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roguespartan6 January 8th, 2017 08:59 AM

Returning to school: Best approach?
 
In preparation to return to school to pursue a B.S. in Mathematics, I was planning to purchase the texts of some prerequisite courses and work through them (namely Pre-Calculus and Calculus 1 & 2).

Are there any better approaches that anyone could recommend? Or anything to supplement this approach? Thanks.

quasi January 8th, 2017 07:05 PM

Fully master precalculus -- don't just skim it. It will serve you well.

At the same time, I recommend working through a Discrete Math text, with the goal of developing basic proof skills.

Joppy January 8th, 2017 08:46 PM

I've always found revising content that you are already familiar with is much more beneficial than self-studying content you think will be assessed in a future class. This is just as much about achieving well in class as it is understanding the content (they are very different things).

For example you might spend hours fiddling around on one area, only to find that the lecturer covers it in 20 minutes.

From your post I'm not sure what your current mathematical experience entails. So, if you've covered pre-calc in the past, then definitely go over that in detail, as quasi has said.

Maschke January 8th, 2017 10:46 PM

Quote:

Originally Posted by roguespartan6 (Post 559349)
In preparation to return to school to pursue a B.S. in Mathematics, I was planning to purchase the texts of some prerequisite courses and work through them (namely Pre-Calculus and Calculus 1 & 2).

Are there any better approaches that anyone could recommend? Or anything to supplement this approach? Thanks.

There are a lot of different kinds of calculus texts. If you're going to major in math you should follow the more abstract and theoretical type of approach, in which rigor is emphasized.

On the other hand it will be very helpful for you to simply get really good at the mechanics of calculus. So I'd suggest a theoretical type book (Spivak's calculus text gets a lot of praise in this regard; though it came out way ofter my time and I'm not personally familiar with it). And I'd supplement that with the Schaum's outlines so you can drill and kill derivative and integral problems till they come out of your ears.

The suggestion to study discrete math is a good one too. Even in abstract courses you always end up needing to sling around the binomial coefficients at some point.

Also if you're new to proofs, a book like How to Prove It by Velleman gets recommended a lot. Again, this is also after my time and I haven't seen it. But I had a great Euclidean geometry course in high school so I always had the "proof gene." If you haven't got the proof gene, you want to pick it up as soon as possible. You won't need it in calculus but you'll need it in linear algebra and beyond.

roguespartan6 January 9th, 2017 04:59 AM

Quote:

Originally Posted by Joppy (Post 559424)

From your post I'm not sure what your current mathematical experience entails. So, if you've covered pre-calc in the past, then definitely go over that in detail, as quasi has said.

Thanks for the replies.

My current mathematical experience is that I haven't taken any math, or done a whole lot, since my undergraduate days, which ended in 1993. I've always liked math, and took pre-calc in high school, and then Calc 1 and 2 in college. I changed majors before taking Calc 3. Other than that, I took CJ statistics as both an undergrad and grad student, though I don't recall them being particularly rigorous, math-wise.

roguespartan6 January 9th, 2017 05:05 AM

Quote:

Originally Posted by Maschke (Post 559431)
There are a lot of different kinds of calculus texts. If you're going to major in math you should follow the more abstract and theoretical type of approach, in which rigor is emphasized.

On the other hand it will be very helpful for you to simply get really good at the mechanics of calculus. So I'd suggest a theoretical type book (Spivak's calculus text gets a lot of praise in this regard; though it came out way ofter my time and I'm not personally familiar with it). And I'd supplement that with the Schaum's outlines so you can drill and kill derivative and integral problems till they come out of your ears.

The suggestion to study discrete math is a good one too. Even in abstract courses you always end up needing to sling around the binomial coefficients at some point.

Also if you're new to proofs, a book like How to Prove It by Velleman gets recommended a lot. Again, this is also after my time and I haven't seen it. But I had a great Euclidean geometry course in high school so I always had the "proof gene." If you haven't got the proof gene, you want to pick it up as soon as possible. You won't need it in calculus but you'll need it in linear algebra and beyond.

Thanks. I really appreciate all the advice, and hadn't even thought about proofs. As soon as I read that, my mind immediately drifted back to my high school geometry class. LOL

Would there be any additional benefit to using the specific text currently being used in the calculus sequence where I'll be attending?

Also, given the amount of time I have been out of practice, would you recommend Spivak/Schaum, or Velleman, first?

Thanks for all the help, folks.

Joppy January 9th, 2017 01:25 PM

Quote:

Originally Posted by roguespartan6 (Post 559441)
Thanks for the replies.

My current mathematical experience is that I haven't taken any math, or done a whole lot, since my undergraduate days, which ended in 1993. I've always liked math, and took pre-calc in high school, and then Calc 1 and 2 in college. I changed majors before taking Calc 3. Other than that, I took CJ statistics as both an undergrad and grad student, though I don't recall them being particularly rigorous, math-wise.

So you'll be taking calculus again?

roguespartan6 January 9th, 2017 03:25 PM

Yes, I'll have to take Calc 3.

Joppy January 9th, 2017 03:47 PM

Quote:

Originally Posted by roguespartan6 (Post 559531)
Yes, I'll have to take Calc 3.

Cool! Well my advice would be revise pre-calc and calc, and if you get time maybe look at what calc 3 involves. As for the proofing side of things, that would be good to look into, as others have mentioned. I started on "How to Read and Do proofs - Daniel Solow", it's very introductory though, but still handy.

quasi January 9th, 2017 05:11 PM

Personally, I found the text "How to Read and Do Proofs" dreary. I would avoid it.

As for using the Calculus text that will be used for your classes, that makes a lot of sense to me. Start from page 1, doing a decent selection of exercises.

But don't forget my suggestion to "master" Precalculus. Weakness in Precalculus almost automatically makes Calculus rough going.

As far as proofs, I advise a "gentle" start, using a Discrete Math text. Besides the usual introduction to Combinatorics and Probability, such texts usually have introductory chapters on Number Theory, Symbolic Logic, Mathematical Induction, Sets, Functions, Relations, all of which are essential for higher levels of math. They also typically include some proofs, and a discussion of proof techniques.


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