Learning real analysis without linear algebra?

In summary: Unless you have a really good reason not to, I would strongly recommend that you take a linear algebra course if you want to study physics in a more in-depth way.
  • #1
Quantumcom
8
0
Well, I am a second year astrophysics student in the UK. However, I want to go for a PHD in theoretical physics after my graduation. So I believe I have to take more maths modules as much as possible. I have taken mathematical techniques 1 and 2 which cover up to vector calculus, differential equations, Fourier series and bit complex analysis (up to contour integration). I can't take real analysis module formally as I didn't take linear algebra in my first year (Initially I thought of go for astrophysics). But I am going to just listen to the lectures. What do you recommend the best for me? What topics should I learn in particular before lectures begin?

Cheers!
 
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  • #2
Wait... you are going to take linear algebra, right? You just won't have the time to take analysis after it? If you will have the time later, just take it then.

Did you get a decent amount of topology in your complex analysis class? I actually haven't taken analysis, but I've taken a topology class and a complex class. My friends in real analysis always seemed bewildered by the basic notions of topology. You can find baby Rudin online and skim the pages as a good guide to what you'll cover.

Have you done much in the way of proofs in your classes? Understanding set notation and logic will be important.
 
  • #3
''Wait... you are going to take linear algebra, right?''

No, I am going to take real analysis. I haven't taken linear algebra yet, but hope to study on my own, only the essential stuff though, as I don't have much time.

No, not topology and I don't think I have done much proofs either, my bad. :(
 
  • #4
There are probably better people to weigh in on this, but I'll keep going anyway.

First: proofs and set notation are going to be important. Most of it isn't terribly difficult, but it is going to make your life hard if you are trying to learn the math as well as the notation at the same time. I don't know the best way to get acquainted with proofs. I had a class that used a book called "How to Prove It". The class was decent, but the book was really wordy. I think it would be difficult to self study from. Do you know what book they use in the class?

Second: I don't know much about astro, but linear algebra is significantly more important to all of the classes I've taken, most notably all of quantum mechanics. Unless your analysis class will focus more on advanced techniques instead of rigor, you probably won't cover much that is directly applicable to physics.

Two points to take when listening to me. I don't know exactly how UK courses are structured and I am not studying astrophysics. If you plan to continue in that direction, my advice may not be good. If you want to study physics in general, linear algebra is extremely important.
 
  • #5
Quantumcom said:
''Wait... you are going to take linear algebra, right?''

No, I am going to take real analysis. I haven't taken linear algebra yet, but hope to study on my own, only the essential stuff though, as I don't have much time.

No, not topology and I don't think I have done much proofs either, my bad. :(

Bad idea. Linear algebra is much more important to physicists. If a physicist doesn't know analysis well, them I'm sure he might miss some things but he'll be ok. But linear algebra must be know very well. It appears in so many places.

I really recommend you to take a thorough linear algebra course. It's even worth it to take a proof-based course. If you study it on your own, then please don't just study the basics but study it very thoroughly.

Finally, if you haven't done much proofs, then you're going to have a bad time in analysis. Be sure to be very comfortable with proofs before doing analysis. For linear algebra, you need to be somewhat less comfortable. In many places, a linear algebra class is a good place to develop proof skills.
 
  • #6
What the others said - this seems like a very bad plan.

Arguably, there are no "prerequisites" for a Real Analysis course, except the right level of mathematical maturity - which you may not have, from courses named "math techniques" not "math".

But the idea that self-studying just the "basics" of linear algebra is enough to get by, is crazy IMO. For any advanced theoretical-based physics or engineering, you need to know LA forwards, backwards, inside-out, upside-down, and in your sleep.
 
  • #7
Yeah, got it. Cheers folks!
 
  • #8
Many basic real analysis courses restrict themselves to the real line rather than R^n, so you might get away with having no Linear Algebra. However, as others have said, LA is so fundamental to anything in mathematics (pure or applied) that it should be a very high proiority.
 

Related to Learning real analysis without linear algebra?

What is real analysis?

Real analysis is a branch of mathematics that deals with the study of real numbers and their properties. It involves the rigorous examination of concepts such as limits, continuity, differentiation, integration, and series.

Do I need to know linear algebra to learn real analysis?

While knowledge of linear algebra can be helpful in understanding some concepts in real analysis, it is not a prerequisite. Real analysis can be learned without prior knowledge of linear algebra.

What are some good resources for learning real analysis without linear algebra?

There are several textbooks and online resources available for learning real analysis without linear algebra. Some popular options include "Understanding Analysis" by Stephen Abbott, "Real Mathematical Analysis" by Charles Pugh, and the MIT OpenCourseWare course on Real Analysis.

What are some key topics covered in real analysis?

Some key topics covered in real analysis include sequences, limits, continuity, differentiation, integration, series, and metric spaces. These concepts are fundamental to understanding the properties of real numbers and their functions.

How can I apply real analysis in real-world situations?

Real analysis has applications in various fields such as physics, economics, computer science, and engineering. It can be used to model and solve real-world problems involving continuous quantities, such as motion, optimization, and probability.

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