Summer practice recommendations

[Mockapp]

I took regents algebra 2/trig this past year and am taking calculus (ab) and physics C next year. I'm looking for a recommendation for a book for practice over the summer and would allow me to get a stronger foundation in the concepts (not just plug and chug) before I move on to calculus and physics.
Thanks!

 

[bacte2013]

Try "Fundamentals of Freshman Mathematics" or "Principles of Mathematics" by Allendoerfer/Oakley. It mostly covers the pre-calculus topics with short introduction to the concepts in calculus in the later chapters. You can also check out books written by Gelfand for algebra and trigonometry.

 

[Mondayman]

I used Basic Mathematics, and Geometry by Serge Lang. These books served me well before taking calculus.

 

[bacte2013]

I used Basic Mathematics, and Geometry by Serge Lang. These books served me well before taking calculus.

I like that book but I think it assumes some mathematical maturity from the prospective students. I assume OP does not have suitable proof skills. I did not read Geometry book yet...

 

[The Bill]

I'd recommend learning some linear algebra. Learning matrix manipulations will help with some of the things you'll be doing soon, and working with matrices and vectors will help your mathematical intuition for thinking in spaces with several dimensions.

Also, linear algebra is a good confidence builder. The basics in an introductory book are easy and fun to learn, but never stop being useful as you move forward in your education.

I recommend David C Lay's Linear Algebra and Its Applications, 3rd Updated Edition, since it's good in several ways, and that edition is very cheap used:

https://www.amazon.com/gp/product/0321287134/?tag=pfamazon01-20

 

[Mondayman]

I like that book but I think it assumes some mathematical maturity from the prospective students. I assume OP does not have suitable proof skills. I did not read Geometry book yet...

I found algebra 2 and trigonometry to be a sufficient enough background. The problems that require proofs aren't really rigorous. They'll require more effort than most students are used to at that point, but it's a good stepping stone for calculus. At least, that's how I felt about it. The books you mentioned are just as suitable.

Working through Geometry probably isn't 100% necessary, but it doesn't hurt. I found it helped my intuition a little bit better compared to my contemporaries when it came to geometric problems. Here in Alberta, we don't get a formal course on geometry - we spend about 2 months on volumes/areas in grade 10 and that's it.

 

[Mockapp]

Would there happen to be any more recent books (that might be easier to find) that you would recommend.
Thank you for your time and recommendations.

 

[smodak]

You want to have strong fundamentals and have some fun doing so over summer? Look no further than ...

What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant.
https://www.amazon.com/dp/0195105192/?tag=pfamazon01-20

For some variety add in
No bullshit guide to math and physics by Savov
https://www.amazon.com/gp/product/0992001005/?tag=pfamazon01-20

Try and see the Amazon previews and see if you like what you see; I believe you will. Hope this helps.

 

[bacte2013]

Would there happen to be any more recent books (that might be easier to find) that you would recommend.
Thank you for your time and recommendations.

I do not think Lang, Gelfand, and Oakley/Allendoerfer are hard to find; you can get them for fairy cheap prices compared to "modern" textbooks.

 

[bacte2013]

You want to have strong fundamentals and have some fun doing so over summer? Look no further than ...

What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant.
https://www.amazon.com/dp/0195105192/?tag=pfamazon01-20

For some variety add in
No bullshit guide to math and physics by Savov
https://www.amazon.com/gp/product/0992001005/?tag=pfamazon01-20

Try and see the Amazon previews and see if you like what you see; I believe you will. Hope this helps.

How is Courant's book? I have been hearing good things about that book, and I am curious what audiences does it gear for?

 

[smodak]

How is Courant's book? I have been hearing good things about that book, and I am curious what audiences does it gear for?

I really like it. You can look at a significant portion of the book in Amazon look inside preview to get an idea.

 

[Mockapp]

I do not think Lang, Gelfand, and Oakley/Allendoerfer are hard to find; you can get them for fairly cheap prices compared to "modern" textbooks.

I was really referring to Oakley/Allendoerfer texts, which are the ones I was trying to find last night. I was able to look at the books by Gelfand and quite like them from what I can tell. How are the problems in the Gelfand books? as keeping in practice is also one of my main goals.

The book by Savov looks quite nice too, I might reference it next year when I begin calculus and physics.

 

[bacte2013]

I was really referring to Oakley/Allendoerfer texts, which are the ones I was trying to find last night. I was able to look at the books by Gelfand and quite like them from what I can tell. How are the problems in the Gelfand books? as keeping in practice is also one of my main goals.

The book by Savov looks quite nice too, I might reference it next year when I begin calculus and physics.

This is link to Amazon for "Fundamentals of Freshman Mathematics": https://www.amazon.com/dp/FUNDAMENTA/?tag=pfamazon01-20. You can also try Half.com or eBay.com. Both "Fundamentals" and "Principles" are mostly identical with former being more modern and organized than later.

I think Gelfand has more challenging problems than Oakley/Allendoerfer, but O/A has better exposition and insights (in my opinion). Gelfand is not typical pre-calculus books that filled with routine exercises.

 

[Mockapp]

I think Gelfand has more challenging problems than Oakley/Allendoerfer, but O/A has better exposition and insights (in my opinion). Gelfand is not typical pre-calculus books that filled with routine exercises.

Would you by any chance be able to give an example of what you mean by better exposition and insights?

 

[micromass]

I was really referring to Oakley/Allendoerfer texts, which are the ones I was trying to find last night. I was able to look at the books by Gelfand and quite like them from what I can tell. How are the problems in the Gelfand books? as keeping in practice is also one of my main goals.

The book by Savov looks quite nice too, I might reference it next year when I begin calculus and physics.

Keep in mind that Gelfand is a top mathematician. And I mean that he really is one of the very best out there. Aside from somebody like Lang it doesn't happen a lot that a top mathematician writes for a high school level. And this really shows in Gelfands books. It really shows the spirit of advanced mathematics, although everything done in the books is high school level. His books have a lot of brilliant insights. They also try to present the beauty of math without lying to you (And sadly, lying is something most high school books are pretty good at. Maybe not really lying but more of a distorting the actual truth). The exercises can be quite difficult though.