Book covering lots of math?

[St_Francis]

I am looking for a book which would allow someone like me to learn a lot of math in a short time. I took algebra 1 and geometry in high school lo these many years ago, and can do them with a lot of thought and sometimes looking things up on the internet. A lot of algebra 2 is similar, with more looking up stuff. Trig… well, I didn’t really get that the first time around, and that was the end of my math education.

So, is there a book which is instructional in nature that will cover algebra 1 all the way up through say calculus? One which does not extend stuff out over several lessons, geared more to the classroom need of x lessons per course, but is instead based more on the math itself, iyswim.

Exercises would be nice, but not absolutely necessary.

Is there a book like that? Or is this too much to ask? (I am asking because I have had people explain weeks’s worth of math in a very short time and it was all very clear. Sometimes I think the lack of clarity in math is due to stretching it out so much!)

Thanks

 

[grasscutter]

Not a book, but a website.

Check out www.khanacademy.org. I highly recommend this website!

 

[Chrissydt]

grasscutter beat me to it! Khan Academy was the first thing that popped into my mind when I read your post. It’s free, but you have to sign up with an email and it tracks your progress as you move through lessons. I haven’t used it for advanced math as you had mentioned, but they do have those subjects. Might be worth checking out to see if it’s a good fit for what you’re looking for?
Blessings!

 

[St_Francis]

Chrissy and Grasscutter,
I will check that out I guess this old lady will have to get used to doing things the internet way now! I didn’t even think of looking for anything other than a book

 

[Charlemagne_III]

Sometimes I think the lack of clarity in math is due to stretching it out so much!)

I have had my own difficulties in life finding math teachers who knew how to teach. I learned to think I had no facility whatever for math. Then one of my teachers ( a nun) made trigonometry easy, and I began to realize that all my previous difficulties were due to horrible teachers.

I discovered the same thing studying books of logic. I used to think I was dumb. Then I began to teach myself syllogistic logic and it all became clear and simple to understand.

When you learn to ask the right questions, whether of a teacher or from a book, you begin to find clarity and ease of understanding.

What I never could figure out is why math teachers, who are supposed to be intelligent, were not intelligent enough to make math intelligible to neophytes.

But I think this is true of many disciplines. I have known great old scholars of literature who could never communicate their knowledge effectively to young scholars.

I had one English teacher in high school in Carlsbad, New Mexico who really could teach a passion for reading and analyzing literature.

So I think it’s really all in the passion for teaching and learning that any discipline is mastered.

 

[Cricket123]

If you prefer a book, you might well ask your local HS Math department head if they have old editions of textbooks for these classes that are no longer in use. You might be able to get them free, and they usually aren’t bad to read. I had a job once clearing out storerooms full of books, some dating back to the 1930s, all being recycled. You could always just work through it in your own time and move on when you are ready.

I might say that, for the most part, the lessons and classes are taught in a specific order for a reason. That is, you may well find calculus difficult if your algebra is weak.

(As an adult… you will likely notice that the chapters themselves cover the material, then the exercises follow. As a student I didn’t catch on to this until my senior year Before that, I just went to class and only looked at the pages assigned for homework.)

Another book I might recommend, that covers lots of branches of Math and is very readable is The Heart of Mathematics, by Edward Burger.

Just a suggestion or two.

 

[St_Francis]

I have had my own difficulties in life finding math teachers who knew how to teach. I learned to think I had no facility whatever for math. Then one of my teachers ( a nun) made trigonometry easy, and I began to realize that all my previous difficulties were due to horrible teachers.

I discovered the same thing studying books of logic. I used to think I was dumb. Then I began to teach myself syllogistic logic and it all became clear and simple to understand.

When you learn to ask the right questions, whether of a teacher or from a book, you begin to find clarity and ease of understanding.

What I never could figure out is why math teachers, who are supposed to be intelligent, were not intelligent enough to make math intelligible to neophytes.

But I think this is true of many disciplines. I have known great old scholars of literature who could never communicate their knowledge effectively to young scholars.

I had one English teacher in high school in Carlsbad, New Mexico who really could teach a passion for reading and analyzing literature.

So I think it’s really all in the passion for teaching and learning that any discipline is mastered.

Yes, a good teacher can really make a difference! Altho even the best math teachers I had never made me feel actually good at math

 

[St_Francis]

If you prefer a book, you might well ask your local HS Math department head if they have old editions of textbooks for these classes that are no longer in use. You might be able to get them free, and they usually aren’t bad to read. I had a job once clearing out storerooms full of books, some dating back to the 1930s, all being recycled. You could always just work through it in your own time and move on when you are ready.

I might say that, for the most part, the lessons and classes are taught in a specific order for a reason. That is, you may well find calculus difficult if your algebra is weak.

