Transitioning to Advanced Math

In summary, the conversation revolves around the difficulty of transitioning from elementary math to higher level math, specifically in complex analysis. The speaker, a high school senior, is seeking advice on how to successfully work through higher level math textbooks and prepare for a math major in college. They have taken AP Calculus BC but have been working with elementary math since then. The other person in the conversation suggests starting with a calculus book like Spivak or Apostol, followed by abstract algebra and linear algebra, before attempting complex analysis. They also recommend using the Khan Academy as a resource.
  • #1
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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. :smile:
 
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  • #2
Site said:
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. :smile:

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?
 
  • #3
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?
 
  • #4
Site said:
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).
 
  • #5
Thank you, micromass--your post is very enlightening. I will definitely get the books you mentioned and try my best to work through them!
 
  • #6
the khan academy provides a good overview
 

1. What is Advanced Math?

Advanced Math, also known as Higher Mathematics, is a branch of mathematics that deals with more abstract and complex concepts such as calculus, linear algebra, and differential equations. It is typically studied at the college level and is essential for many fields such as physics, engineering, and computer science.

2. How do I know if I am ready to transition to Advanced Math?

If you have a strong foundation in basic math concepts such as algebra and geometry, and you enjoy solving challenging problems and working with abstract concepts, you may be ready to transition to Advanced Math. It is also helpful to have a good grasp of logic and critical thinking skills.

3. What are the benefits of studying Advanced Math?

Studying Advanced Math can improve your problem-solving skills, critical thinking abilities, and analytical reasoning. It can also open up many career opportunities in fields such as science, technology, and finance. Additionally, it can help you develop a deeper understanding and appreciation for the beauty and complexity of mathematics.

4. How can I prepare for Advanced Math?

To prepare for Advanced Math, it is important to have a strong foundation in basic math concepts. You can also practice solving challenging problems and puzzles, as well as developing your critical thinking skills. Additionally, familiarizing yourself with the fundamental concepts and formulas of Advanced Math can help you transition more smoothly.

5. What are some tips for success in Advanced Math?

Some tips for success in Advanced Math include practicing consistently, seeking help from teachers or tutors when needed, staying organized and on top of assignments, and actively participating in class discussions. Additionally, it is important to approach each problem with patience, persistence, and a willingness to learn from mistakes.

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