# I want to learn something new.

• SlammaJamma
In summary, the conversation is about a math/physics major who wants to teach themselves a new subject during their summer break. They have taken courses in vector analysis/calc III, linear algebra, and advanced calculus, and are looking for recommendations on what to study next. Suggestions are made for studying ODEs, differential geometry, or group theory. The advantages of starting to teach oneself ODEs before taking a course on it in the fall are also discussed. There is a disagreement about the quote "In mathematics, you don't understand things, you just get used to them", with one person believing it is true and the other not. It is also mentioned that some calculus courses may not cover the epsilon-delta notation for limits.
SlammaJamma
I'm a math/physics major, and I just finished my freshman year of college. I have almost 4 months off, so I decided I'd like to teach myself some subject in the realm of math. I've taken vector analysis/calc III, linear algebra, and advanced calculus.

Advanced calc. at my university is, as I understand it, supposed to be a somewhat rudimentary version of real analysis. We used Rudin's text (Principles of Mathematical Analysis), and went through chapter 6 (on integration), skipping sections liberally (ie, we completely ignored Lebesgue integration).

So, what would you recommend I do with myself? I'm looking for something interesting, that doesn't necessarily have to build on what I've already learned (chaos theory, I believe, is like this [am I right?]). I really enjoyed Calc III, so I was thinking about something like fluids, but I'm not sure if I have the background for that.

Any help would be appreciated, I have no idea where to start looking, what books to look into, etc.

Edit: I'll be taking probability and ODE (diff eq's) in the fall, if this is of any consequence.

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double post

Start studying those ODEs, they are the basis of mathematical physics.

How about differential geometry or group theory? Both have direct applications in physics, and both are very interesting in their own right.

- Warren

Crosson said:
Start studying those ODEs, they are the basis of mathematical physics.

Is there any advantage to start teaching myself ODE now? I figured there would be no point since I'm going to take the course in the fall.

chroot said:
How about differential geometry or group theory? Both have direct applications in physics, and both are very interesting in their own right.

- Warren

Sounds good, I'll look into those two.

Thanks for the responses, if anyone has any more ideas I would be grateful.

Is there any advantage to start teaching myself ODE now? I figured there would be no point since I'm going to take the course in the fall.

Advatage #1: You will get an easy A in your course and be able to concentrate on other studies.

Advantage #2: You will get a head start on learning something that would take many lifetimes to learn.

Advantage #3: You have already taken linear algebra. LA is a very elegant viewpoint from which to study linear differential equations, but this is angle is usually not explored in a first course on ODEs. If you begin studying ODEs now, by the time you actually take your course you will have a much more sophisticated perspective of what's going on in class.

Advantage #4: In mathematics, you don't understand things, you just get used to them (Von Neumann). So the sooner you expose yourself, even a little, the better off you are.

Crosson said:
In mathematics, you don't understand things, you just get used to them (Von Neumann).

I don't agree, but it seems that is certainly the philosophy behind math classes for non-science students. A friend of mine is taking "calculus for commerce", in which they don't even learn the delta epsilon notation for a limit. They are learning it a la "1/x^n goes really small when n is infinity, so let's call it zero!"

In mathematics, you don't understand things, you just get used to them (Von Neumann).

I think Neumann's quote is about how symbolic manipulation is at the root of what we call "understanding".

A friend of mine is taking "calculus for commerce", in which they don't even learn the delta epsilon notation for a limit.

The idea of a limit is directly useful to an economist, but the epsilon-delta formalism is only indirectly useful for increasing mathematical maturity. I think it is possible to understand limits without the epsilon delta notation. (As many great mathematicians did).

## 1. What are the benefits of learning something new?

Learning something new can have many benefits, including expanding your knowledge and skills, boosting your self-confidence, keeping your mind sharp, and providing new opportunities for personal and professional growth.

## 2. How can I find something new to learn?

There are many ways to find something new to learn. You can explore your interests and hobbies, take a class or course, join a club or group, or even try something completely out of your comfort zone. The key is to be open-minded and willing to try new things.

## 3. How can I stay motivated while learning something new?

Staying motivated while learning something new can be challenging, but there are a few strategies that can help. Setting specific goals, breaking the learning process into smaller, manageable tasks, and finding a support system or accountability partner can all help keep you motivated.

## 4. How long does it take to learn something new?

The time it takes to learn something new can vary greatly depending on the complexity of the topic and your individual learning style and abilities. Some skills may be picked up quickly, while others may take months or even years to master. The important thing is to be patient and persistent in your learning journey.

## 5. Can learning something new be intimidating?

Yes, learning something new can definitely be intimidating, especially if it is a completely new subject or skill. It's important to remember that it's okay to make mistakes and that learning is a process. Take it one step at a time, ask for help when needed, and celebrate your progress along the way.

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