(As an adult… you will likely notice that the chapters themselves cover the material, then the exercises follow. As a student I didn’t catch on to this until my senior year Before that, I just went to class and only looked at the pages assigned for homework.)

Another book I might recommend, that covers lots of branches of Math and is very readable is The Heart of Mathematics, by Edward Burger.

Just a suggestion or two.

The book looks really good, thank you. The suggestion about getting textbooks from a school sounds good too!

 

[jimmy]

I am looking for a book which would allow someone like me to learn a lot of math in a short time. I took algebra 1 and geometry in high school lo these many years ago, and can do them with a lot of thought and sometimes looking things up on the internet. A lot of algebra 2 is similar, with more looking up stuff. Trig… well, I didn’t really get that the first time around, and that was the end of my math education.

So, is there a book which is instructional in nature that will cover algebra 1 all the way up through say calculus? One which does not extend stuff out over several lessons, geared more to the classroom need of x lessons per course, but is instead based more on the math itself, iyswim.

Exercises would be nice, but not absolutely necessary.

Is there a book like that? Or is this too much to ask? (I am asking because I have had people explain weeks’s worth of math in a very short time and it was all very clear. Sometimes I think the lack of clarity in math is due to stretching it out so much!)

Thanks

It seems like what you want is what they have in the Matrix, in which they automatically upload knowledge into the brain. In order to learn math you have to take a lot of time and do a lot of exercises. You can’t learn Algebra, geometry, trigonometry and calculus all in a few months. It takes time to get the rules down and to learn to think in a way that they make sense. Particularly calculus.

 

[ThinkingSapien]

Sometimes I think the lack of clarity in math is due to stretching it out so much!

I don’t think that stretching it out is an obstacle by itself. What I do think to be an obstacle is that a lot of the math is usually not habitually applied after it is learned; if something is learned and not used memory of it may decay.

Where I work most of the workers are labeled as either technical or creative. There are instances of creatives that took higher math classes than the techs did in school but the techs are generally a lot more familiar with math and physics since they use it much more frequently. Finding time based functions for moving elements in a manner that match some animation, calculating the change in angles between the joints on some one’s body to figure out what the person is gesturing to a computer, or performing physics modelling to give elements on a screen more realistic movement are examples of the types of math problems the techs work on. The math behind these is usually covered in high school or college math courses. But not every one remembers it.

I’m taking a break from something I’m working on right now. I’m working on some code to calculate the positions of natural and artificial satellites that will be used to control a telescope mounted camera. Referring back to what I said about memory decaying it’s been a couple of years since I’ve had to do something like this. So I’ve had to go back through some references for parts of it. But there are some areas of math that I frequently use and I can more quickly work out solutions to problems that are dependent on them .

 

[St_Francis]

I don’t think that stretching it out is an obstacle by itself. What I do think to be an obstacle is that a lot of the math is usually not habitually applied after it is learned; if something is learned and not used memory of it may decay.

Maybe I am looking at this from an older-adult point of view rather than a student-age perspective… as an example, my children had a textbook where they taught addition and subtraction along a number line. This was very much in line with the way to look at addition and subtraction with negative numbers. Later, sometimes my children would learn something using only positive numbers and then in a separate lesson with negative numbers, when it could all be done in one lesson once one has the idea of negative numbers down.

Which I understand that one cannot be sure all students do, so I understand why textbooks are set up in this way, and why I hoped to find a book which is not a textbook.

But I do totally agree with you about “getting rusty” with math Amazingly enough, before they had electronic cash registers, I worked in a little drive-through place with *no cash register at all! *We had to write the orders on paper, then the prices, and then add them on the paper itself! That was when my arithmetic was at its best

Where I work most of the workers are labeled as either technical or creative. There are instances of creatives that took higher math classes than the techs did in school but the techs are generally a lot more familiar with math and physics since they use it much more frequently. Finding time based functions for moving elements in a manner that match some animation, calculating the change in angles between the joints on some one’s body to figure out what the person is gesturing to a computer, or performing physics modelling to give elements on a screen more realistic movement are examples of the types of math problems the techs work on. The math behind these is usually covered in high school or college math courses. But not every one remembers it.

Wow, sounds like you work in an interesting place! I never thought of the need to mathematically calculate these things for animation, altho my son told me today that the people who made his game figured out how to draw a pig, but it kept exploding… And I read that in the Incredibles, they had trouble getting the hair of the characters to stay with the characters!

I’m taking a break from something I’m working on right now. I’m working on some code to calculate the positions of natural and artificial satellites that will be used to control a telescope mounted camera. Referring back to what I said about memory decaying it’s been a couple of years since I’ve had to do something like this. So I’ve had to go back through some references for parts of it. But there are some areas of math that I frequently use and I can more quickly work out solutions to problems that are dependent on them .

