the how. Does this make any sense to you guys?

6. Jul 24, 2004

### arildno

"I have to accept that there are just some things that I have to assume are true until I get a real grasp on the why beyond the how. Does this make any sense to you guys?"

What, in particular, are you thinking of?
In general, maths is the least esoterical science, in the sense that the students are taught truths/axioms which remain true even at a "higher" level.

However, you might occasionally encounter theorems which, in their full generality, are very difficult to prove, and hence, that proof is not given (even if proofs of special cases might be easy).
Is this close to what you had in mind?

7. Jul 24, 2004

Although I'm one of the better math students in my class, I know exactly what you are talking about when it comes to physical science. I couldn't handle the hybrid nature of the class, i.e., much information is explained, but much is still supposed to be taken as truth without any explanation or proof. For instance, I was taught that atoms can somehow "catch" energy and store it by bumping an electron to a bigger orbit. The atom can also release the energy by bringing the electron closer and kicking out a photon. That explanation was just fine and dandy for most of my classmates, but I have to understand every part of something completely before I am satisfied. Therefore I kept wondering how exactly an atom "catches" energy, how the heck moving an electron to a bigger orbit "stores" energy, where the photon comes from, etc. I once asked someone about it but was told that it was advanced chemistry or something. So you are not alone in being able to accept something as true but also having an insatiable appetite for an explanation of everything about it.

8. Jul 24, 2004

### gravenewworld

I'm not trying to burst your bubble or anything but teaching yourself precalculus is far from learning real analysis, even at the undergraduate level. For many math majors Advanced calculus is the hardest class they will take. Try to set reasonable goals for yourself, if you have not mastered basic calculus and algebra you will be disappointed later on. Advanced Calc is MUCH different than regular Calcululs I and II. Its when the real mathematics begins. You are not given problems to solve like in highschool algebra or Calc I and II, you are given statements that you must PROVE, which is much harder.

I believe it will take at least a year or more if you are highly motivated to lay the foundation before you can learn real analysis. Lay your foundation first with Basic differential and integral calculus, proceed then to multivariable calculus (calc 3), and some differential equations. The best course to take before you start doing upper level mathematics is Abstract algebra. From my experience, I believe Abstract algebra should be the first upper level course any math major should take. It teaches you to think abstractly (obviously) and learn how to use logical steps to prove a statement. So before you jump into real analysis, I would definitely recommend that you read an undergraduate book on abstract algebra.

9. Jul 24, 2004

### JohnDubYa

First rule: Don't blame the teachers.

10. Jul 24, 2004

### nerdygirl

Here's an example that popped right out of my head: Why does 1 + 1 = 2? Apparently that question wasn't answered until the early 20th century by Bertrand Russell, IIRC. Questions like that bother me.

11. Jul 24, 2004

### nerdygirl

Yes! That is exactly what I mean.

12. Jul 24, 2004

### nerdygirl

You edited out the part where I blamed myself for my overinquisitive mind. I didn't intend to blame the teachers for me asking too many questions that distract the class. I had some very good teachers in high school and college. If anything, I need to recall and accept the axioms better.

13. Jul 24, 2004

### Math Is Hard

Staff Emeritus
I am not sure I see the point in skipping the classes and teaching yourself the material. If you go back and get your B.S. in one of the sciences, won't you eventually have to take the math classes anyway?
At the universities I am familiar with, you need to take and pass single variable calculus (at the very least) just to enroll in some of the science courses. It's a pretty strict prerequisite.

14. Jul 24, 2004

### Integral

Staff Emeritus
I have BS degrees in both Physics and Math (they are separate degrees) so I have trod very nearly the road you are considering. If you concentrate on Real Analysis you will not be learning much that will complement your Physics math needs.

Generally in math and physics you will go multiple times through essentially the same material, each time through increases the level of detail and depth of understanding required. If you complete an upper division undergrad level Real Analysis course you will be able to understand and discuss RA with your Grad student boy friend. (Frankly I do not see this as adequate reason to spend \$ on college level course work,... is this a case of More dollars then cents?)

For Physics you really will only need a minimal understanding of RA, what you will need is Differential Equations (ODE and PDE) If your first love is Physics devote your time in Math to learn supporting skills such as Diff Eqs and Numerical Analysis.

15. Jul 24, 2004

### nerdygirl

That's an interesting thought. Perhaps I could major in Physics with a minor in mathematics. At the university my boyfriend is attending, you only need two more courses to create a math minor, and Real Analysis is a requirement in the minor. I haven't decided what university I'd go to, though, so it all depends. A lot of this college talk is just dreaming, am I allowed to dream aloud? I certainly hope so.

16. Jul 24, 2004

### nerdygirl

You make a good point. In my experience, a lot of people have prepared for some of the college introductory courses in high school or on their own. I suppose I could alter my plans a bit by only covering Calculus I and II on my own, studying a first year physics text, and taking AP tests to see how I did (and possibly get college credit.) What do you think about that?

17. Jul 25, 2004

### JohnDubYa

Shouldn't you marry him before letting his academic interests influence your own?

18. Jul 25, 2004

### nerdygirl

Shouldn't you marry him before letting his academic interests influence your own?

My first love is physics, and that's because of my own interests. If it were my boyfriend's choice, I would become a mathematician just like him. However, I'm not interested in doing that. I think majoring in Physics and minoring in math will satisfy my needs quite nicely. Afterwards, I can become either a) a university librarian for the physical sciences or b) a physicist. I haven't decided whether I want to put in the time and effort into getting a Ph.D. or not. Or, I may do both. I don't know.

19. Jul 25, 2004

### Math Is Hard

Staff Emeritus
You might want to consider auditing or visiting some classes if it's permitted. I do this sometimes to shop around for a good teacher in a class I plan to take later.

20. Jul 25, 2004

### hello3719

Uff, now teachers are like fruits. Can't wait till they modify them genetically.