Few questions regarding Algebra and Precalculus

  • #1
Okay so I have a couple of questions. Firstly, I'm a self taught math student. I'm teaching myself math and want to see how far I can go before i need a teacher.

I've successfully, taught myself Algebra. However, I'm still confused weither the book I used taught me Algebra 1 and 2, or only Algebra 1.

I'll give you the table of contents of my book:
1. The basics
2. Linear Equations and Inequalities
3. Linear Equations and Inequalities in Two Variables
4. Systems of Linear Equations
5. Exponents and Polynomials
6. Factoring
7. Rational Expressions
8. Roots and Radicals
9. Quadratic Equations

That's what I've learned in my book. So my question is, is this Algebra 1 and 2, or only Algebra 1?

My next question is regarding Precalculus and Trigonometry. Right now I'm attempting to teach myself Precalculus, but I'm using a book that I do not like.

The book I'm using is "Precalculus, Seventh Edition" By Ron Larson and Robert Hostetler

Here's the link: https://www.amazon.com/dp/0618643443/?tag=pfamazon01-20&tag=pfamazon01-20

Frankely I hate this book. I understand everything this book says, and so far I've had no problem understanding the concepts. It's actually really easy, but the book spends too much time talking about things that I think are a waste of time, and things that you can figure out with common sense. Also, the book talks too much and doesn't actually do math enough. When I'm doing the chapters, I feel like I'm reading an actual book instead of a math book. The book spends way too much time in my opinion, talking instead of showing examples of how to actually do the problems.

My number one problem with this book though is that I find it boring. It was easy for me to teach myself Algebra because the book was fun. My Precalculus book is extremely boring, and since I'm a self taught math student, motivation is an extremely important thing for me because I have no concern about getting a bad grade if I put off learning material.

I loved my algebra book because the author spent little time talking, but spent a lot of time showing you how to do the problem. Also the algebra book I used was concise and to the point. My precalculus book is anything but concise, and spends too much time talking about irrelevant garbage in my opinion.

Can anyone reccommend me a book that's good for teaching yourself Precalculus, but is concise and to the point?

Also, could I just teach myself Trigonometry, and then go straight to Calculus? Or should I actually teach myself Precalculus? I've heard lots of people say that you don't even need to learn Precalculus, you just need to learn Algebra and Trig.

And my last question is, could I skip precalculus and trigonometry altogether and just go straight into Calculus? I already have lots of Calculus books, and all of them spend their beggining chapters talking about things you need to know before they start the new Calculus material. Could I just learn what I need to know in these beginning chapters in the Calculus books and jump right into Calculus? Or is this not recommended?
 
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Answers and Replies

  • #2
5,439
9
Welcome to PF Reagan!

That's a long text from someone who prefers maths to english!

I am not sure of the American designations Calc1 and 2, but does it really matter? American books certainly make a huge meal of this stuff.

In you position you might like to look at the Teach Yourself series, originally published by the English Universities Press.
They can be had new or second hand very cheaply and are concise but really very good, withs lots of worked examples.
With your listed background I would say they are better for you than the Schaum series (which are also good).
In the series you will find

Teach Yourself Calculus
Teach Yourself Algebra
Teach Yourself Trigonometry
Teach Yourself Geometry

http://www.abebooks.co.uk/servlet/SearchResults?bt.x=24&bt.y=13&sts=t&tn=teach+yourself+calculus

A smattering of each of these will be useful when you come to the applications (there are so many) of calculus. If you understand what the basics of, say trigonometry is all about, it is easier to pick up more at a later stage.


go well
 
  • #3
Your description of the topics you've covered suggests that you have studied mostly algebra II. You are still missing matrices, complex numbers, sequences and series, and conics to complete algebra II.

As to whether you could go all the way to calculus without precalculus, a qualified answer is yes. You will need trig to be successful in calculus I. In calculus II you will need vectors as well. Some calcululs books introduces vectors either in an appendix or in the prolog. Look at the table of contents of a book before you buy it.

A reasonable background in geometry should be very helpful in calculus.
 
  • #4
352
2
Not a book, but Khan Academy is a great resource for self teaching math/science. Over 2000 10 minute videos explaining concepts very well.

http://www.khanacademy.org/" [Broken]
 
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  • #5
Your description of the topics you've covered suggests that you have studied mostly algebra II. You are still missing matrices, complex numbers, sequences and series, and conics to complete algebra II.

As to whether you could go all the way to calculus without precalculus, a qualified answer is yes. You will need trig to be successful in calculus I. In calculus II you will need vectors as well. Some calcululs books introduces vectors either in an appendix or in the prolog. Look at the table of contents of a book before you buy it.

A reasonable background in geometry should be very helpful in calculus.
Okay cool, that's good news that I've studied Algebra II.

My book did cover complex numbers, however it did not cover conics and matrices. I'm not sure about Sequence and series however.

I haven't bothered to teach myself geometry because in highschool I thought geometry was a joke. I'm a very visual learner and I'm very good at spacial reasoning so geometry is no problem for me even if I don't remember all the equations. I know I can just either skim through a geometry book if I really need to or I'll just relearn what I need to know in geometry as I do calculus.

Thanks for the advice.
 
  • #6
5,439
9
I haven't bothered to teach myself geometry because in highschool I thought geometry was a joke.
Think again unless you understand co-ordinate geometry.
 
  • #7
Think again unless you understand co-ordinate geometry.
Yes I know coordinate geometry.
 
  • #8
mathwonk
Science Advisor
Homework Helper
11,063
1,254
see what you think of thee books:

http://cemse.uchicago.edu/node/135 [Broken]

if they are too easy, try some books by courant, like what is mathematics? or

differential and integral calculus.
 
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  • #9
724
0
Make sure you know how to manipulate indeterminate forms(like 0/0). For example, you'll need to know how to turn [tex]\frac{x^2-9}{x-3}[/tex] into [tex]x+3 \mbox{ where x \neq 3}[/tex]. These are used in the early weeks of calculus to learn how differentiation works. (Later, you get to use shortcuts.)
 
  • #10
Make sure you know how to manipulate indeterminate forms(like 0/0). For example, you'll need to know how to turn [tex]\frac{x^2-9}{x-3}[/tex] into [tex]x+3 \mbox{ where x \neq 3}[/tex]. These are used in the early weeks of calculus to learn how differentiation works. (Later, you get to use shortcuts.)

x^2 -9 is the same thing as (x-3)(x+3)

(x-3)(x+3)/(x-3) both of the (x-3) cancel each other out, thus leaving (x+3)
 

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