Not sure what to do for college

[SpiffyKavu]

I hate to jump on the bandwagon (there seems to be a good amount of topics like this floating around), but I would like some more advice on this:

First, I will be a freshman this fall in college, and I'll be taking Calc III (multivariate calc). My primary major is physics, but I was thinking of adding a math major to it. Now this all hinges on how my calc class goes, but I'm betting it will go smoothly.

All the schedule changes will be for the spring semester. I am contemplating whether I should push a gen. ed. course back a semester and move my linear algebra up to this coming spring. That would mean that I would be taking Differential Eq. and linalg in the same semester, for a total of what looks like 16 credit hours. Then I could take Intro Analysis over the summer and move into advanced calculus in my sophomore year. Intro analysis is basically a stepping stone to adv. calc, designed to ease people into writing proofs, since adv. calc is very rigorous in terms of proofs, and is among the hardest undergrad math classes offered.

This would greatly increase my flexibility in my last two years, and I think I should have the momentum and motivation needed when the time comes.I will be talking to my adviser soon (when I move in soon probably), but I would still like some input saying whether to do it or not.

I will be going to UMD College Park, btw, and if anyone would like, I can post the course descriptions.


Now it has been suggested to me to keep Advanced Calculus to my junior year and take some other math classes to deepen my mathematical knowledge base before I leap into real analysis. I have played around with a 4-year plan (I have to make on anyway) and both approaches are interesting to me.

 

[CPL.Luke]

try the harder schedule first and then if you feel your not getting a deep understanding of it, then drop a the linear algebra and work on other things

 

[mathwonk]

this all depends on how strong you are. you sound confident to me, so why not try it, if your advisor agrees. advanced courses can be fun and challenging and help set a mental standard even if you have to back out temporarily and return later.

your problem, when it gets hard, will be deciding whetehr your abilitya nd work ethic can make uop for possible lack of background. where did you go to high school that you are entering in several variabkes calc? presumably you got 5's in AP calc, hopefully BC?

 

[axeae]

is there linear algebra included in the multivariate course? at my school they include linear algebra and then the actual linear algebra is really like a second course in it

 

[SpiffyKavu]

this all depends on how strong you are. you sound confident to me, so why not try it, if your advisor agrees. advanced courses can be fun and challenging and help set a mental standard even if you have to back out temporarily and return later.

your problem, when it gets hard, will be deciding whetehr your abilitya nd work ethic can make uop for possible lack of background. where did you go to high school that you are entering in several variabkes calc? presumably you got 5's in AP calc, hopefully BC?

Yeah, I took both calc AB and BC tests (in consecutive years) and easily got 5's in both of them. But I do question my background in math. I think the Calc book I used just skimmed over the proofs and was more application intensive. We kind of went over proofs of major theories, but most of the time after that was how to work problems and to identify what to use and where to use it. While this should be sufficient for my physics major, I may have to work harder for my math major.

But I'll see. School starts in a couple of weeks, and I can talk to my advisor and some professors and see how my calculus class is taught.

is there linear algebra included in the multivariate course? at my school they include linear algebra and then the actual linear algebra is really like a second course in it

There is no linear algebra included (or very little) in this multivariate calc course. There is another one offered, though. It is a year long sequence which includes Calc III, linear algebra and differential equations at a more rigorous level than the regular classes (the ones I'll be taking).

And thanks for the responses, mathwonk and axeae.

 

[mathwonk]

you might to try that more rigorous one. thers where you may feel out of your depth at first, but could have the ability to hang in there and get up on a higher level that could be fun and useful.

i think you can do it. but it will be more time consuming. but it sounds likea better course, since it puts the linear algebra in the context where it belongs namely to do sev vbls calc and ode.U Md is a good school.

 

[mathwonk]

idon't know if thi is right for you, but usually with strong students like you i recokmmend geting in the more rigorous sequence even if you have to go back and take one variable to do it. i.e. those honors level classses have smarter students and better teachersa nd present the amterial in a better way.

it is boring for a strong student like you to go to a non honors class, even if it is "advanced".

i.e. what is the point in using your honors AP prep to place into a non honors college course with non honors students? The goal is usually to move along faster of course, but in terms of course quality, a high level rigorous honors one variable course is usually superior to a non honors several variables course.

but ask your honors or math advisor or the professors in the calc classes.

