# Reference request for preliminaries to Calculus, Algebra

I am studying calculus, real analysis, and abstract algebra. Sometimes while solving problems in books such as Apostol's calculus I get stuck because I need to refresh my preliminaries. The preliminaries I am referring to include:

• inequalities involved summation upto n terms,

• properties of polynomials and their roots,

• sometimes even geometrical properties of circles, spheres etc, and

• another topic is the properties of factorials and nth powers etc, these come up quite often when trying to find out limits of sequences.

Can you suggest books which deal with one or more of these? Usually when I get stuck due to some mathematical inequalities I search for them on the net. But it would be great if I am able to strengthen my foundations. Thanks

P.S :- the geometry topics don't come up that often so if some book covers the other topics well, it would be great.

(Just some suggestions here. These are all free online resources.)

You may find Basic Concepts of Mathematics by Elias Zakon useful.

Or these textbooks (Calculus I and Calculus II) by Mooculus.

Or PDFs by Professor Kiryl Tsishchanka from New York University.

Or cheat sheets and notes on Paul's Online Math Notes.

Or Geometry Formulas and Facts by Silvio Levy.

Or Analytic Geometry by L. P. Siceloff, G. Wentworth.

Or Analysis - An Introduction by Dr I F Wilde.

Or Basic Analysis: Introduction to Real Analysis by Jiří Lebl.

Or Elementary Real Analysis by B. S. Thomson.

Since you are studying Calculus, maybe what you need is a good Precalculus book to use as reference when needed. There are many good books out there. For example, "Precalculus: A Prelude to Calculus" by Sheldon Axler.

• Can you suggest a resource for inequalities and factorials. The other topics are well covered in Axler it seems. – ameyask86 Feb 24 '14 at 7:46
• Inequalities are covered in College Algebra courses. I know that "Algebra for College Students" by Blitzer covers inequalities. Factorials are usually covered in the subject of summation. Precalculus by Blitzer contains a chapter on sequences, induction and probability that introduces factorials and summation. I think that possibly there are other textbooks that have a better treatment of these subjects but that is what I can remember now that may help. – NumBee Feb 25 '14 at 15:20
• I also need to work on problems involving series where we have to make reasoning based on how n! grows as compared to functions such as e^n or x^n or such stuff. Can you suggest which subject of Maths covers this. Can you suggest a book for the same. – ameyask86 Mar 24 '14 at 16:58
• I'm not sure if I understand what you're looking for, but it is possible you'll find what you what in Taylor Series. – NumBee Mar 31 '14 at 3:27