Calculus Take Math Further: Hubbard and Hubbard at UCSD

[RubinLicht]

I am currently in 11th grade and will, by the end of the year, complete calculus I II and III, as well as linear algebra. The rigor of these programs at my school is, from my point of view, hardly satisfying, though I haven't had issues with it yet. (we use the stewart book, and anton for linear algebra) Next year, i have the choice of taking an honors track for an integrated linear algebra and multivariate calculus course at UCSD since i live so close by, they use the Hubbard and Hubbard book. Here are my choices:

1) take at UCSD
2) self study (then instead of taking free periods i would actually have to take more periods so that colleges don't think I am slacking off, but it is doable, i am learning from purcell, resnick, and kleppner by myself, i do not think math would be that much harder)
3) put it off until college and spend all my time cramming physics for physics olympiad next year.

Thanks for your time

 

[QuantumQuest]

It is not clear from what you write, what is your goal. Best time and efforts management, is based on this.

 

[RubinLicht]

It is not clear from what you write, what is your goal. Best time and efforts management, is based on this.

Rewritten:

I am currently in 11th grade and will, by the end of the year, complete calculus I II and III, as well as linear algebra. The rigor of these programs at my school is, from my point of view, hardly satisfying, though I haven't had issues with it when applying it in physics yet. (we use the stewart book for calculus, and anton for linear algebra) Next year, i have the choice of taking the honors track for the integrated linear algebra and multivariate calculus course at UCSD since i live so close by, they use the Hubbard and Hubbard book. Here are my choices:

1) take the class at UCSD, take two free periods in school
2) self study (then instead of taking free periods i would actually have to take more periods so that colleges don't think I am slacking off, but it is doable, i am learning from purcell, resnick, and kleppner by myself, i do not think math would be that much harder)
3) put it off until college and spend all my time cramming physics for physics Olympiad next year.

My goals for next year (senior year) : get gold/make camp in physics Olympiad.
Goals overall: would like to double major in ee and physics, so I want to take the course for rigor, but also have time left for physics.

Concerns:
Time: ap classes, college apps, preparing more for physics Olympiad.
Money: it's like 1000 per quarter, my dad should do it
Difficulty: perhaps I'll have trouble with Hubbard and Hubbard.

Just input any thoughts you have about any of this, thanks!

 

[bacte2013]

Rewritten:

I am currently in 11th grade and will, by the end of the year, complete calculus I II and III, as well as linear algebra. The rigor of these programs at my school is, from my point of view, hardly satisfying, though I haven't had issues with it when applying it in physics yet. (we use the stewart book for calculus, and anton for linear algebra) Next year, i have the choice of taking the honors track for the integrated linear algebra and multivariate calculus course at UCSD since i live so close by, they use the Hubbard and Hubbard book. Here are my choices:

1) take the class at UCSD, take two free periods in school
2) self study (then instead of taking free periods i would actually have to take more periods so that colleges don't think I am slacking off, but it is doable, i am learning from purcell, resnick, and kleppner by myself, i do not think math would be that much harder)
3) put it off until college and spend all my time cramming physics for physics Olympiad next year.

My goals for next year (senior year) : get gold/make camp in physics Olympiad.
Goals overall: would like to double major in ee and physics, so I want to take the course for rigor, but also have time left for physics.

Concerns:
Time: ap classes, college apps, preparing more for physics Olympiad.
Money: it's like 1000 per quarter, my dad should do it
Difficulty: perhaps I'll have trouble with Hubbard and Hubbard.

Just input any thoughts you have about any of this, thanks!

I am currently self-studying the Hubbard/Hubbard (5th edition) to prepare myself before jumping into the differential geometry and the classic books on the multi-variable analysis like Spivak and Loomis/Sternberg. I like this book very much as it treats both the theoretical and computational aspects of the vector calculus, and it also explains very well the relationship between the linear algebra to vector calculus. The book can be used as a first introduction to the proof writing. The book is verbose, and it will hand-hold you a lot if you decided to use it.

However, I recommend the "Vector Calculus" by Marsden/Tromba if your goal is to prepare yourself for the areas in physics. M/T heavily emphasizes the applications of vector calculus, particularly on the physics. Many of the problems are physics-related, and most of the problems are very challenging. Unfortunately, M/T does not really emphasize the theoretical background, and it skips quite a lot of proofs (they are on the book website though).

 

[QuantumQuest]

As a general rule of thumb - this is of course my opinion, what I prefer to do, is doing as many things as I can in parallel and mostly try what I find difficult. But there is a clear warning here: you must know for sure if something is easy for you or not and not just think that it is so. But trying what you find difficult is usually more worthwhile, provided that it is absolutely relevant to the educational path you've chosen. So, I cannot get more specific than this; the goal is the best management of your time and resources and the choice is up to you.

 

[RubinLicht]

As a general rule of thumb - this is of course my opinion, what I prefer to do, is doing as many things as I can in parallel and mostly try what I find difficult. But there is a clear warning here: you must know for sure if something is easy for you or not and not just think that it is so. But trying what you find difficult is usually more worthwhile, provided that it is absolutely relevant to the educational path you've chosen. So, I cannot get more specific than this; the goal is the best management of your time and resources and the choice is up to you.

thank you for your reply.