How difficult is Topology for a pure Physics student?

In summary, topology is a relatively easy mathematics subject, but requires some familiarity with proofs and set theory.
  • #1
rwooduk
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Hi, I'm hoping someone here can shed some light,

I'm currently in my 3rd year of my Physics degree and have discovered I really don't have the mind to memorise / reproduce paragraphs of text. Even if I understand the concepts it takes me a LONG time for my brain to take text in. Maths however I find much easier and feel as though I understand it and can learn it with less effort.

So to my question, I'm on track to do a Bionanophysics module in my final semester and thinking of changing it to topology. I have real trouble grasping biology and remembering everything. Topology sounds interesting and would be much preferred to learning any Biology. But how difficult is the subject? Obviously I have covered a lot of maths in my Physics module, but is it a topic that goes above and beyond?

Thanks in advance for any input!
 
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  • #2
If you have the right background, then topology really shouldn't be that difficult. In fact, it's a really visual and intuitive piece of mathematics, and for that reasons it should really be fun for physics students.

But on the other hand, topology is the generalization of certain mathematical things which you need to know first. Specifically, you need to be comfortable with epsilon-delta definitions of continuity and sequences. And it helps to be familiar with metric spaces. My advice to you is to self-study metric spaces so that you really have an intuitive feel for the concepts. There's quite a lot of terminology involved, but it's really important to have the concepts right. Self-studying metric spaces shouldn't take a lot of effort, there's not a lot you need to know anyway.
 
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  • #3
micromass said:
If you have the right background, then topology really shouldn't be that difficult. In fact, it's a really visual and intuitive piece of mathematics, and for that reasons it should really be fun for physics students.

But on the other hand, topology is the generalization of certain mathematical things which you need to know first. Specifically, you need to be comfortable with epsilon-delta definitions of continuity and sequences. And it helps to be familiar with metric spaces. My advice to you is to self-study metric spaces so that you really have an intuitive feel for the concepts. There's quite a lot of terminology involved, but it's really important to have the concepts right. Self-studying metric spaces shouldn't take a lot of effort, there's not a lot you need to know anyway.

Many thanks for the reply! I will take a look at metric spaces over the weekend, the course starts next week. There is just one thing however, I've looked at the past exam papers and it's the notation / symbols I have never seen before, such as the red circled question below:

ftnNFCQ.jpg


it looks completely foreign to me, is being unfamiliar with such notation a possible issue?

thanks again
 
  • #4
Oh. That's not good. That's the language of set theory, which you will need to be very familiar with. It's absolutely fundamental. I recommend going through Kaplansky's "Set theory and metric spaces". It's a very short book. Doing chapter 1, 4 and 5 should prepare you adequately.
 
  • #5
And how comfortable are you with proofs? Does "proof by contradiction" mean anything to you?
 
  • #6
micromass said:
Oh. That's not good. That's the language of set theory, which you will need to be very familiar with. It's absolutely fundamental. I recommend going through Kaplansky's "Set theory and metric spaces". It's a very short book. Doing chapter 1, 4 and 5 should prepare you adequately.

I will give it a go, perhaps this isn't the module for me but will certainly take a look.

micromass said:
And how comfortable are you with proofs? Does "proof by contradiction" mean anything to you?

If by proofs you mean mathematical derivations then yes I'm very comfortable (from the Physics side). however I haven't heard of the term "proof by contradiction"

appreciate the input!
 
  • #7
Oh, so you are entirely new to proofs! Hmm, taking topology is not a good idea then unless you're willing to spend quite some time filling up certain mathematical gaps. If you're thinking of taking topology next semester that starts now, I would have to recommend against that, since you need be very comfortable with proofs, logic and set theory. However, if you're willing to fill up the gaps, then topology really is a very nice subject.
 
  • #8
micromass said:
Oh, so you are entirely new to proofs! Hmm, taking topology is not a good idea then unless you're willing to spend quite some time filling up certain mathematical gaps. If you're thinking of taking topology next semester that starts now, I would have to recommend against that, since you need be very comfortable with proofs, logic and set theory. However, if you're willing to fill up the gaps, then topology really is a very nice subject.

that's just what I needed, many thanks for your time!
 

1. How does Topology relate to Physics?

Topology is a branch of mathematics that studies the properties of space and shapes. In Physics, topology is used to describe the behavior of complex systems, such as those found in quantum mechanics and cosmology.

2. Is a strong background in Mathematics necessary for understanding Topology in Physics?

While a strong foundation in mathematics can be helpful, it is not necessary to have a deep understanding of mathematical concepts in order to grasp the basics of topology in physics. However, some familiarity with calculus and linear algebra is recommended.

3. What are some real-world applications of Topology in Physics?

Topology has a wide range of applications in physics, including the study of phase transitions in materials, the behavior of fluids, and the properties of exotic states of matter such as topological insulators and superconductors.

4. How difficult is it to learn Topology for a pure Physics student?

The level of difficulty in learning topology for a pure physics student can vary, as it depends on the individual's background in mathematics and their ability to grasp abstract concepts. However, with dedication and practice, topology can be understood and applied by anyone.

5. What resources are available for learning Topology for Physics?

There are many resources available for learning topology in physics, including textbooks, online lectures, and courses. Some universities also offer specialized courses in topology for physics students. Additionally, collaborating with experienced mathematicians can also be helpful in gaining a deeper understanding of the subject.

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