I spoke to my maths lecturer today

[K.I.L.E.R]

I told him about what I was studying in my spare time and how I was going about it.
Apparently some of the maths I was doing was PhD level stuff.

He mentioned that I shouldn't put much priority in it until I build a base of knowledge first on the basics.
The thing that I'm wondering is that even though I do understand a fair amount of it and I was capable of doing a few things from the latter chapters without trouble from my engineering book would that count as wasted time?

How should I go about studying topics in maths?
How much should I strain to understand PhD topics related to engineering?

 

[Nick]

There's not really such thing as PhD level math. For some engineering fields it's useful to know every little detail about e.g. signal processing. In another it suffices to know the very basics of Fourier transforms but you need all about discrete math and statistics.

It's definitely a good thing that you have an interest in math subjects outside your courses. Don't let anyone tell you're wasting your time. As long as you're learning things and enjoy yourself you will benefit from it in the long term as well. And you'll definitely notice when you're a little short on fundamental theory and need to focus on that first. Besides, you'll quickly learn that in your courses anyway, and it's no problem to take a head start.

Succes!

 

[K.I.L.E.R]

The maths isn't difficult but notation and language of engineers/mathematicians can be difficult to pick up sometimes.
It's usually "how do I apply this concept to this problem?" scenarios that I really need to work towards.
That skill usually comes from experience.

 

[DudeMiester]

I think it also has a lot to do with how you percieve problems. You can't take them at face value, but rather you have to look at the underlying conceptual structure. Then you can match that pattern with things you already know.

 

[AlNom]

Keep doing what you're doing. You're doing fine so far.

He mentioned that I shouldn't put much priority in it until I build a base of knowledge first on the basics.

He's clearly trying to hold you back! But first, you should follow example and betray your fellow students and then take over the faculty. Then you can make it safe and secure.

P.S. watch out for lava

 

[Fred]

"There's not really such thing as PhD level math."

K-Theory, Ricci flow, eliptic cohomology, Langlands conjecture, the Riemann hypothesis, 2-category theory, quiver diagrams etc etc

Theres a lot to a PhD in mathematics, all those example subjects require so much background they more or less all require the time and effort of years of study to be able to understand the material thoroughly, much less contribute to the field.

For an applied theorist like me, its a lifelong affair. Many discoveries in physics for instance are parrelel to new discoveries in mathematics, so it requires continually learning new mathematical material in hopes that you can apply them to a physical situation. I've had to learn a lot about quiver diagrams recently (and Ktheory the year before), and let me just say the time investment is nontrivial unless you are some type of a genius and can absorb it all in 3 months...