Is Number Theory Too Much to Handle with Other Physics Courses?

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SUMMARY

The discussion centers on the challenges of taking a Number Theory course alongside multiple physics courses, including Quantum Mechanics (QM), Relativity, and Electromagnetism (E&M). Participants emphasize that the rigor of Number Theory varies significantly based on the instructor and the course structure. A solid foundation in reading and writing proofs, typically gained from a Linear Algebra course, is beneficial but not mandatory. Students are advised to assess their workload and consider dropping the course if it becomes overwhelming, especially given the one to two-week drop window available at many universities.

PREREQUISITES
  • Understanding of proof techniques, ideally from a course in Linear Algebra.
  • Familiarity with foundational concepts in Quantum Mechanics (QM) and Electromagnetism (E&M).
  • Basic knowledge of calculus, particularly Calculus II.
  • Awareness of course structures and grading expectations in abstract mathematics.
NEXT STEPS
  • Research effective proof-writing techniques to enhance understanding of abstract mathematics.
  • Explore course syllabi and textbooks for Number Theory and Probability Theory.
  • Investigate strategies for managing course loads in rigorous academic environments.
  • Learn about the epsilon-delta arguments in Analysis to prepare for advanced mathematics courses.
USEFUL FOR

Students considering a heavy course load in mathematics and physics, particularly those interested in abstract subjects like Number Theory and Analysis. This discussion is beneficial for anyone seeking advice on managing academic challenges in higher education.

mateomy
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I was planning on just taking physics courses next quarter (3, maybe 4 total) but I have an interest in taking a number theory course. Would it be too much to pile on with QM, Relativity, a physics-based math course, and part II of E&M? I know this question is impossible to answer because each individual person handles things differently. So let me rephrase the question: How rigorous is Number Theory? Am I potentially putting a gun to my head in attempting to take on these courses all at once? Any advice would be appreciated.
 
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mateomy said:
I was planning on just taking physics courses next quarter (3, maybe 4 total) but I have an interest in taking a number theory course. Would it be too much to pile on with QM, Relativity, a physics-based math course, and part II of E&M? I know this question is impossible to answer because each individual person handles things differently. So let me rephrase the question: How rigorous is Number Theory? Am I potentially putting a gun to my head in attempting to take on these courses all at once? Any advice would be appreciated.

Number Theory, just like many other abstract subjects, can be made extremely difficult or quite manageable, so it really depends on how the class will be run. In my opinion, the most important factor is the instructor. Of course there are always subjects that are inherently more difficult for us to grasp, but a good instructor can really make the difference.

As far as things you can control, you should be comfortable with reading and writing proofs. Usually this is introduced in a course like Linear Algebra, but it is by no means required. It will just require more time on your part if you haven't had any experience writing proofs.
 
Hmmmm, I'm just finishing a course on Proofs this quarter, and I've taken Intro Linear Algebra. But, still kinda nervous taking an abstract math course on top of the physics stuff. Maybe I'm being a wimp.
 
mateomy said:
Hmmmm, I'm just finishing a course on Proofs this quarter, and I've taken Intro Linear Algebra. But, still kinda nervous taking an abstract math course on top of the physics stuff. Maybe I'm being a wimp.

It's good to be cognizant of your limitations; this does not mean you're being a wimp. It is a useful skill to develop and your future employers/advisers will appreciate it.

Does your university permit you to drop courses within a certain time-frame? If so, you can take the course, and within the first few weeks get a feel for what is going to be expected of you. If you find that you aren't going to be able to devote the time necessary to be successful in it, then drop it and try again when your load is a bit lighter.
 
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Yeah, we have a one to two week window (I believe). That's good advice and much appreciated. What would/are your thoughts on Probability Theory? None of these classes are required of me, I'm only interested in them.
 
mateomy said:
Yeah, we have a one to two week window (I believe). That's good advice and much appreciated. What would/are your thoughts on Probability Theory? None of these classes are required of me, I'm only interested in them.

My university does have a course titled "Probability Theory", but I haven't taken it yet. Honestly, the only courses about which I've heard horror stories are Analysis, Topology and Functional Analysis. Most complaints are about a given professor's teaching style and/or expectations.
 
Analysis huh? I was actually just signing up for that for the Summer Session. Crap. Haha.
 
mateomy said:
Analysis huh? I was actually just signing up for that for the Summer Session. Crap. Haha.

I am taking Analysis and Abstract Algebra in the fall, so I cannot yet give advice based on personal experience.

However, some of my classmates have taken it and say that most people struggle in the beginning due to unfamiliarity with the epsilon-delta arguments. You will need to work much harder than you did in your Calculus courses. Just be patient and work a lot of the exercises in whatever text you're using. And don't forget about PF. :smile:
 
Can you list the course contents and the book you're using??

If you're planning on ever taking abstract algebra, then it would probably be wise to take abstract algebra first.

As for probability theory, it can be made very easy or extremely hard (just like with number theory). We saw measure-theoretic probability (without even seeing measures or probability), so it was very difficult at the time. Posting a course contents and the book you're using would be good.
 
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It depends on how they teach it. At my school, Number Theory is an intermediate elective requiring only Calc II as a prereq. We did some proofs and some computational stuff, and overall it wasn't that hard. I thought it was a lot of fun. But your school could be different.
 

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