What Should I Do After Acing Calculus and Struggling with Proofs?

[GcSanchez05]

I aced Calc 1,2, & 3...now what?

I've also taken Diffeq and Linear Alg, but when I took an introductory proof course and a number theory course I failed miserably, like they took all my time and consequently made me do bad on the easier classes I was also taking. The material didn't seem to interest me that much either way and I can only assume that it's going to be more difficult for me in an Analysis or Algebra class...

So my questions is, what is the next step that I should take considering that I'm so much better at the lower division math?

I'm guessing its engineering, but to complete that degree I'll be stuck at my school for 4 more years basically. I'm leaning towards a Physics degree but are the upper division classes (Modern Physics, Mechanics, etc...) just as abstract as the math classes??

So confused >>.<<

 

[flyingpig]

Ace Calc IV then!

 

[TylerH]

How do you plan to make a living with an undergraduate degree in physics?

As for the difficulty of advanced physics, you could look at the problems here, https://www.physicsforums.com/forumdisplay.php?f=154, to get an idea.

 

[Pengwuino]

Is it safe to assume you're doing a math degree at this point?

Physics courses can get abstract but for the most part, you're never bothering yourself proving the convergence of a geometric series or something like that. The best thing to do if probably grab an introductory e/m or classical mechanics text out of the library and just look through it and see whether or not you feel physics is in a better direction or you.

 

[hitmeoff]

I've also taken Diffeq and Linear Alg, but when I took an introductory proof course and a number theory course I failed miserably, like they took all my time and consequently made me do bad on the easier classes I was also taking. The material didn't seem to interest me that much either way and I can only assume that it's going to be more difficult for me in an Analysis or Algebra class...

So my questions is, what is the next step that I should take considering that I'm so much better at the lower division math?

I'm guessing its engineering, but to complete that degree I'll be stuck at my school for 4 more years basically. I'm leaning towards a Physics degree but are the upper division classes (Modern Physics, Mechanics, etc...) just as abstract as the math classes??

So confused >>.<<

I had a similar experience. Lower Division math was absolute cake for me and I carried that attitude into my proof based classes. Not saying you are carrying some sort ego as well, but rather you have to learn at higher level math differently than lower div math.

You were probably a very good calculator. You could bust out all those crazy integrals in Calc, those problems that required 3 pages of calculations and bookkeeping etc...but now things aren't very clear. The books don't give you a "Step 1 Step 2 Step 3 Answer" format, half the time you probably aren't even sure what is being asked of you and you flip through the book trying to find an example like your homework problem and you don't see it.

I understand. Now is when you have to change your thinking. Math at this level IS going to be abstract. You have to often be creative with your proofs. There will usually be more than one way to attack a problem: one will usually be shorter and the other will involve jumping through hoops...at first you won't know which one leads where (sometimes no one really knows where an attempt at a proof will lead).

It takes lots of time, lots of effort to become GOOD at abstract math. It took me about a solid year at a hard school, with hard professors to get up to speed. Some people pick up quicker, others may take longer.

I understand that at this point what you are studying may not seem interesting. My first go at abstract was a disaster, not only did I horribly, but I often found myself sitting there asking myself "who cares?" "seriously, this sounds like ********" etc etc...but eventually I began to GET IT, and now I LOVE IT.

Though a Physics major isn't as rigorous mathematically, its still damn hard. HIgher level physics classes are similar to higher level math classes in that there isn't always (hardly ever) a consistant "1-2-3 Answer" way of doing given problems. You have to really understand the concepts before you can set up your problems. The formulas aren't plug and chugg and usually aren't even in a concrete format. Equations given to you are usual "generalized" equations, and its up to your analysis of the physical system to come up with a concrete formula on which to begin calculating.

I can't speak on what Engineering at a higher level is like since I have ZERO experience there.

Best advice I can give is to give upper level math one more try. Don't hesitate to bug the living hell out of your professors and TAs when you don't understand something. Email then, go to their office hours, pause them in lectures, etc. Find people to study with, find a chalk or dry erase board and go to town on problems. Read your books actively, try to rewrite proofs given in your own language...try to find examples to go with theorems and definitions, etc etc etc...

