What level of math is needed for a theoretical physics career?

[Gurasees]

I want to become a theoretical physicist. I was wondering the LEVEL of maths i will need to do. For example i downloaded a book for sets "INTRODUCTION TO SET THEORY" BY HRBACEK, JECH. It has got a lot about sets. But when i look into another book it has limited concepts. So i don't have any idea how much math i need to do. and please recommend some books. before doing calculus i need to know about sets, relations, functions and conituity. so please recommend some books. It's like i want to completely study both mathematics and physics.

 

[jedishrfu]

Prof Gerard T'Hooft has a website devoted to becoming a theoretical physicist that could give a roadmap on what to do:

http://www.staff.science.uu.nl/~Gadda001/goodtheorist/

And ZapperZ wrote a similar excellent article here on what to expect as you proceed along the track of becoming a physicist:

https://www.physicsforums.com/threads/so-you-want-to-be-a-physicist.240792/

So check these out and then we can suggest books when you know where you are on the path.

 

[chiro]

Hey Gurasees.

I would suggest you do what most do in mathematics courses and those who make heavy use of it.

Get the intuition for mathematics by doing applied coursework and theoretical coursework without the graduate style approach to mathematics first.

Once you get the intuition for what the symbols mean and what the ideas represent, then move towards a book with proofs and theorems.

If you don't have the necessary intuition to know the ideas and the symbols in context then a proof book will just go way over your head.

Focus on the physics courses to give you the applied intuition and focus on the mathematics courses in the order that they are recommended to get the theoretical ideas and the rigorous approach to mathematics.

The subject that deals with the things you are talking about in upper undergraduate or graduate studies is known as analysis which is the rigorous approach to studying and proving things related to calculus - but in precise and general ways.

Take it one step at a time - but always think about what you are studying and get the intuition for what the symbols and ideas really represent because you won't be able to look at the higher level stuff without this intuition.

 

[DataGG]

@Gurasees,

In what grade are you in? If you're already majoring in Physics, you should have the required math classses for now. If not, I'd take a look at a Physics program and see what kind of math they learn...

 

[Matrix0]

I can tell you that a strong foundation in mathematics is essential for a career in theoretical physics. However, the specific level of math needed may vary depending on your specific research interests and goals. Generally, a strong understanding of calculus, linear algebra, and differential equations is necessary for theoretical physics. Additionally, knowledge of advanced mathematical topics such as group theory, topology, and complex analysis may also be beneficial.

In terms of specific books, it is difficult to recommend a single resource as different books may have varying levels of depth and complexity. It is important to find a book that is suitable for your level of understanding and offers a comprehensive coverage of the topics you need to learn. Some popular textbooks in the field of theoretical physics include "Mathematical Methods for Physicists" by Arfken and Weber, "Mathematical Methods in the Physical Sciences" by Boas, and "Mathematical Methods of Classical Mechanics" by Arnold.

In addition to textbooks, there are also many online resources and lecture notes available that can supplement your learning. It is also important to remember that in addition to studying math, you will also need to have a strong understanding of physics principles and theories. So, it is important to strike a balance between studying math and physics.

Overall, becoming a theoretical physicist requires a significant amount of dedication and hard work in both mathematics and physics. It is important to continuously challenge yourself and seek out resources that will help you deepen your understanding of these subjects. I wish you the best of luck in your academic pursuits.