Find Calculus Education Outside Community College

[contramundum]

Hello everyone. So here is my dilemma. I am currently attending a community college where there are no honors math classes offered. I am starting calc 1 in the fall and I know that my school uses Stewart. However, I would very much like to learn calculus the "proper" way a la Spivak or Apostol. What would you guys do in my situation?

 

[GreatEscapist]

Learn it on your own- pick up a book, while learning it on your own.

Or the more complicated way, switch schools.

Or the sad but simple way- just deal with that system.

 

[thrill3rnit3]

Learn it the "normal" way first, take the class, ace it. Once you got the basics down, get a copy of Spivak, and spend 1-2 hours a day reading it and solving end of chapter problems.

You need to learn how to crawl before attempting to fly.

 

[arunma]

Hello Against the World (no I don't speak Latin, just those two words),

Just wondering: why do you think Stewart is a bad way to learn calculus? Correct me if I'm wrong, but aren't Spivak and Apostol meant for advanced undergrads? When I was doing my math degree, I learned calc out of Stewart. I've read other calc books just for fun. Honestly I think that at the calc 1 level, mathematical formalism with all the theorems and lemmas is sort of pointless. First and foremost, you've got to learn how to do calculus really well. And as odd as this sounds, I thought Stewart was a great book because it had a lot of pictures to help me understand mathematical concepts.

I'm guessing you'll be attending a four year school for your last two years. If so, the math department will have a class called "Advanced Calculus." This would be right up your alley. Math departments know that the calculus sequence is designed for us physicists and engineers more than it is for the mathematicians. Therefore they offer this class so that you guys can learn calculus the "right way," complete with all the derivations and proofs.

 

[contramundum]

Arunma, haha, very impressive that you know the phrase. As to your question, I was reading the "who wants to be a mathematician" thread and most of the people in there seemed to think Spivak or Apostol is where it's at. So I am not saying that Stewart is "bad". I'm more saying that I am ignorant and I'm not sure which way to go. Basically I want the best understanding of calculus that will help me down the road in other math classes.

I appreciate your input.

 

[thrill3rnit3]

Arunma, haha, very impressive that you know the phrase. As to your question, I was reading the "who wants to be a mathematician" thread and most of the people in there seemed to think Spivak or Apostol is where it's at. So I am not saying that Stewart is "bad". I'm more saying that I am ignorant and I'm not sure which way to go. Basically I want the best understanding of calculus that will help me down the road in other math classes.

I appreciate your input.

learn from Stewart first. You have to start from a solid foundation.

 

[FieldDuck]

Hello everyone. So here is my dilemma. I am currently attending a community college where there are no honors math classes offered. I am starting calc 1 in the fall and I know that my school uses Stewart. However, I would very much like to learn calculus the "proper" way a la Spivak or Apostol. What would you guys do in my situation?

There's no one stopping you from reading either of those books at the same time. However, I personally would not worry to much right now about NOT learning Calculus in it's completely formal way right now. At this point in time, I think it would behoove you to get a better practical understanding of the concepts before you attempt to go back and understand why everything is true.

The reason I suggest this is because this mathematics can become pretty abstract and if it is your first exposure it may be a bit to much and you might just get completely discourage and get the silly notation in your head that you're not cut out for mathematics. However, if you have a good idea of the concepts already then the rest becomes filling in the details and you can probably handle that more easily after you know the general idea of what you are doing.

Besides reading Spivak/Apostol doesn't give you the complete picture of what Real Analysis is. So even if you read those two books, you're knowledge will still be lacking when you get right down to it. The main advantage in reading these two books is that they get you thinking like you should be thinking, (ie why is the inequality true, why is this proof true, why can i say this, etc.)

 

[contramundum]

Thank you all.

 

[Saladsamurai]

Why don't you learn from Stewart and then in your "down time" read the sections from Spivak that correspond to those your class is covering in Stewart? That way you are learning the way you need to (to get the grade) and at the same time you have an opportunity to correlate the less formal material from Stewart to the more formal from Spivak.

You don't have to read Spivak cover-to-cover while also taking a class using Stewart. You can just take a peak at Spivak along the way. This will help you be aware of the types of things you should be thinking about for later.

Just a thought.