Self-Teaching Math Sequence: How to Build Strong Foundation?

In summary, it sounds like you're new to the world of mathematics and you're unsure of where to start. Studying any kind of math will help you think better, but you should focus on the kinds of math that are relevant to your area of study.
  • #1
jsoong1
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I'm currently an Aerospace major/Physics minor who's interested in delving further into mathematics. What is the optimal sequence of topics that I should follow for self-studying. I know this forums has links to a lot of interesting books, but I don't really know which one to start with.

Thanks for helping and sorry if this isn't the correct place to post about this.
 
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  • #2
The usual answer to this question would be without any risk of a wrong choice some linear algebra and calculus. However, I guess we may assume that you already have these foundations which raises the question of where to start with and even more important, where to go to. So what do you want to learn? Abstract concepts like logic or topology out of interest or more sophisticated tools in the field of your studies, e.g. in aerodynamics, in which case differential geometry might be an appropriate answer.
 
  • #3
Pretty much echo @fresh_42 . There's a lot of math out there. Some may have no bearing on your main area of study. Are you looking to deepen your knowledge in relevant math or branch out into other types of math just for fun? (i.e. number theory or something. Won't help you but it's fun).

-Dave K
 
  • #4
dkotschessaa said:
(i.e. number theory or something. Won't help you but it's fun).
Don't be a pistolero! I've heard (without knowing it for sure), that numerical analysis is used in arms industry.
I guess because of its algorithmic approaches to problems that cannot be solved otherwise. So even number theory might be a step towards applications - oops, wrong thread.
 
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  • #5
fresh_42 said:
Don't be a pistolero! I've heard (without knowing it for sure), that numerical analysis is used in arms industry.
I guess because of its algorithmic approaches to problems that cannot be solved otherwise. So even number theory might be a step towards applications - oops, wrong thread.

haha. Well like I said, (also in another thread) studying any kind of math will help you think better. I would just warn the O.P. not to lose focus.

-Dave K
 
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  • #6
jsoong1 said:
delving further
Starting from what? Have you done the calculus, differential equations and linear algebra that engineering and physics majors usually have to take? Are you thinking along the lines of "pure math" (theorems and logical structures) or "applied math"?
 
  • #7
dkotschessaa said:
Pretty much echo @fresh_42 . There's a lot of math out there. Some may have no bearing on your main area of study. Are you looking to deepen your knowledge in relevant math or branch out into other types of math just for fun? (i.e. number theory or something. Won't help you but it's fun).

-Dave K

I was a bit more interested in branching out into other types. I'm pretty sure that I'll learn differential geometry in one of my classes, but the area of mathematics with topics such as number theory definitely won't pop up in my curriculum. Besides, a lot of my classes are kind of programming-heavy, and I'd assume doing some practice in that area would help me understand Computer Science aspects easily.
 
  • #8
jsoong1 said:
I was a bit more interested in branching out into other types. I'm pretty sure that I'll learn differential geometry in one of my classes, but the area of mathematics with topics such as number theory definitely won't pop up in my curriculum. Besides, a lot of my classes are kind of programming-heavy, and I'd assume doing some practice in that area would help me understand Computer Science aspects easily.

I'm not sure how to answer really for self study, since you could justify studying just about anything on the grounds that a) you never know what you can use later and b) ANY math is good for training rigorous thinking. I'd say if you're going to branch out, you should do it within the confines of your school, i.e. see what interesting classes pop up in the math department and see if you can take those. For self studying you probably would want to stick closer to the kind of math you need in your major.

I didn't see an answer to the earlier inquiries posed to you here. What have you taken so far?

-Dave K
 

FAQ: Self-Teaching Math Sequence: How to Build Strong Foundation?

1. How do I know if I need to work on my math foundation?

There are a few signs that indicate you may need to work on your math foundation. These include struggling to understand more advanced math concepts, making careless mistakes, and feeling overwhelmed when solving math problems.

2. What are the key components of building a strong math foundation?

The key components of building a strong math foundation include mastering basic arithmetic operations (addition, subtraction, multiplication, and division), understanding and applying mathematical concepts and principles, and developing problem-solving skills.

3. How can I self-teach myself math effectively?

Self-teaching math requires a solid plan and commitment to practice regularly. Some effective strategies include reviewing fundamental concepts, practicing with a variety of problems, seeking help from online resources or textbooks, and seeking assistance from a tutor or mentor if needed.

4. Is it necessary to start from the very beginning when building a strong math foundation?

It is not always necessary to start from the very beginning when building a strong math foundation. It is important to assess your current understanding and identify any gaps in your knowledge. You may need to review certain concepts before moving on to more advanced topics.

5. How long does it take to build a strong math foundation?

The time it takes to build a strong math foundation varies for each individual. It depends on your current level of understanding, how much time you dedicate to practicing, and your learning style. It is important to be patient and consistent with your practice in order to see progress.

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