How to prep for University Mathematics

[tmlfan_179027]

Hey, guys I'm in my last year of high school and I am wondering how i could do some self preparation for University mathematics next year? This is the case as I have been told college math is very challenging and less directed toward algorithms. Right now I am currently enrolled in a standard Calculus and vectors course and I don't think it alone will be enough to give me a solid background for what is ahead.

 

[djeitnstine]

read some calculus 1 and 2 books to keep yourself up to date...I don't know how your university is but I know most do not recognize high school calculus. So just read read read =]

 

[Nabeshin]

Hey, guys I'm in my last year of high school and I am wondering how i could do some self preparation for University mathematics next year? This is the case as I have been told college math is very challenging and less directed toward algorithms. Right now I am currently enrolled in a standard Calculus and vectors course and I don't think it alone will be enough to give me a solid background for what is ahead.

If you find most of the stuff you're doing right now in calculus and easily use things you learned in pre-calculus (trig identities, fraction decomposition, manipulation of properties of logarithms and exponents) you're definitely in good shape. As was mentioned above, most universities don't recognize normal high school calculus (unless it's AP), so you will likely end up taking calculus again your first year of college. In this case, if you remember your calculus from this year and keep fundamentals of pre-calculus and geometry in mind, it should be relatively easy for you.

 

[Wellesley]

This is the case as I have been told college math is very challenging and less directed toward algorithms. Right now I am currently enrolled in a standard Calculus and vectors course and I don't think it alone will be enough to give me a solid background for what is ahead.

What course was the person you asked enrolled in? As you get into the 300 and 400+ level math courses, I'd imagine they'd get more challenging. For me, Calculus I and II didn't really require much prior preparation. If you're comfortable now, you should be fine. If you're taking AP Calculus (especially BC), you'll be more than prepared.

What are you planning to Major in?

 

[tmlfan_179027]

im planning on doing a double major in math and another subject that I am unsure of at the moment. my math teacher is the one who gave the class his input on University Math. I kinda regret not choosing AP Calc. Its too late now. Is AP calc. similar to university calc.?

 

[Nabeshin]

im planning on doing a double major in math and another subject that I am unsure of at the moment. my math teacher is the one who gave the class his input on University Math. I kinda regret not choosing AP Calc. Its too late now. Is AP calc. similar to university calc.?

Yes, AP calculus (AB) is the equivalent of university calculus I, and AP calculus (BC) is the equivalent of university calculus I and II. The courses (should) cover the same material in the same amount of depth, which is why universities will grant credit for an appropriate score on the AP exam.

 

[elterrible]

im planning on doing a double major in math and another subject that I am unsure of at the moment. my math teacher is the one who gave the class his input on University Math. I kinda regret not choosing AP Calc. Its too late now. Is AP calc. similar to university calc.?

Yeah its comparable. In high school you are doing a year, which is two semesters. AP AB does 1 semester of Calc, AP BC is equivalent to Calc I and Calc II.

I had done Chemistry AP in high school and then college level Chemistry and the AP class was actually far more challenging. The Chem in college was a joke and all multiple choice tests as they didnt want to hand grade all 400 students tests.

It is better if you can take it in high school, you are spending about 5 hours a week in class compared to college where you are about 2.5 to 3 hours a week in class.

 

[Unknot]

If you are doing well in BC (although I did see some people doing BC and having trouble with a proof-heavy course), I would go on and learn some linear algebra and multivariable calculus (Calc III).

 

[qntty]

Not trying to steal the thread at all, but since you mentioned it... I have a 95 in Calc BC and I find that the course grasps my attention quite well and I pick up on the concepts rapidly. Is there a good book that you know of to go ahead and continue my Calc II at an accelerated rate along with Calc III? I absolutely detest our book (it covers I, II, and III). It's probably one of the only books I've never been able to self-learn anything to adequacy.

Thanks in advance. And sorry again for detracting from the thread starter

Spivak is what you're looking for.

 

[Unknot]

It's the right one, but that doesn't have Calc III though.

 

[Unknot]

Well in spirit of self-prepping yourself for University Mathematics...

I've found the 3rd Edition for sale online, does it contain the Calc III? Or what am I looking for?

Spivak's calculus book deals only with single variable. It does not have calc III. If you are looking for a book that is more of a continuation of your AP calculus course, I would NOT recommend that you get something like Spivak's second calculus book ("Calculus on Manifolds"). Great book, but I personally think it might be too difficult for you. You really need to know proof-heavy calc I and calc II, and even then it's very difficult and if you are more on computation side, you better look at something else.

I really don't know any "applied" calculus books that deal with several variables other than something like Stewart. But it's an OK book and it's widely used, so you might want to consider that.

