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

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Discussion Overview

The discussion revolves around the optimal sequence of mathematical topics for self-study, particularly for an Aerospace major with a Physics minor. Participants explore various branches of mathematics, considering both foundational knowledge and areas of interest, including applied and pure mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant inquires about the optimal starting point for self-studying mathematics, expressing uncertainty about which topics to pursue first.
  • Another participant suggests that foundational topics like linear algebra and calculus are typically essential, but questions what the individual wants to learn next, whether abstract concepts or tools relevant to their studies.
  • Some participants emphasize the importance of aligning mathematical study with the individual's major, while others suggest exploring different areas of mathematics for personal interest.
  • One participant mentions that while number theory may not directly apply to the individual's studies, it could still be enjoyable and beneficial for developing rigorous thinking skills.
  • Another participant raises the idea that numerical analysis has applications in various fields, including the arms industry, suggesting that even seemingly unrelated topics could have practical relevance.
  • There is a discussion about the balance between pursuing relevant mathematics and branching out into other areas, with some advocating for a focus on applicable topics while others encourage exploration of diverse mathematical fields.

Areas of Agreement / Disagreement

Participants express differing views on whether to focus on mathematics directly relevant to the individual's major or to explore other areas of interest. There is no consensus on a specific sequence of topics or the best approach to self-study.

Contextual Notes

Participants reference various mathematical fields and their potential applications, but there are limitations in terms of specific recommendations for self-study paths and the individual's prior mathematical background.

Who May Find This Useful

Students in STEM fields, particularly those interested in self-studying mathematics, may find this discussion relevant as it addresses different approaches to building a mathematical foundation.

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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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.
 
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
 
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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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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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"?
 
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.
 
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
 

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