These are three books that I would recommend to somebody trying to prepare for calculus. They're all written by the mathematician Gelfand and his colleages, and they're some of the best-written math books I've ever read. You come away from reading them really understanding the subject matter. I'd read them in that order, too.
'Geometry' means different things to different people. So far the books that have been suggested range from elementary Euclidean geometry (Euclid) to differential geometry (Spivak) to algebraic geometry (Hartshorne, Grothendieck). In order to get more helpful suggestions, you should be more specific about what you're looking for.
Since it sounds like you want to solidify the geometry you learnt in high school, I'll suggest some elementary resources:
There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:
First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.
Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the why of the problem under consideration, not just the how... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.
And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.
After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.
The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're really studying it. It's a pretty straightforward process (bar the moments of frustration, of course).
If you have any other questions about learning math, shoot me a PM. :)
Since you have strong backgrounds in math, you could try Geometry: A Guided Inquiry out (I recommend getting the home study companion and Geometer's Sketchpad, as well). It relies heavily on working the exercises to find the important results yourself, which is best done with mathematically-inclined mentors to help. A review for these products can be found here.
For Trigonometry, I recommend Gelfand's text by the same name. It is very much made with future math students in mind, with appendices on approximating pi and on Fourier series.
Most of all, I recommend making your own stuff if you find yourself with extra time. If you find your daughter getting close to the end of the Geometry textbook, for example, set up some examples or further projects that round everything up and introduces her to another world of mathematics. If she is able to understand the material in the textbook rather well, it is entirely possible to prove Euler's Polyhedron Formula, look into the 5 platonic solids, as well as go into a little detail about the Euler Characteristic using the tools learned in Geometry, which would give her a glimpse into the world of Topology (Don't forget the Donut and Coffee Mug example).
For trigonometry in particular if you want something more useful than a typical American textbook you could try the book by Gelfand & Saul, https://amzn.com/0817639144
These are all 1900's Russian math text books (probably the type that /u/oneorangehat was thinking of) edited by I.M. Galfand, who was something like the head of the Russian School for Correspondence. I basically lived off them during my first years of high school. They are pretty much exactly what you said you wanted; they have no pictures (except for graphs and diagrams), no useless information, and lots of great problems and explanations :) There is also I.M Gelfand Trigonometry {[.pdf] (http://users.auth.gr/~siskakis/GelfandSaul-Trigonometry.pdf) | Amazon} (which may be what you mean when you say precal, I'm not sure), but I do not own this myself and thus cannot say if it is as good as the others :)
I should mention that these books start off with problems and ideas that are pretty easy, but quickly become increasingly complicated as you progress. There are also a lot of problems that require very little actual math knowledge, but a lot of ingenuity.
Sorry for bad Englando, It is my native language but I haven't had time to learn it yet.
I am doing this very thing. I found some fantastic books that might help get you (re)started. They certainly helped me get back into math in my 30s. Be warned, a couple of these books are "cute-ish", but sometimes a little sugar helps the medicine go down:
That's sounds like a horrible way to try to learn. If you think this problem is not representative of the school itself, complain (politely) to the department or dean.
I normally do not recommend Khan Academy because his methods are inefficient and boring at best, but that might actually be a step up for you.
Meanwhile, try to find a book to read out of. Unfortunately, textbook writing is a tough thing to be good at, and then a lot of publishers will get in the way of half of those.
First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.
Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:
For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books: Middle & high school:
and elementary linked from their main page. I have seen the latter myself.
Some more very good books that should be used more, by Gelfand:
If you loved math before, don't let some bad grades convince you you're bad at it. Math isn't that hard to study on your own, without stressing out about what someone else thinks about your progress. If you're interested in some books to go with Khan Academy, I'd check these out:
Note that in the US system, often "Algebra and Trigonometry" and "Precalculus" are taught out of the same book with the first course covering the earlier chapters and the second covering the later chapters. In some cases (like OpenStax) you'll see that there are separate books for the two subjects but most of the chapters are the same, with A&T including a bit of extra basic material and precalc including limits at the very end.
Algebra
Trigonometry
Functions and Graphs
These are three books that I would recommend to somebody trying to prepare for calculus. They're all written by the mathematician Gelfand and his colleages, and they're some of the best-written math books I've ever read. You come away from reading them really understanding the subject matter. I'd read them in that order, too.
'Geometry' means different things to different people. So far the books that have been suggested range from elementary Euclidean geometry (Euclid) to differential geometry (Spivak) to algebraic geometry (Hartshorne, Grothendieck). In order to get more helpful suggestions, you should be more specific about what you're looking for.
Since it sounds like you want to solidify the geometry you learnt in high school, I'll suggest some elementary resources:
I like Algebra and Trigonometry by I.M. Gelfand. They are cheap books too.
