Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.

(NOTE: Each chapter contains exercise and problem sets.)

 1. Logic and Proofs.

 2. Integers and Diophantine Equations.

 3. Congruences.

 4. Induction and the Binomial Theorem.

 5. Rational and Real Numbers.

 6. Functions and Bijections.

 7. An Introduction to Cryptography.

 8. Complex Numbers.

 9. Polynomial Equations.

Appendix: Trigonometry.

Appendix: Inequalities.

Further Reading.

Answers.