Self-Study Math Guide: Achieving Goals in Physics and Pure Mathematics

[MrMarvel]

Hello,

I've endeavored to self-teach math so I can eventually go on to study Physics or Pure Mathematics.

I was hoping someone may be able to give me a list of areas I should study and in what order and an equation or problem to work out throughout each section so I can monitor my progress and ability in said field.

I've tried to Google the lists and equations for that sort of thing but I've either fallen short or read a variety of differing opinions.

Thanks!

 

[micromass]

What's your current level in mathematics??

an equation or problem to work out throughout each section so I can monitor my progress and ability in said field.

No idea what you mean with this.

 

[MrMarvel]

I'm starting from scratch with Algebra.

As for what did I mean by the equations or problems - Aren't there any equations or problems I wouldn't be able to figure out unless I had a solid understanding of the corresponding area of mathematics?

 

[micromass]

Aren't there any equations or problems I wouldn't be able to figure out unless I had a solid understanding of the corresponding area of mathematics?

For sure, but if you get a good textbook, then this will already contain many such problems.

Did you ever do algebra before in HS?? If you didn't, then I recommend the books by Gelfand. This: https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20 is a very good and basic introduction to algebra.

If you already know some algebra from HS (but somehow want to start over again or forgot everything), then you might want to go for Lang: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

Another book that I've heard good things about is Euler. I have never looked into it though. It is freely available: http://archive.org/details/elementsofalgebr00euleuoft Some people call the book "outdated" though. Not because the contents isn't good, but because the writing style is strange and old. If you don't mind that, then Euler is fine.

 

[Matrix0]

I commend your motivation and determination to self-teach math in order to pursue your interests in Physics and Pure Mathematics. Self-study can be a challenging but rewarding process, and I'm happy to provide some guidance on how to structure your learning.

Firstly, it's important to have a solid foundation in algebra and basic geometry before moving on to more advanced topics. This will help you understand and solve more complex problems in the future. I would recommend starting with topics such as equations, functions, and graphing, and then moving on to geometry and trigonometry.

Once you have a strong grasp on these fundamentals, you can start delving into more specific areas of math that are relevant to Physics and Pure Mathematics. These may include calculus, linear algebra, differential equations, and complex numbers. It's important to have a good understanding of these topics as they are the building blocks for advanced concepts in Physics and Pure Mathematics.

In terms of the order in which to study these topics, it ultimately depends on your personal learning style and goals. However, a common sequence is to start with calculus, followed by linear algebra, and then differential equations. Complex numbers can be studied concurrently with these topics.

As for monitoring your progress, I would recommend working through practice problems and exercises in each topic and periodically taking practice tests to assess your understanding. Additionally, seeking out online resources or joining study groups can also be helpful in clarifying any areas you may be struggling with.

In terms of specific equations or problems to work on, I would suggest focusing on those that are commonly used in Physics and Pure Mathematics, such as the laws of motion, Newton's laws, and the fundamental theorem of calculus. These can be found in textbooks or online resources.

Overall, self-study can be a challenging but rewarding journey. It's important to stay motivated and dedicated, and to seek out resources and support when needed. Best of luck in your studies!