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i have missed pre-calculus knowledge in my school but i was good at maths, and now i am a computer science student, i am feeling bad being bad in maths, so i am looking for the best Pre-Calculus book, i love maths, i need the right well of precalculus books.

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I have converted the question to community wiki, as it's asking for a big list of examples and there is no single right answer. –  Zev Chonoles Dec 24 '12 at 14:13
    
thanks, Zev, i forgot that! great –  doniyor Dec 24 '12 at 14:14
1  
Good question, dude. I had a lot of troubles studying Infinitesimal Calculus because i didn't have the idea to study the pre-calculus part, which was my real problem with calculus. You are in the right way. –  Bruno Garcia Dec 24 '12 at 14:39
    
yeah, because with some holes in my precalculus, i dont understand anything, or mostly nothing in calculus or higher parts which is very very sad –  doniyor Dec 24 '12 at 14:44

5 Answers 5

You might want to have a look at the following (peruse them at your favorite online book store).

Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry, George F. Simmons

Pre-calculus Demystified 2/E, Rhonda Huettenmueller

Some other food for thought.

You may also want to look at actual calculus books at your local university library and see some of the topics you might need.

You might want to get and learn to use a Computer Algebra System. You want to learn to explore mathematics and ask all sort of what-if questions and also learn about programming.

Regards

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If someone wants me to know a great book as you wanted, I'll suggest him "Modern Calculus", an old book written by R.A.Silverman. I don't know why; but I've got much more basic concepts in Calculus from the old books. This book makes an student a solid root in Calculus.

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yeah, thanks, i also love old math books –  doniyor Dec 24 '12 at 14:23
    
do you know where i can get the free pdf version of that book? –  doniyor Dec 24 '12 at 14:25
    
I don't think you can get that because this book is ruling well in Calculus nowadays in universities around the world (I know that). He was great; one of greats in Analysis. –  Babak S. Dec 24 '12 at 14:30
    
@doniyor - Here you can find a preview of Silverman's Modern Calculus, e.g. "look inside", etc. It's a "Dover book," so it's considerably less expensive than most Calculus texts! –  amWhy Dec 24 '12 at 14:44
    
Thanks @amWhy great –  doniyor Dec 24 '12 at 14:48

As a computer science student, you might also want to check out Knuth, Graham, and Patashnik Concrete Mathematics, which I consider to be absolutely indispensable for comp sci students. It's a very thorough book! Not necessarily recommended to replace Calculus, but provides the nuts and bolts of the basics in math that you'll want to master!

Major topics include:

Sums
Recurrences
Integer functions
Elementary number theory
Binomial coefficients
Generating functions
Discrete probability
Asymptotic methods

And more...

"This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline."

"The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study."

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More often than not Amazon's search has got the best book listed first. For precalculus it's "The Complete Idiot's Guide to Precalculus". I guess the title is refering to the guy that named those books.

You could search on Google Books too, but their results are not listed by numbers of copies sold.

Also I have been told that Calculus On Manifolds is very popular among computer science students. From amazon:

This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

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I would recommend: David Cohen - Precalculus with unit circle trigonometry

It's a $1200$ pages book that covers quiet a lot of useful and interesting topics:

  1. Fundamentals.
    Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
  2. Equations And Inequalities.
    Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
  3. Functions.
    The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions.
  4. Polynomial and Rational functions. Applications to optimization.
    Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
  5. Exponential and Logarithmic functions.
    Exponential Functions. The Exponential Function $y = e^x$. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
  6. The Trigonometric functions.
    Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry.
  7. Graphs of the Trigonometric functions.
    Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of $y = A \sin(Bx-C)$ and $y = A \cos(Bx - C)$. Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
  8. Analytical Trigonometry.
    The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
  9. Additional topic in Trigonometry.
    Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
  10. Systems of equations.
    Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
  11. Analytic Geometry.
    The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
  12. Roots of Polynomial equations.
    The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
  13. ADDITIONAL TOPICS.
    Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem. Appendix 1: Using a Graphing Utility. Appendix 2: Significant Digits and Calculators.

[RV] I used this book in high school and absolutely loved it. It's very skimpy on proofs, and really should not be used for that sort of insight. However, in terms of understanding how to apply various mathematical concepts it's wonderful. It has a large number of graphs, examples, and easy reference tables. It covers all the algebra, trig, and cartesian geometry that any good high school math sequence should deal with. I have used it for years as a reference book (e.g., what exactly is Cramer's rule again...) Solutions to a number of the problems are in the back, and the problems are not entirely applications.

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