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MostafaAlkady

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- Studying
- Thread starter MostafaAlkady
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In summary: However, I would recommend looking into the "Real Analysis from an Applied Point of View - Stephen Abbott" book, or at least reading the first few chapters. It's a bit more challenging, but it'll teach you more about the concepts behind real analysis.

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MostafaAlkady

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Thank you for your time!

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romsofia

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If you're tired of analysis, then go for group theory! It's a change of pace, and cyclic groups are a pretty fun concept when tied to some other modulo concepts.

Neither of these will really prepare you for anything you'll face in graduate school, they should just be for the joy of mathematics. If you want to study things that'll get you "ready" for your graduate physics course, then math wise you should be hitting functional analysis, PDEs, and getting comfortable manipulating series ala perturbation theory.

Either way, I've always studied math for the joy of math, and graduate school is a fun place where you have a bunch of other people interested in these areas who are always up to chat about some wild math concept you learned the night before from my experience.

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MostafaAlkady

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I enjoyed analysis so much. The book was pretty basic (probably the easiest analysis book out there), but I have studied it thoroughly and done most of the exercises. However I guess I'd like to try group theory now because I know so little about it and I hear it's ubiquitous in physics.romsofia said:

If you're tired of analysis, then go for group theory! It's a change of pace, and cyclic groups are a pretty fun concept when tied to some other modulo concepts.

Neither of these will really prepare you for anything you'll face in graduate school, they should just be for the joy of mathematics. If you want to study things that'll get you "ready" for your graduate physics course, then math wise you should be hitting functional analysis, PDEs, and getting comfortable manipulating series ala perturbation theory.

Either way, I've always studied math for the joy of math, and graduate school is a fun place where you have a bunch of other people interested in these areas who are always up to chat about some wild math concept you learned the night before from my experience.

What are the prerequisites for functional analysis? And do you know of any good textbook for self-study?

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MostafaAlkady

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I guess I'm going to go for it. I have the book "Group Theory in a nutshell for physicists - A.Zee" in mind, but I would appreciate if you know any other book that was useful for your study.Orodruin said:

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MostafaAlkady

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That's a good idea. Hopefully in the next summer after I get to know some decent group theory first, and then I can work on linking both later on.dextercioby said:

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romsofia

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I didn't have to self study it, luckily, so I can't comment on a book that would help. However, having self studied other things, the textbook isn't going to make or break you anymore. The most important part of learning, imo, is feedback. Find an author who you can understand and derive the things in the text, then look for problem sets from universities.MostafaAlkady said:What are the prerequisites for functional analysis? And do you know of any good textbook for self-study?

Ultimately, to be confident in your self studied abilities you have to test your knowledge. So, find a textbook you think you'll enjoy (whether it be how they write, their layout, etc), find some problem sets, and get cracking.

Prerequisites for my course were linear algebra, and PDEs.

Topology is a branch of mathematics that studies the properties of geometric shapes and spaces, while Group Theory is a branch of abstract algebra that studies the structure and properties of groups. Topology focuses on continuous transformations and the concept of proximity, while Group Theory focuses on the algebraic structure of groups and their operations.

Both Topology and Group Theory have applications in various fields such as physics, engineering, computer science, and economics. However, Topology is more commonly used in fields that deal with continuous objects, such as fluid dynamics and differential geometry, while Group Theory is more commonly used in fields that deal with discrete objects, such as cryptography and particle physics.

This largely depends on the individual's strengths and interests. Some may find Topology more challenging due to its abstract nature and reliance on visual intuition, while others may find Group Theory more challenging due to its use of complex algebraic concepts and structures.

Yes, it is possible to study both subjects simultaneously, as they are closely related and often used together in mathematical research. However, it is recommended to have a strong foundation in abstract algebra before delving into Group Theory.

Both subjects have a wide range of applications in various fields, making them valuable skills to have in many industries. Additionally, studying these subjects can also improve problem-solving and critical thinking skills, which are highly sought after in many job markets.

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