Maybe take a junior level physics class while your at it to see if maybe that appeals to you more, but at least give math one more try.

 

[Sankaku]

It takes lots of time...

hitmeoff, that is an awesome post. Very nicely said.

 

[cjl]

I can't speak on what Engineering at a higher level is like since I have ZERO experience there

From my experience, which is admittedly rather limited, engineering at the undergraduate level never reaches quite the level of abstraction that physics or math does. The abstraction starts to come in more at the graduate level, rather than in upper division undergraduate courses.

(For what it's worth, I'm an Aerospace engineering graduate student at the moment, and I have no idea how this applies to other engineering fields, such as chemical or electrical)

 

[GcSanchez05]

hitmeoff, you're a genius. I think I am going to give it another try. My Number Theory teacher found me and gave me pretty much the same advice to pass the class (study as much as I can in groups and bother him during lectures and office hours). I opened up a Modern Physics textbook and the exercises seemed just like math proofs. I'll take Modern in the fall and probably end up minoring in it...

But when I was researching what to do with a physics degree, there seemed like there's a lot more career choices than a math degree, (like if you like Optics, there's Optics engineering). Let's say that I find my passion in math to be Differential Geometry or Topology (which is what I'm leaning towards), is it required that I get Masters or PhD to be considered for a job in R&D or an engineering company? I don't know what career I truly want, but I definitely don't want to be in a cubicle. Maybe a Lab(?)

 

[hitmeoff]

hitmeoff, you're a genius. I think I am going to give it another try. My Number Theory teacher found me and gave me pretty much the same advice to pass the class (study as much as I can in groups and bother him during lectures and office hours). I opened up a Modern Physics textbook and the exercises seemed just like math proofs. I'll take Modern in the fall and probably end up minoring in it...

But when I was researching what to do with a physics degree, there seemed like there's a lot more career choices than a math degree, (like if you like Optics, there's Optics engineering). Let's say that I find my passion in math to be Differential Geometry or Topology (which is what I'm leaning towards), is it required that I get Masters or PhD to be considered for a job in R&D or an engineering company? I don't know what career I truly want, but I definitely don't want to be in a cubicle. Maybe a Lab(?)

Some of my TAs who are considering leaving with just their Masters are always telling me that jobs at national labs are available to math majors (with masters). There's always the applied math route, but I think any math major with some programming and/or numerical analysis experience will always be employable in a tech setting. Minoring in physics (especially if you choose your minor classes to be the core classes: Classical Mechanics, E&M, Quantum) will obviously help out greatly. Most of my friends who graduated with B.S. in Physics are now employed as engineers.

What a math, physics, and engineering major at the Bachelor's level really teaches you is how to take a complicated problem, break it down to its essential components and build up a solution. Those skills are applicable in many many settings.

 

[Pyrrhus]

From my experience, which is admittedly rather limited, engineering at the undergraduate level never reaches quite the level of abstraction that physics or math does. The abstraction starts to come in more at the graduate level, rather than in upper division undergraduate courses.

(For what it's worth, I'm an Aerospace engineering graduate student at the moment, and I have no idea how this applies to other engineering fields, such as chemical or electrical)

Yes, Engineering at the graduate level can get quite abstract.

 

[gungywamp]

Now is when you have to change your thinking. Math at this level IS going to be abstract. You have to often be creative with your proofs.

This is completely true. What has happened to you has happened to most math undergrads, if not the the same degree. Most students, upon first being subjected to proof based math, will see a severe drop in their grades until they get the hang of it. You will have to learn to think in a completely different way than you are used to thinking in, and even when you think you have the hang of it, it will still be difficult. My professor for Real Analysis told my class on the first day that there would be times when we would pass in a homework assignment knowing we got everything right, only to receive a failing grade on it. Don't worry too much about it now, just practice. It's not something that comes easily, and it's likely that your professors went through a similar ordeal in their time.

 

[GcSanchez05]

Ahhhh, I know. I'm just used to acing everything math related -_-

I'm definitely giving it a second try this coming fall semester and imma bother all these professors until I start acing this too. (I got the "Imnotgonnaletnopunkassmathclassbeatme" mentality haha)