How To Self Study Spivak's Calculus

[iratern]

Hi, so I'm going to attend university this fall, and I'm planning to double major in math and physics. So I will be taking a calculus course based on Spivak and an Algebra course that uses Friendberg's Linear Algebra.

So currently I'm trying to start studying these books so that I can get up to speed with school. I just got Freindberg so until recently I have used Strang's Linear Algebra with Applications + MIT OCW. Should I continue this or should I do both together or what?

I'm not really planning to go far, I just want to get a feel of the material, before school. But I do want to learn whatever I can as effective as I can.

So how do you guys think I should study these books? They will be my first encounter with rigorous mathematical proofs.

 

[General_Sax]

hhhhmmm, if I were you, I would first read a chapter, and then I think I would try some of the practice problems. Yeah, I think I would do just that.

I don't get too hung up on any individual problem when I self-study. Just try to get a feel for the types of problems you'll have to do in the future. If I can visualize the problem, then I feel like I'll have a far easier time with it in class, because I'll actually know what the prof. is talking about.

 

[iratern]

hhhhmmm, if I were you, I would first read a chapter, and then I think I would try some of the practice problems. Yeah, I think I would do just that.

Yeah, that's what you usually do but the book is theorem-proof oriented, so it's confusing sometimes. I mean I know the chapter (like the fist chapter is about the properties of the numbers), but it's different then from what I've seen until now.

My main question is whether to try and prove every theorem/statement he writes before he proves it? Or is that too much of a waste of time?

 

[mathwonk]

trying to prove something is never a waste of time. of course at some point you might want to give up and read his proof. the point is you benefit from trying even when you are unsuccessful.

 

[iratern]

Thanks Mathwonk, I was kind of worried that I was looking at his proofs too much for hints and such. Hearing YOU say that, makes me feel better about how I'm currently approaching the books.

I have another question, how should I go about linear algebra? Should I use Strang's book( Linear Algebra and it's applications) or Friendberg's? I mean just for the last 3.5 weeks before school starts, after that my course requires Friendberg's.

Also is there any other advice you can give a 18 year old college freshman (who enjoys both math and physics), attending a large public university (in Canada to be specific)?

Thank you for your time, I really appreciate it as well as your sticky

 

[yossell]

Try and find a balance between pushing and challenging yourself without depressing and demotivating yourself. Sometimes, a proof is included in the main text rather than set as a question to explain and introduce a new and subtle technique, something you really wouldn't have thought of on your own over a couple of days. Don't be too hard on yourself if you can't do it.