Transitioning to Advanced Math

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So far I've been working elementary math problems where the main focus is on creative ideas. I want to up my game but I find it hard to get past the first few chapters of more advanced books because they seem so daunting. For example, I wanted to get a foundation for complex analysis and learn to tackle some hard problems, so I purchased Complex Numbers from A to Z. But immediately I was bombarded by a ton of formulas and very dense notation. It was hard to see through to the underlying concepts with all the rigor and formality.

I would love to major in math in college. How can I get over this hump and be able to successfully work through higher level math textbooks? All tips are appreciated.

 

[chiro]

So far I've been working elementary math problems where the main focus is on creative ideas. I want to up my game but I find it hard to get past the first few chapters of more advanced books because they seem so daunting. For example, I wanted to get a foundation for complex analysis and learn to tackle some hard problems, so I purchased Complex Numbers from A to Z. But immediately I was bombarded by a ton of formulas and very dense notation. It was hard to see through to the underlying concepts with all the rigor and formality.

I would love to major in math in college. How can I get over this hump and be able to successfully work through higher level math textbooks? All tips are appreciated.

Hey Site and welcome to the forums.

Are you currently doing a degree or is all of this self-study?

If you are studying a degree, your main lecturer should really outline what all of this is about early on if they are good.

I am a math major, but I haven't done Complex Analysis yet, but my educated guess is that it is the transition of calculus to include functions that are complex. For this reason it is required (or strongly recommended) that you have a good solid real analysis background to build from.

Chances are if you understand the real analysis very well, the transition to complex analysis will be more straightforward than if you did not.

What is your current level of understanding of ordinary real variable (single, and multivariable) calculus?

 

[Site]

I'm a high school senior right now and I'm trying to get a head start on higher math before heading to college. My calculus isn't great--I took AP Calculus BC last year but since then I've been working with elementary math. Would it be a good idea to try a real analysis book like Rudin?

 

[micromass]

I'm a high school senior right now and I'm trying to get a head start on higher math before heading to college. My calculus isn't great--I took AP Calculus BC last year but since then I've been working with elementary math. Would it be a good idea to try a real analysis book like Rudin?

No, don't try Rudin. And you're way to inexperienced to even touch complex analysis! Real analysis and complex analysis are really difficult and require a lot of prerequisites. Also, they require a lot of mathematical maturity!

If you want to study math, then you'll have to do the very basics first. What I recommend is that you read the following books:

- A calculus book like Spivak or Apostol (yes, you already did calculus, but Spivak and Apostol are more of an intermediate step before doing real analysis)

- Abstract algebra. For example: "a book on abstract algebra" by Pinter

- Linear algebra. Try "linear algebra" by Friedberg. Supplement it with Schaum's outline on linear algebra.

Begin with studying these things. If you done them (and if you understood them well!), then perhaps complex analysis is within your grasp (depending on which book you're looking at).

 

[Site]

Thank you, micromass--your post is very enlightening. I will definitely get the books you mentioned and try my best to work through them!

 

[bangthatdrum]

the khan academy provides a good overview