Next destination in my voyage through Mathematics

[jegues]

Hello all,

I'm simply a student who has a passion for mathematics. I'm just curious as what domain of mathematics I should study next. I'm a university student who plans on persuing an electrical engineering degree.

I've already learned Calculus 1&2 along with linear algebra. What would be the next level of mathematics after things such as calculus 2 or even advancements in what I've already learned in linear algebra?

Thanks in advance!

 

[mathman]

After calculus there are many different directions you can go into. Related to elec. eng., you could consider complex variables, Fourier analysis, differential equations, for starters.

 

[jegues]

you could consider complex variables, Fourier analysis, differential equations, for starters.

Any good resources/notes/problems you could point me to by chance?

 

[HallsofIvy]

Don't forget Linear Algebra. Easily one of the most general and most important areas of mathematics after calculus.

 

[jegues]

I've already taken Linear Algebra and I enjoyed it a lot, complex variables seems to relate a lot to what I've already seen in my linear algebra course as well. Could you guys be more specific at what I should be looking at?

 

[JSuarez]

Has a former electrical engineer, who later drifted to mathematics, I would agree and suggest Differential Equations and Complex Variables. Probability and Stochastic processes are also something you should learn, but later (to really understand probability you'll need Real Analysis and a bit of Measure Theory).

As for references, try Martin Braun's "Differential Equations and their applications" and Marsden and Hoffman's "Basic Complex Analysis".

 

[jegues]

I'm just curious, how did you go from being an electrical engineer to working in mathematics?

 

[JSuarez]

My first degree (called a License, in my country; a 5-year degree) was in electrical engineering; I got interested in Signal Processing and Control Theory and that led to Mathematics. Eventually, I decided that it was really that I wanted, and enrolled in a PhD program.

An Electrical Engineering course, if done properly, will give you a flexibility that few other courses can match.

 

[jegues]

Thats something I may look into in the future, I'm just not sure I can jump from an electrical engineering degree to a PhD in mathematics? How can I figure this out?

 

[JSuarez]

Depends where you are and how the system works there. It's possible that you may have to do a Masters degree first, but many math departments accept PhD students from other fields without this requirement. Why don't you try to talk with the people in the math department where you are studying? Tell them about your interests and ask for advice. Check if it's possible to do a minor, for exemple.