Yes, it’s the same with cooking: even if I used a recipe frequently in the past, if it’s been a while I need to look it up for the details.

 

[ThinkingSapien]

But I do totally agree with you about “getting rusty” with math Amazingly enough, before they had electronic cash registers, I worked in a little drive-through place with *no cash register at all! *We had to write the orders on paper, then the prices, and then add them on the paper itself! That was when my arithmetic was at its best

I had a physics teacher that strongly encouraged us not to use calculators. Seemed a little unrealistic at first since we were not used to performing trig functions and square roots in our head. Some of us tried it out and got surprisingly better over time! Then after passing the course I must admit I’ve not had much reason to do math like that again without a calculator; that capability is long gone.

Wow, sounds like you work in an interesting place!

It’s been a fun place.

I never thought of the need to mathematically calculate these things for animation

Yeah, when looking at it most people won’t think of it in terms of mathimatical models. Though they will recognize when the movement of something looks unnatural quick quickly.

And I read that in the Incredibles, they had trouble getting the hair of the characters to stay with the characters!

Hair and clothing can be troublesome. It’s not not unusual to start off animating characters naked before figuring out the clothing and the hair.

 

[polytropos]

Math can be a fairly forbidding subject as well. There is a lot of research to the effect that teachers present math as an abstract and inaccessible subject, so students who don’t have an immediate knack for it are less inclined to try.

Khan Academy is not too bad. Getting a textbook (doesn’t need to be new) is useful for the exercises since you don’t really learn math except by doing math.

 

[St_Francis]

I had a physics teacher that strongly encouraged us not to use calculators.

Wow, we didn’t even have the option of using calculators; we had to look stuff up! Those who went further along learned to use slide rules.

Seemed a little unrealistic at first since we were not used to performing trig functions and square roots in our head. Some of us tried it out and got surprisingly better over time! Then after passing the course I must admit I’ve not had much reason to do math like that again without a calculator; that capability is long gone.

It’s been a fun place.

Yeah, when looking at it most people won’t think of it in terms of mathimatical models. Though they will recognize when the movement of something looks unnatural quick quickly.

Hair and clothing can be troublesome.** It’s not not unusual to start off animating characters naked before figuring out the clothing and the hair.**

I had to laugh!!!

 

[miguel]

The CRC standard mathematical tables has anything you want to know summarized…
amazon.com/Standard-Mathematical-Formulae-Mathematics-Applications/dp/1439835489

 

[Just_Lurking]

Schaum’s Outline series (see here) is fairly fast-paced, but still mathematically self-contained.

 

[Ismael]

I am looking for a book which would allow someone like me to learn a lot of math in a short time. I took algebra 1 and geometry in high school lo these many years ago, and can do them with a lot of thought and sometimes looking things up on the internet. A lot of algebra 2 is similar, with more looking up stuff. Trig… well, I didn’t really get that the first time around, and that was the end of my math education.

So, is there a book which is instructional in nature that will cover algebra 1 all the way up through say calculus? One which does not extend stuff out over several lessons, geared more to the classroom need of x lessons per course, but is instead based more on the math itself, iyswim.

Exercises would be nice, but not absolutely necessary.

Is there a book like that? Or is this too much to ask? (I am asking because I have had people explain weeks’s worth of math in a very short time and it was all very clear. Sometimes I think the lack of clarity in math is due to stretching it out so much!)

Thanks

Not really possible IMO.

Schaum Outlines ARE GOOD, but they are mainly exercizes. They are meant to e ‘companions’ to do a lot of practice (to learn math you have to DO math!!!)

If you had high school math then find books on:

Calculus and Vector Calculus (it’s the basic!)

Differential Equations

Probability and Statistics

Linear Algebra

Tensor Calculus

Advanced Geometry, Differential Geometry, Group Theory, Topology

Analysis (Real Analysis, Complex A., Fourier A., Special Functions

Algebra (this is NOT high school algebra but abstract algebra)

Set Theory

There are OTHER more advanced topics (like Category Theory and Topoi, combinatronix, discrete mathematics, etc…) but they are pretty hard, master the above first.

I also reccomend: The Book of Proof by Richard Hammack, since it explains mathematical proofs in detail which is a must to understand.

A Concise Introduction to Pure Mathematics by Martin Liebeck, which is a more advanced book but helpful when you mastered some of the basics.

Math is a HUGE discipline in terms of diversity of topics.

PS: also find:

How To Solve It by G. Polya

it’s a gem of a book on how to solve math problems

 

[Just_Lurking]

For the OP, Schaum’s Outline for Precalculus would probably be the most appropriate. There are other Schaum’s Outlines for specific high school math subjects, such as Trigonometry or Geometry or Intermediate Algebra.