 

[mathwonk]

well maryland does not seem to have an honors one variable course, so i would suggest investigating the 340-341 sequence, honors several vabls with ode and lin alg.

 

[axeae]

for me, having the background in linear algebra wasn't exactly necessary for differential equations but definently helped the understanding (I took the multivariate and differential equation courses concurrently and some topics were introduced in multivariate after diffeq)

so many things overlap (Eigenvalue, Eigenvectors, linear indepdenence, Wronskian) that it would probably not be too difficult to do, and would probably be pretty beneficial since your class is strictly linear algebra rather than a hodgepodge of calculus and la.

 

[SpiffyKavu]

Ok then. The 340-341 sequence if full, so I can't register for it (though I can see what books they are using). And for next semester I'll check out the honors courses for ode and linear algebra.

For next year, though, should I go into Advanced Calculus, or perhaps take some other math courses? Introduction to Absract Algebra and then Linear Algebra come to mind (among a few others), both rigorous and proof based, and ranking in difficulty along with adv calc. If I do that, I'll then take adv calc in my junior year. As for my physics classes, well I don't have as much flexibilty in that part of the schedule as I do in my math major. And, as to be expected, the only math requirements are through ode, so I may be finished with that after my freshman year.

 

[mathwonk]

you might talk with the instructor of the 340-341 sequence about enrolling anyway. If he/she thinks you belong in there he might let you.

there is likely to be some attrition before long anyway.

 

[axeae]

could you post the course descriptions for the 340-341 and the individual courses it covers?

 

[SpiffyKavu]

MATH340 Multivariable Calculus, Linear Algebra and Differential Equations I (Honors); (4 credits)
Prerequisite: MATH140; MATH141; and permission of department. Credit will be granted for only one of the following: MATH241 or MATH340. First semester of the MATH 340-341 sequence which gives a unified and enriched treatment of multivariable calculus, linear algebra and ordinary differential equations, with supplementary material from subjects such as differential geometry, Fourier series and calculus of variations. Students completing MATH 340-341 will have covered the material of MATH 240, MATH 241, and MATH 246, and may not also receive credit for MATH 240, MATH 241 or MATH 246.

MATH341 (PermReq) Multivariable Calculus, Linear Algebra, Differential Equations II (Honors); (4 credits)
Prerequisite: MATH340. A student receiving credit for MATH341 cannot receive credi t for MATH240, MATH246, MATH400, or MATH461. A continuation of MATH 340.


MATH241 Calculus III; (4 credits)
Prerequisites: MATH141. Credit will be granted for only one of the following: MATH241 or MATH340. Introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections will use MATLAB.

MATH240 Introduction to Linear Algebra; (4 credits)
Prerequisite: MATH141 or equivalent. Credit will be granted for only one of the following: MATH240, MATH341, MATH400, or MATH461. Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms.

MATH246 Differential Equations for Scientists and Engineers; (3 credits)
Prerequisite: MATH141; and anyone of the following: MATH240 or ENES102 or PHYS161 or PHYS171. Credit will be granted for only one of the following: MATH246 or MATH341. An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations. All sections will use MATLAB.


These are the decriptions from the catalogue.

 

[axeae]

it seems kinda weird that they would be able to fit MORE material than 11 credits of math into an 8 credit course over two semesters... it also doesn't mention MATLAB for the honors course. the supplementary material makes it sound like a nice course though..

as mathwonk said, there will probably be an opportunity for you to join the class despite it being full. most math classes that I've been in have very many drops--the professors should be willing to overfill the course because of this. what I would probably do is sign up for the multivariable as a safety and then attend the first lecture of the honors sequence, and talk to the professor AFTER the lecture. unless it's a small class that usually works. if you can talk to an advisor or professor before everything starts though, that would probably be the best.

 

[SpiffyKavu]

Alright, I'll keep that in mind. I also know a couple of people in the honors course. An old friend is on the second section, in which I can attend the first lecture, but not the second. It also may be worth mentioning that there are a total of 8 people waitlisted for the three sections at this point. And the only section that can work with my scedule is the first section, which has 6 of the 8 waitlisted.