## Reviews

This book approaches the teaching of algebra to first year undergraduate students with a unique use of the art’s history and development. Students that have already encountered many of these topics in a traditional format in high school or college may find this engaging framework a boon to understanding.

The book is well organized and thorough. The authors take a conglomeration of discoveries and inventions over three millennia and present them in an ordered, coherent manner.

The book was clearly written with extreme care, and for such a large first edition... I fully expect to make frequent use of the text as a resource for material to incorporate in my current classes, including mathematical content courses for elementary school teachers.

## Book Details

Preface

Introduction**Part I**1. Number Bases

1.1. Base 6

1.2. Base 4

2. Babylonian Number System

2.1. Cuneiform

2.2. Mathematical Texts

2.3. Number System

3. Egyptian and Roman Number Systems

3.1. Egyptian

3.1.1

Preface

Introduction**Part I**1. Number Bases

1.1. Base 6

1.2. Base 4

2. Babylonian Number System

2.1. Cuneiform

2.2. Mathematical Texts

2.3. Number System

3. Egyptian and Roman Number Systems

3.1. Egyptian

3.1.1. History

3.1.2. Writing and Mathematics

3.1.3. Number System

3.2. Roman

3.2.1. History

3.2.2. Number System

4. Chinese Number System

4.1. History and Mathematics

4.2. Rod Numerals

5. Mayan Number System

5.1. Calendar

5.2. Codices

5.3. Number System

5.4. Native North Americans

6. Indo-Arabic Number System

6.1. India

6.1.1. History

6.1.2. Mathematics

6.2. The Middle East

6.2.1. History

6.2.2. Mathematics

6.3. Number System

6.3.1. Whole Numbers

6.3.2. Fractions

7. Exercises

**Part II**

8. Addition and Subtraction

9. Multiplication

9.1. Roman Abacus

9.2. Grating or Lattice Method

9.3. Ibn Labban and Chinese Counting Board

9.4. Egyptian Doubling Method

10. Division

10.1. Egyptian

10.2. Leonardo of Pisa

10.3. Galley or Scratch Method

11. Casting Out Nines

12. Finding Square Roots

12.1. Heron of Alexandria

12.2. Theon of Alexandria

12.3. Bakhshalı Manuscript

12.4. Nicolas Chuquet

13. Exercises

**Part III**

14. Sets

14.1. Set Relations

14.2. Finding 2n

14.3. One-to-One Correspondence and Cardinality

15. Rational, Irrational, and Real Numbers

15.1. Commensurable and Incommensurable Magnitudes

15.2. Rational Numbers

15.3. Irrational Numbers

15.4. I Is Uncountably Infinite

15.5. card(Q), card(I), and card(R)

15.6. Transfinite Numbers

16. Logic

17. The Higher Arithmetic

17.1. Early Greek Elementary Number Theory

17.1.1. Pythagoras

17.1.2. Euclid

17.1.3. Nicomachus and Diophantus

17.2. Even and Odd Numbers

17.3. Figurate Numbers

17.3.1. Triangular Numbers

17.3.2. Square Numbers

17.3.3. Rectangular Numbers

17.3.4. Other Figurate Numbers

17.4. Pythagorean Triples

17.5. Divisors, Common Factors, and Common Multiples

17.5.1. Factors and Multiples

17.5.2. Euclid's Algorithm

17.5.3. Multiples

17.6. Prime Numbers

17.6.1. The Sieve of Eratosthenes

17.6.2. The Fundamental Theorem of Arithmetic

17.6.3. Perfect Numbers

17.6.4. Friendly Numbers

18. Exercises

**Part IV**

19. Linear Problems

19.1. Review of Linear Equations

19.2. False Position

19.3. Double False Position

20. Quadratic Problems

20.1. Solving Quadratic Equations by Completing the Square

20.1.1. Babylonian

201.2. Arabic

201.3. Indian

20.1.4. The Quadratic Formula

20.2. Polynomial Equations in One Variable

20.2.1. Powers

20.2.2. nth Roots

20.3. Continued Fractions

20.3.1. Finite Simple Continued Fractions

20.3.2. Infinite Simple Continued Fractions

20.3.3. The Number

21. Cubic Equations and Complex Numbers

21.1. Complex Numbers

21.2. Solving Cubic Equations and the Cubic Formula

22. Polynomial Equations

Relation between Roots and Coefficients

Viète and Harriot

22.3. Zeros of a Polynomial

22.3.1. Factoring

22.3.2. Descartes's Rule of Signs

22.4. The Fundamental Theorem of Algebra

23. Rule of Three

23.1. China

23.2. India

23.3. Medieval Europe

23.4. The Rule of Three in False Position

23.5. Direct Variation, Inverse Variation, and Modeling

24. Logarithms

24.1. Logarithms Today

24.2. Properties of Logarithms

24.3. Bases of a Logarithm

24.3.1. Using a Calculator

24.3.2. Comparing Logarithms

24.4. Logarithm to the Base e and Applications

24.4.1. Compound Interest

24.4.2. Amortization

24.4.3. Exponential Growth and Decay

24.5. Logarithm to the Base 10 and Application to Earthquakes

25. Exercises

Bibliography

Index