Is non-rigorous maths more useful for undergraduate physics?

  • #1
Hi, I'm starting a (theoretical) physics degree this year and I have a choice between a rigorous proof based calculus/linear algebra class and a non-rigorous calculus/linear algebra class for the first semester. I wanted to ask which one is more useful for undergraduate physics.

Here are the topics covered in both classes:

Rigorous class
Topics to be covered include: Analysis - axioms for the real numbers, completeness, sequences and convergence, continuity, existence of extrema, limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations; Linear Algebra - complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes.

Non-rigorous class
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions.Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Linear Algebra - Complex numbers. Solution of linear system of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Emphasis is on understanding and on using algorithms.
 

Answers and Replies

  • #2
Rolen
Gold Member
23
1
First of all, you should read more about "theoretical physics". By theoretical you're not saying which area of physics you want do follow. Also, you're first semester, there's a lot more down the road.

So, to your problem. The first semester is always a troubled time. And if you never study calculus is gonna be ever worse. I don't know if you ever studied calculus before, so I can't advice much. But, a more mellow calculus course is gonna be better for you. I think that if you start easy and learn that you want to do this the rest of your life you can take more rigorous math classes afterwards.
 
  • #3
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
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Hi, I'm starting a (theoretical) physics degree this year and I have a choice between a rigorous proof based calculus/linear algebra class and a non-rigorous calculus/linear algebra class for the first semester. I wanted to ask which one is more useful for undergraduate physics.

Here are the topics covered in both classes:

Rigorous class
Topics to be covered include: Analysis - axioms for the real numbers, completeness, sequences and convergence, continuity, existence of extrema, limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations; Linear Algebra - complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes.

Non-rigorous class
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions.Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Linear Algebra - Complex numbers. Solution of linear system of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Emphasis is on understanding and on using algorithms.
I am a bit puzzled why you ask this here. I am certain that your school/department has a clearer recommendation on what courses you SHOULD take for your degree. At the very least, your academic advisor (you do have one, don't you?) should know a lot more on what you need to take. He/she should be quite familiar not only with the degree requirements, but also what those math courses are and if they are relevant for what you want to do.

So, have you sought out those resources first?

Zz.
 
  • #4
jgens
Gold Member
1,581
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I am certain that your school/department has a clearer recommendation on what courses you SHOULD take for your degree. At the very least, your academic advisor (you do have one, don't you?) should know a lot more on what you need to take. He/she should be quite familiar not only with the degree requirements, but also what those math courses are and if they are relevant for what you want to do.
I second ZZs advice that you should seek recommendations from people in your department. Academic advisors, however, are generally laughably ignorant of these matters (unless you major in general studies or something) so I would probably ask other professors instead.
 
  • #5
Thanks for answering guys. Yeah I think I'll just ask my university, I'm starting in a month which is why I haven't been able to see them yet.
 
  • #6
I'd also suggest you look into what faculty are teaching the course... sometimes a course can be very different depending on who teaches it. Oh -- and the text. Check out the texts at the book store.
 
  • #7
25
1
Hi, I'm starting a (theoretical) physics degree this year and I have a choice between a rigorous proof based calculus/linear algebra class and a non-rigorous calculus/linear algebra class for the first semester. I wanted to ask which one is more useful for undergraduate physics.

Here are the topics covered in both classes:

Rigorous class
Topics to be covered include: Analysis - axioms for the real numbers, completeness, sequences and convergence, continuity, existence of extrema, limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations; Linear Algebra - complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes.

Non-rigorous class
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions.Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Linear Algebra - Complex numbers. Solution of linear system of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Emphasis is on understanding and on using algorithms.
OMG I knew these course descriptions sounded familiar. Interesting that I found another Australian on an American forum. I was going to go to ANU to study theoretical physics (got accepted to the Bachelor of Advanced Science), but ended up choosing The University of Melbourne. It's a shame I didn't get into the PhB program, because you would've seen me there :P

To answer your question, I suggest taking the rigorous stream. You will gain a deeper understanding of the mathematical tools used in physics, which can't hurt. Also, real analysis is very important in physics even though it's considered pure maths.
 
  • #8
If you want to study physics, take 1115 (if it's still that) for the networking. All of the top students will be in that class and will drop down second semester if they don't like it.

Disclaimer: I barely went to ANU; was there for a few weeks before getting into H/P/Y and after that, basically dropped out. I was enrolled in MATH1115 though, and it wasn't bad (at least, it wasn't bad for the first few weeks and I can't really comment after that).
 

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