This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high-school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one.
Readers will see how various mathematical concepts are tied and will see that mathematics is not a pile of formulas and facts; rather, it has an orderly and beautiful edifice.
The author begins with basic rules of logic and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader.
Reviewer Comments:
I find the book very impressive. The choice and sequence of topics is excellent, and it is wonderful to have all of these things together in one volume. Theorems are clearly stated, and proofs are accurate. – Michael Comenetz
The thoroughness of the narrative is one of the main strengths of the book. The book provides a perfect illustration of mathematical thinking. Each step of a given derivation is precise and clear. – Julie Gershunskaya
Draganov’s book stands out from the many competing books. Draganov’s goal is to show that mathematics depends on the notion of proof. Unlike other transition books, he addresses mathematical topics at an accessible level, rather than topics studied later in the university curriculum. – Ken Rosen
Table of Contents:
Preface
How to Read This Book
1. A Few Rules of Logic
2. Numbers
3. Inequalities
4. Functions
5. Polynomials
6. Power Law, Exponents, and Logarithms
7. Trigonometry
8. Conic Sections
9. Sequences and Sums
10. The Fibonacci Sequence
11. Onward to Calculus (not sure if this belongs to this book)
Conclusion
Further reading
Index
About the Author :
Alexandr Draganov holds a PhD in Electrical Engineering from Stanford. After a career in high-tech, he pivoted to teaching and writing.