 

[Unknot]

Ah okay. I thought we were looking for a single book with Calc II and III in it. So you just suggest Spivak to cover what I'm probably missing in the speed of BC Calc to be sure that I understand the concepts more thoroughly and go on to take Calc III in college?

There are many factors. First, you won't understand calc III (there's a thread about this) without basic linear algebra. Spivak is, people might disagree, primarily geared towards math majors. I don't know what book you are using, but it will be different. And what are you planning to go into? If you are going to be an engineer, Spivak could be a good challenge but probably not the optimal choice.

Again, I don't know any single book that has calc II and calc III together. Many books separate these two.

 

[Unknot]

Yes I've been reading the Linear Algebra pre req. thread as well

And as of right now I'm going into Computer Eng. but this won't last because I have no passion to major in computers anymore. It's really all in math/physics right now, so in answer to your question, probably an extremely oriented math major perhaps even math itself.

I really just want to be sure I pass the AP exam (both parts), but NOT at the cost of a full understanding of what I'm possibly exempting in college. I don't want to be one of the many cases I've heard of where kids get on their high horse after making a 5 on the BC exam, then struggle with the simplest precursors for Calc III in the first weeks of the course!

Spivak series or Apostol series would be good. But maybe it's a good time to start a thread?

 

[Feldoh]

Be warned, Spivak and Apostol are difficult relative to your typical AP calculus class. These books deal more with proofs of the mathematical concepts. The only reason I bring it up is that I don't know about you but for me intro to real analysis was difficult, it's a lot of work.

Oh and I wouldn't worry about the first part of Calc III. As long as you've done vectors in a physics/math class previously the first part of calc 3 will just be review.

 

[Werg22]

The best prep. for university math is to get your body used to only 5 hours of sleep a night.

 

[Bourbaki1123]

Unless you pad your mornings with easy A, skip-class, gen eds. Then get cracking later in the day...

Seriously though, I would suggest finding a good proofs book. I think Spivak or Apostle are substantially easier after you have developed a strong notion of proofs and set theory. Proofs are something which require a sort of knack but can start out as very mechanical with good results. If you can get the broad concepts and techniques of proof writing down, you will be way ahead. I would recommend the text my class used but its a ripoff(even though it isa pretty solid survey/proofs text).

What about Lang's calculus text? I have never looked at it, does anyone know if that is any good?

 

[tmlfan_179027]

milking the thread was actually good. I've learned quite a lot . thanks guys :P. wat kind of books does anyone suggest in terms of starting to understand proofs? my teacher has shown us a couple and they are not my favourite thing to comprehend.

 

[Wretchosoft]

Unless you pad your mornings with easy A, skip-class, gen eds. Then get cracking later in the day...

Or your math class starts at 8:30 every day of the week for the entire year.

I strongly recommend Spivak over learning Calculus III. Multivariable calculus at the level it's typically presented is mostly computational and application-based (particularly towards electromagnetism). It won't do much to sate any real mathematical curiosity.

milking the thread was actually good. I've learned quite a lot . thanks guys :P. wat kind of books does anyone suggest in terms of starting to understand proofs? my teacher has shown us a couple and they are not my favourite thing to comprehend.

I don't think anyone book will help you understand proofs. What you need to do is understand the definitions and write some proofs on your own. I also recommend acquainting yourself with some of the (simple) classic proofs, as they are relatively easy to understand and illustrate the importance of applying definitions. For example, the proof that the square root of 2 is irrational, or Euclid's proof that there are infinitely many primes, or the proof that the natural numbers are not bounded above. All of these can easily be found online.

 

[khemix]

Hey, guys I'm in my last year of high school and I am wondering how i could do some self preparation for University mathematics next year? This is the case as I have been told college math is very challenging and less directed toward algorithms. Right now I am currently enrolled in a standard Calculus and vectors course and I don't think it alone will be enough to give me a solid background for what is ahead.

This depends, are you going to study pure math as a major or math for scientists. School prepares you well enough for the sciences, but if you want to do pure math I suggest you read books like Gelfand Trigonometry and Niven's Numbers to get up to speed.

 

[tmlfan_179027]

yea pure mathematics is what i want to get into.

 

[driscol]

Hi, do any of you know if MIT's Open CourseWare Calculus I (http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/Calendar/index.htm) is the equivalent of the high school AP BC Calculus / Calculus I + II at many other less math intensive colleges?

 

[qntty]

Yes it's the standard Calc I/II curriculum (though the problem sets might be harder).

 

[Wellesley]

Hi, do any of you know if MIT's Open CourseWare Calculus I (http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/Calendar/index.htm) is the equivalent of the high school AP BC Calculus / Calculus I + II at many other less math intensive colleges?

Yes, it does look like the course covers everything Calculus BC covers, although it moves at a faster pace.