I also have scans of them, PM me if you want to check them out.
Edit:
Also, Khan Academy is great resource for explanations. But I would recommend aiding Khan Academy with a text just for the problem set and solutions.
There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:
First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.
Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the why of the problem under consideration, not just the how... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.
And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.
After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.
The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're really studying it. It's a pretty straightforward process (bar the moments of frustration, of course).
If you have any other questions about learning math, shoot me a PM. :)
Since you have strong backgrounds in math, you could try Geometry: A Guided Inquiry out (I recommend getting the home study companion and Geometer's Sketchpad, as well). It relies heavily on working the exercises to find the important results yourself, which is best done with mathematically-inclined mentors to help. A review for these products can be found here.
For Trigonometry, I recommend Gelfand's text by the same name. It is very much made with future math students in mind, with appendices on approximating pi and on Fourier series.
Most of all, I recommend making your own stuff if you find yourself with extra time. If you find your daughter getting close to the end of the Geometry textbook, for example, set up some examples or further projects that round everything up and introduces her to another world of mathematics. If she is able to understand the material in the textbook rather well, it is entirely possible to prove Euler's Polyhedron Formula, look into the 5 platonic solids, as well as go into a little detail about the Euler Characteristic using the tools learned in Geometry, which would give her a glimpse into the world of Topology (Don't forget the Donut and Coffee Mug example).
“Precalc” doesn’t have a super well-defined scope, but often includes:
Here’s a free precalculus textbook, http://stitz-zeager.com
For trigonometry in particular if you want something more useful than a typical American textbook you could try the book by Gelfand & Saul, https://amzn.com/0817639144
These are, in my opinion, some of the best books for learning high school level math:
These are all 1900's Russian math text books (probably the type that /u/oneorangehat was thinking of) edited by I.M. Galfand, who was something like the head of the Russian School for Correspondence. I basically lived off them during my first years of high school. They are pretty much exactly what you said you wanted; they have no pictures (except for graphs and diagrams), no useless information, and lots of great problems and explanations :) There is also I.M Gelfand Trigonometry {[.pdf] (http://users.auth.gr/~siskakis/GelfandSaul-Trigonometry.pdf) | Amazon} (which may be what you mean when you say precal, I'm not sure), but I do not own this myself and thus cannot say if it is as good as the others :)
I should mention that these books start off with problems and ideas that are pretty easy, but quickly become increasingly complicated as you progress. There are also a lot of problems that require very little actual math knowledge, but a lot of ingenuity.
Sorry for bad Englando, It is my native language but I haven't had time to learn it yet.
http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773
http://www.amazon.com/Trigonometry/dp/0817639144
EDIT: I don't know what ACT is, so I don't know how well it will prepare you for that.
I am doing this very thing. I found some fantastic books that might help get you (re)started. They certainly helped me get back into math in my 30s. Be warned, a couple of these books are "cute-ish", but sometimes a little sugar helps the medicine go down:
I wish you all the best!
If you need to brush up on some of the more basic topics, there's a series of books by IM Gelfand:
Algebra
Trigonometry
Functions and Graphs
The Method of Coordinates
If you're really ambitious, try this book by I. M. Gelfand:
http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144
It will give you a deeper understanding than most trig books.
That's sounds like a horrible way to try to learn. If you think this problem is not representative of the school itself, complain (politely) to the department or dean.
I normally do not recommend Khan Academy because his methods are inefficient and boring at best, but that might actually be a step up for you.
Meanwhile, try to find a book to read out of. Unfortunately, textbook writing is a tough thing to be good at, and then a lot of publishers will get in the way of half of those.
Here are some to try though: http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144
http://www.amazon.com/Precalculus-Mathematics-Nutshell-Geometry-Trigonometry/dp/1592441300
And they're on the cheaper side
First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.
Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:
Geometry and solutions
Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.
A First Course in Calculus
For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.
Some more very good books that should be used more, by Gelfand:
The Method of Coordinates
Functions and Graphs
Algebra
Trigonometry
Lines and Curves: A Practical Geometry Handbook
Here is a good book on trigonometry.
Here is one for algebra.
Here's another
If you loved math before, don't let some bad grades convince you you're bad at it. Math isn't that hard to study on your own, without stressing out about what someone else thinks about your progress. If you're interested in some books to go with Khan Academy, I'd check these out:
Free online:
Dead tree books that cost money:
Note that in the US system, often "Algebra and Trigonometry" and "Precalculus" are taught out of the same book with the first course covering the earlier chapters and the second covering the later chapters. In some cases (like OpenStax) you'll see that there are separate books for the two subjects but most of the chapters are the same, with A&T including a bit of extra basic material and precalc including limits at the very end.