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Undergraduation and Graduation

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
How different have you perceived the two? Personally undergrad hasn't been any bed of roses for me. If people start to comment I'll give more details why, it has to do with a great overlap with graduate duties.

Do you feel things were better when you were an undergrad? Do (did) you prefer you graduate student time? Let's share experiences of a certainly turmoiled period.
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
Graduate math versus undergraduate math: tests about the same. Homework 5000 times harder. So in undergraduate, my homework-completion-strategy was simply the following:

1. Determine which homework set was due next.
2. Complete that homework set.
3. Repeat steps 1 and 2 for the entire semester.

That worked in undergraduate, where I could generally figure things out in a straight-forward manner. It didn't work in graduate school. What would happen is that I would sit and stare at a homework set for hours, getting nowhere. The best advice I ever got in graduate school was to change my algorithm to the following:

1. Start with one class's homework. Give it a good go. If you're on a roll, keep going.
2. As soon as you get good and stuck, STOP.
3. Move to the next class's homework, and repeat Steps 1 and 2.

In graduate school homework, it wasn't the sheer amount of time you threw at a homework set that got it done for you, it was the number of fresh starts. In addition, this approach allows inter-class pollination. An idea in one class might help in another.
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Thank you for your reply, Ackbach! I'm thoroughly familiar with this piece:

What would happen is that I would sit and stare at a homework set for hours, getting nowhere.
1. Start with one class's homework. Give it a good go. If you're on a roll, keep going.
2. As soon as you get good and stuck, STOP.
3. Move to the next class's homework, and repeat Steps 1 and 2.
But not the other. The explanation is simple: at my university, Mathematics majors are enrolled in almost all graduate subjects (all except 2, actually) during undergrad. In our fourth semester you are thrown into your first graduate course, and it keeps on a steady two subjects per semester after that (they recently altered slightly the order, leaving the sixth semester with three!), however you're not treated as an undergrad. In fact, some people don't even acknowledge the fact that part of the students aren't enrolled in PhDs yet.

The end result is we're treated like trash, facing odds tougher than our average level (quite tougher) without the due benefits. Honestly, memories of when I could do homework like your first algorithm are almost forgotten memories, tracing back to the three basic calculus courses.

Another small interesting piece of information, although not a complaint this time, is that mathematics major have no other contacts with different areas after you finish the basic three semesters. That means you get to do basic physics up to electromagnetism, and that's it.

I find it sad that we get to miss some of the more interesting (mathematically and physically) advanced subjects, such as Analytical Mechanics, Quantum Mechanics, General Relativity, Electromagnetism (done right) and several others.
 

CaptainBlack

Well-known member
Jan 26, 2012
890
I find it sad that we get to miss some of the more interesting (mathematically and physically) advanced subjects, such as Analytical Mechanics, Quantum Mechanics, General Relativity, Electromagnetism (done right) and several others.
All of those subjects should be offered as part of a maths course (though you should never encounter them first, if you can avoid it, from the maths department since they are taught devoid of their meaning)

CB
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
All of those subjects should be offered as part of a maths course (though you should never encounter them first, if you can avoid it, from the maths department since they are taught devoid of their meaning)

CB
I agree with you entirely, I feel like I'm missing a great deal in my undergraduation not having exposure to these topics from the physics department. Have you seen Spivak's new book, Physics for Mathematicians: Mechanics 1? This might be one book right on the spot. Apparently it grew out of some lecture notes for elementary physics courses. He said he always wanted to learn physics and decided to create the series as a way to do that.

There's this quote from the Lecture 1 that I find amusing and true:
Spivak said:
So then people would say, Ah, so you're going to be writing about symplecticstructures, or something of that sort. And I would have to say, No, I'm not trying to write a book about mathematics for mathematicians, I'm trying to write a book about physics for mathematicians; of course, symplectic structures will eventually make an appearance, but the problem is that I could easily understand symplectic structures, it's elementary mechanics that I don't understand.