Is My First Quarter Schedule at Western Washington University Balanced?

[phun]

I wish more people thought of it that way Mathwonk, I would much rather take 3 or 4 classes and learn the material very thoroughly than take 5 and learn only what is necessary to do well from each. However, many programs such as mine require you to take a full 5 class courseload which I think is unfortunate but oh well.

Learning the material very thoroughly in, say 3 classes, is of course more beneficial than "getting by" in 5 classes.
However, from my personal experience I've come to decide that there is another side to this problem.
I have taken from 3 to 5 quarter classes in the past, and my conclusion is that one has to strike the right balance between depth and breadth.
I think it is very important to get EXPOSURE to a wide range of topics at the undergraduate level than FOCUS yourself to a narrow range of topics.

By exposure I mean enough background for you to recognize when the knowledge is needed and be able to refresh memory or even go a little bit deeper than you knew as need arises.

By focus I mean studying a topic so throughly that you would be walking down the street and someone asks you for a proof on page 123, and you can reproduce it.

Assuming I can get the same gpa by either "focusing" on 3 classes or getting "exposure" in 5 classes, I would take 5 classes.

 

[scorpa]

Learning the material very thoroughly in, say 3 classes, is of course more beneficial than "getting by" in 5 classes.
However, from my personal experience I've come to decide that there is another side to this problem.
I have taken from 3 to 5 quarter classes in the past, and my conclusion is that one has to strike the right balance between depth and breadth.
I think it is very important to get EXPOSURE to a wide range of topics at the undergraduate level than FOCUS yourself to a narrow range of topics.

By exposure I mean enough background for you to recognize when the knowledge is needed and be able to refresh memory or even go a little bit deeper than you knew as need arises.

By focus I mean studying a topic so throughly that you would be walking down the street and someone asks you for a proof on page 123, and you can reproduce it.

Assuming I can get the same gpa by either "focusing" on 3 classes or getting "exposure" in 5 classes, I would take 5 classes.

I completely agree, 3 classes in my opinion would not be enough for me. Either a 4 or 5 course load is best in my opinion, and of course this completely depends on which classes you are taking. I think exposure is very important at all levels, especially the undergraduate, however it is up to the individual to decide what they can and can not handle. I only meant that one should not take a 'normal' 5 course load because they are told that it is what everyone else does, they need to decide what works best for them.

 

[mathwonk]

you may be right but i suspect you have never had a really hard math class, like a spivak calculus class, or an algebraic topology class, or a differentiable amnifolds class, or a several complex variables class, or an advanced abstract algebra class, modules, commutative algebra, galois theory, or real analysis including measure and integration.

i could be wrong though. my point is that a really hard class studied deeply does expose you to a lot of stuff needed to even understand that one. but maybe you are right that young people should see things broadly rather than deeply at first.

 

[jbusc]

I could never really see the point of rushing through stuff trying to do so many courses and overload each semester. Some may find that to be hypocritical given that I skip prerequisites and substitute more advanced courses for lesser ones, but I don't think there really is a comparison. I take only 4 classes per semester and that is enough for me (though I may have to take a 5-class semester sooner or later)

Taking say 5 or 6 courses in a semester encourages you to do the absolute minimum in each course rather than really master the material which let's you do better in the future rather than just what you need to get an A.

The only real reason I can imagine for overloading is if you have financial constraints and you have to in order to get through and get a job, or if opportunities arise which would disappear if you wait too long. But even the financials doesn't make complete sense, because if you are paying $100k for an education you want to make sure you get your money's worth and a head full of knowledge instead of a piece of paper with your name on it (which admittedly is all some people want)

 

[phun]

you may be right but i suspect you have never had a really hard math class, like a spivak calculus class, or an algebraic topology class, or a differentiable amnifolds class, or a several complex variables class, or an advanced abstract algebra class, modules, commutative algebra, galois theory, or real analysis including measure and integration.

i could be wrong though. my point is that a really hard class studied deeply does expose you to a lot of stuff needed to even understand that one. but maybe you are right that young people should see things broadly rather than deeply at first.

I agree. There are some core courses that an undergraduate could spend ungodly amount of time on and still not become comfortable with, such as if you are taking real analysis using Rudin or quantum mechanics using Shankar. With one of those classes, taking more than 3 would definitely be a struggle. I guess I was thinking of more "normal" undergrad courses.

 

[Lucretius]

I was just thinking: I will be learning this stuff really fast! I will be going through all of single-variable calculus in less than a full academic year! Is it recommended to go into multivariable calculus right afterwards, or linear algebra?

 

[mathwonk]

linear algebra is a prereq for advanced calc done right, but some advanced calc courses include linear aklg.

 

[Lucretius]

Looking at my course guide (I'm already getting ahead of myself, trying to plan out my first year) it says that I can take a Linear Algebra and Differential Equations I course, but then in the guide it says Multivariable calculus is recommended. Maybe I should wait before looking any further into this?

 

[mathwonk]

talk to the profs there, they are usually petty helpful and know the ropes there better than i do.

but the sooner you get linear algebra the beter. and multilinear calc. thise are the two most important math subjects, bar none. and lin alg comes first.

 

[Lucretius]

Man, it's going to be a long wait, this month and a half before school. I'm already prepped to go! As soon as I can, I am going to declare my major. Looking into the very distant future, it's a shame that WWU has no graduate program for physics, but one for mathematics. Guess I'll have to find another school for that —*but I'm getting ahead of myself.

 

[jbusc]

linear algebra is a prereq for advanced calc done right, but some advanced calc courses include linear aklg.

I say this all the time and people always give me strange looks. I'm glad that I'm not the only one who thinks that.

When I took multivariable calc most of the people in the class hadn't taken linear algebra yet, I however had done an advanced linear algebra course, and I thought everything was pretty straightforward. All that you are doing is calculus on vectors essentially.

 

[Lucretius]

I got a response from a professor there:

They said that while Linear Algebra and Multivariable Calculus are related, and it often seems natural to take Linear Algebra before Multivariable Calculus, that Linear Algebra is a more abstract topic, and the first quarter of multivariable calculus is designed so as not to rely heavily on Linear Algebra. His recommendation is to take a quarter of Multivariable Calculus (at least) before attempting Linear Algebra.