Math Help for Reviewing Algebraic Foundations Before Calculus | Expert Tips

[Yawzheek]

It's not that I'm a total beginner in mathematics, so please allow me to explain:

I've worked through everything UNTIL Calculus, quite hard at that, when I was in college. I took a series of general physics courses, passed with no problem, and everything was good, EXCEPT...

Years ago, I purchased a physics book (for about $4, though that's not important) hoping to work through it as well, but I left school. It has been some 4 years later, and I want to work through it, but it's calculus based. Problem is, I never had any formal schooling for Calculus (minus the introduction to limits in precalculus) and forget the overwhelming majority of mathematics from then.

I know this seems lazy, and largely it is, and is asking much from the community, but knowing that I've done this before, what algebraic areas need I review before calculus, so that I may have a firm foundation for calculus?

I say again, I've done it all before, but most I've forgotten as I haven't used it in years, so it's not as though you're telling a child to perform differentiation, and I made my way through the algebraic physics courses as well, but what is ABSOLUTELY ESSENTIAL so that I may review it all properly? I've always been poor on exponential functions, so I know those, but what else? I feel like occasionally I'm reviewing things that don't matter in my old books (completing the square? Quadratic equation) so I ask you guys, because I want to get back into it, but I don't think I need to take three more quarters worth of mathematics just to remember what I once knew.

Probably a stupid question, I know, but I must ask it.

 

[phion]

Study a lot of trigonometry.

 

[Yawzheek]

In fact, it's possible I may compress all of this into a sentences:

I've neglected my math studies until precalculus, but I want to learn calculus for calculus based physics - what is essential to review?

 

[symbolipoint]

You should be able to find cheap, used textbooks for Intermediate Algebra, and for Trigonometry. Study from them as if you are going to school again. You should then be ready for Calculus 1. Intermediate Algebra may take you three or four months. Trigonometry should take another three or four months. If you did it before, you can do it again, and you will learn everything better than before.

 

[Yawzheek]

Study a lot of trigonometry.

Thank you, friend! Indeed, my trigonometric abilities were fine, so long as I didn't need to actually understand them.

You should be able to find cheap, used textbooks for Intermediate Algebra, and for Trigonometry. Study from them as if you are going to school again. You should then be ready for Calculus 1. Intermediate Algebra may take you three or four months. Trigonometry should take another three or four months. If you did it before, you can do it again, and you will learn everything better than before.

Ha! Thank you, friend!

I did do trigonometry before (as part of the precalculus curriculum,) and remembered SOME of it - that namely being SOHCAHTOA, and how to find angles using the inverse function, though I never did understand how or why. I think you and Phion may be on to something.

If it helps, I studied an "engineering technician" field in a community college, which effectively meant I needn't study any of that, but... I always wanted more, which is why I took it as far as I did.

Thank you for your responses! I've been utilizing KhanAcademy as well, and it has been giving me a decent review of things as well. Most algebraic operations I'm more than comfortable with, except exponential, logarithmic, cubic, and trigonometric exponents. Most everything else is falling back into place quite well, I'm happy to say!

 

[SteamKing]

If you found a physics book for $4, then there's probably a $4 book which can teach you basic calculus (and provide a review of the necessary algebra and trig.)

If you Google "Schaum's Outline of Calculus" you may even get lucky and find a version online which you can download and study.

 

[Yawzheek]

If you found a physics book for $4, then there's probably a $4 book which can teach you basic calculus (and provide a review of the necessary algebra and trig.)

If you Google "Schaum's Outline of Calculus" you may even get lucky and find a version online which you can download and study.

Incidentally, I possesses two calculus books (ISBN-13 978-0-33611-8) and (ISBN: 0-618-14180-4) already. Perhaps you didn't read my original post, but I never studied past precalculus, and want a better review of the algebraic laws before I tackle them, as a person that hadn't studied mathematics for years. I have the books, this is no problem (and will likely lead to more questions in the future,) but I wish to reinforce the necessities of algebra strongly BEFORE I try to dive into them (again.)

What I mean is, I can certainly understand the fundamental purpose of calculus, but what can I do in algebra to better understand calculus? Does that make sense?

 

[SteamKing]

Incidentally, I possesses two calculus books (ISBN-13 978-0-33611-8) and (ISBN: 0-618-14180-4) already. Perhaps you didn't read my original post, but I never studied past precalculus, and want a better review of the algebraic laws before I tackle them, as a person that hadn't studied mathematics for years. I have the books, this is no problem (and will likely lead to more questions in the future,) but I wish to reinforce the necessities of algebra strongly BEFORE I try to dive into them (again.)

What I mean is, I can certainly understand the fundamental purpose of calculus, but what can I do in algebra to better understand calculus? Does that make sense?

Yes, Yes, I read your post.

If you don't at least look inside a book, how do you know that there isn't review material included which covers algebra and trig?

Not every calculus text hits the ground running at limits and goes from there. Many calculus books have a review section for earlier math as an appendix, or they start out with a quick review for students who may have been away from formal math study for a while and need to catch up.

Just as there are plenty of cheap (or free!) calculus books out there, you can also do a Google search for cheap Algebra (or Trig) texts as well.

 

[phion]

What I mean is, I can certainly understand the fundamental purpose of calculus, but what can I do in algebra to better understand calculus? Does that make sense?

Here's what I used.

https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20

 

[Yawzheek]

Yes, Yes, I read your post.

