Math Analysis Course: Is it Helpful for Chem/Phys Undergrads?

[MAins]

Hi, I am a Chem/Physics undergrad and was wondering if a math course called "intro to analysis" would be helpful for me to take.

The course's topics are: "Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration."

Are those helpful for the physical sciences, specifically chem. physics or related areas?

I've already had calc, linear alg./diff. equations, and am taking some advanced courses on diff. equations.

 

[MAins]

The book is "Principles of Math. Analysis" by Rudin.

 

[Howers]

Not sure how helpful it would be, but it would be useful if you eventually go to grad school and take some harder QM. Basically, you won't have need for this kind of math until later down the road.

 

[MAins]

Thanks. I was told some courses in Real Analysis and Complex Analysis might be helpful. I'm not sure my school offers that; so would these topics not be covered at all in this mathematical analysis class? Any suggestions as to what I should take otherwise?

Also, in a somewhat related vein, I was told a class in Fourier analysis might be helpful. Any idea about what sort of class offers that? I know I'll learn some in my PDE class, but was wondering if it's typically presented in other math classes as well.

 

[Howers]

Thanks. I was told some courses in Real Analysis and Complex Analysis might be helpful. I'm not sure my school offers that; so would these topics not be covered at all in this mathematical analysis class? Any suggestions as to what I should take otherwise?

Also, in a somewhat related vein, I was told a class in Fourier analysis might be helpful. Any idea about what sort of class offers that? I know I'll learn some in my PDE class, but was wondering if it's typically presented in other math classes as well.

definitely helpful, and I still suggest you take them, but only if you intend to go beyond undergrad. Real analysis will also prepare you for functional analysis, which is essential in a physical chemist/physicists tool kit. Aside from PDE, real/complex analysis is the other place you'd see Fourier. Not to mention real analysis is very interesting, albeit painfully difficult. So if you've good a heavy course load this year, don't mind postponing it until next year. And I also suggest you do complex analysis before real, not because it is a pre-requisite but rather because complex is more strucuted and can get you used to the analyst type of thinking.

 

[MAins]

definitely helpful, and I still suggest you take them, but only if you intend to go beyond undergrad.

Would this "introduction to mathematical analysis" course include any topics relevant to real/complex analysis? Or would it be mostly of value to mathematicians and certain kinds of physicists (i.e., a bit too esoteric for chemistry)?

Like I said, I'm not sure my school offers complex or real analysis. I forgot also to mention there's a second semester of this analysis course which is "Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem."

 

[Howers]

This introduction to analysis course is real analysis, sorry I didn't make that clear. Complex analysis should be in your math department, under the name of something like complex variables. Yes, real analysis is likely too out there for most chemists, even theoretical ones. In fact, the same can be said about most physicists. It is useful if you ever study the mathematical foundations of quantum mechanics, and even that is not neccessarily required by either physicists or chemists unless you go into heavy field theories.

It is unusual that your real analysis course is so slow paced. Typically, both of your courses are covered in one semester, so I don't know why your school needs two.
Basically in your first half, you will prove why derivatives and integrals work. This knowledge is not essential to scientists, as you are only required to know computations. The second half is even more useless to you as a chemist, as it pure math stuff. So yeah, don't take this unless you fancy maths and loved linear algebra as this is one of the most difficult math courses in university (though your school does it at half speed, so that might not hold). definitely consider complex variables/analysis though, which is easier and far more applicable.