Essential Algebra: A Self-Teaching Guide

This no-nonsense guide provides students and self-learners with a clear and readable study of algebra's most important ideas. Tim Hill's distraction-free approach combines decades of tutoring experience with the methods of his old-school Russian math teachers. The result: learn in a few weeks what conventional schools stretch into months.

• Teaches general principles that can be applied to a wide variety of problems.
• Avoids the mindless and excessive routine computations that characterize conventional textbooks.
• Treats algebra as a logically coherent discipline, not as a disjointed collection of techniques.
• Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
• Omits digressions, excessive formalities, and repetitive exercises.
• Covers all the algebra needed to take a calculus course.
• Includes solutions to all problems.

Contents

1. A Few Basics

2. Exponents

3. Polynomials

4. Factoring

5. Linear & Quadratic Equations

6. Inequalities & Absolute Values

7. Coordinates in a Plane

8. Functions & Graphs

9. Straight Lines

10. Circles

11. Parabolas

12. Types of Functions

13. Logarithms

14. Dividing Polynomials

15. Systems of Linear Equations

16. Geometric Progressions & Series

17. Arithmetic Progressions

18. Permutation & Combinations

19. The Binomial Theorem

20. Mathematical Induction

21. Solutions

About the Author

Tim Hill is a private math tutor and data scientist living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.