If you don't at least look inside a book, how do you know that there isn't review material included which covers algebra and trig?

Not every calculus text hits the ground running at limits and goes from there. Many calculus books have a review section for earlier math as an appendix, or they start out with a quick review for students who may have been away from formal math study for a while and need to catch up.

Just as there are plenty of cheap (or free!) calculus books out there, you can also do a Google search for cheap Algebra (or Trig) texts as well.

And you're absolutely correct! I worked my way through the practice areas (review), but then I ran into problems such as:

x^2/3 - y^2/3 = 1

And immediately I hit a standstill.

That's why I ask for help in reviewing necessities in algebra BEFORE I go further, because if I see something like this in any sense, I'll instantly freeze and not know what to do, which is the reason for my question.

I don't want to think I need to drop everything and work through beginning algebra to precalculus yet again, though I understand I may need to do that. I also don't want the answer to that (I graphed it). Just what is necessary, and what should be reviewed. That's really all I'm asking.

 

[Yawzheek]

Here's what I used.

https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20

https://www.amazon.com/dp/0321717651/?tag=pfamazon01-20

I used that. Afterwards I gave it to a friend learning Algebra I, because I thought my notes in it might help him. He never actually read it...

 

[phion]

https://www.amazon.com/dp/0321717651/?tag=pfamazon01-20

I used that. Afterwards I gave it to a friend learning Algebra I, because I thought my notes in it might help him. He never actually read it...

You can purchase what's called WebAssign, and it helps you develop a personal study plan by offering section quizzes and chapter quizzes online, as well as some other things. It's pretty neat, and very helpful and challenging enough to sharpen the skills of even the most adept.

 

[SteamKing]

And you're absolutely correct! I worked my way through the practice areas (review), but then I ran into problems such as:

x^2/3 - y^2/3 = 1

And immediately I hit a standstill.

OK, you wrote an equation down. What are you supposed to do with it? You haven't fully expressed a well-defined problem.

If you submitted this to the PF homework forum, you'd get some questions asking what you're supposed to do with this equation.

 

[symbolipoint]

And you're absolutely correct! I worked my way through the practice areas (review), but then I ran into problems such as:

x^2/3 - y^2/3 = 1

And immediately I hit a standstill.

That's why I ask for help in reviewing necessities in algebra BEFORE I go further, because if I see something like this in any sense, I'll instantly freeze and not know what to do, which is the reason for my question.

I don't want to think I need to drop everything and work through beginning algebra to precalculus yet again, though I understand I may need to do that. I also don't want the answer to that (I graphed it). Just what is necessary, and what should be reviewed. That's really all I'm asking.

The equation as written means (x^2-y^2)/3=1 but this might not be what you meant.

 

[phion]

The equation as written means (x^2-y^2)/3=1 but this might not be what you meant.

No, it means the variables are raised to fractional powers.

 

[Mark44]

No, it means the variables are raised to fractional powers.

This is what Yawzheek wrote in post #10:

x^2/3 - y^2/3 = 1

According to rules of precedence, the above means this:
$\frac{x^2}{3} - \frac{y^2}{3} = 1$
This is equivalent to what symbolipoint wrote (but in slightly different form).
What Yawzheek probably meant is this:
$x^{\frac2 3} - y^{\frac 2 3} = 1$

 

[Mark44]

Thank you, friend! Indeed, my trigonometric abilities were fine, so long as I didn't need to actually understand them.

Then they aren't fine. Calculus is where you actually need to understand the trig stuff.

 

[Yawzheek]

What Yawzheek probably meant is this:
$x^{\frac2 3} - y^{\frac 2 3} = 1$

Then they aren't fine. Calculus is where you actually need to understand the trig stuff.

And you are indeed correct on both areas, and I thank you!

The reason I created the post was because I've always wanted to get further into mathematics so that I could pursue the next level of physics, beyond algebraic. Life happens, of course, and I suspect we all understand that. The OTHER reason is because, some four years ago, I could have (and SHOULD have) dove directly into calculus when all of the previous math courses were still fresh, but as I allowed them to stagnate for as long as I did, I lost enough of it that I'm not as confident in my abilities as I was, but there is a silver lining!

I acquired another copy of my previous precalculus text, and am going back through all three of the trigonometry chapters again. This time, however, it's not with the intent of, "going through the motions," but to better understand the theories behind them. What's also not ideal is that what I had hoped would be a few days of refresher topics is almost certainly going to be a few weeks of rigorous, "pound the old stuff back in, and really go deep with the things you learned purely by reflex" study, but... that's the price you pay, I reckon, and that's the worst part, because much of it wasn't based on TRUE understanding, but largely repetition. Oh, I passed the courses with flying colors, best believe that, but now that I go back through the text, I realize it was largely based on the thought you can teach a chimp a sequence, and if he repeats it often enough, he'll learn it.

I know it probably sounds stupid, but a few years back I went to algebra again just for practice, and I "proved" the distance formula by utilizing the Pythagorean Theorem (with no prior knowledge that this was at least one way to prove it anyway) and it was at that point I realized that some of my mathematical skills were suspect. I could certainly arrive at the correct answer for most anything precalculus and less, but did I actually understand how or why it made sense? No, in many cases I didn't, and now I'm seeing why that's a problem.

Many thanks to you guys and gals that offered advice! I really do appreciate it!