Algebra in Context

Amy Shell-Gellasch is an associate professor of mathematics at Montgomery College. She is the editor of Hands on History: A Resource for Teaching Mathematics, the author of In Service to Mathematics: The Life and Work of Mina Rees, and the coeditor of From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom. J. B. Thoo is a mathematics instructor at Yuba College.

• PrefaceIntroductionPart I1. Number Bases1.1. Base 61.2. Base 42. Babylonian Number System2.1. Cuneiform2.2. Mathematical Texts2.3. Number System3. Egyptian and Roman Number Systems3.1. Egyptian3.1.1. History3.1.2. Writing and Mathematics3.1.3. Number System3.2. Roman3.2.1. History3.2.2. Number System4. Chinese Number System4.1. History and Mathematics4.2. Rod Numerals5. Mayan Number System5.1. Calendar5.2. Codices5.3. Number System5.4. Native North Americans6. Indo-Arabic Number System6.1. India6.1.1. History6.1.2. Mathematics6.2. The Middle East6.2.1. History6.2.2. Mathematics6.3. Number System6.3.1. Whole Numbers6.3.2. Fractions7. ExercisesPart II8. Addition and Subtraction9. Multiplication9.1. Roman Abacus9.2. Grating or Lattice Method9.3. Ibn Labban and Chinese Counting Board9.4. Egyptian Doubling Method10. Division10.1. Egyptian10.2. Leonardo of Pisa10.3. Galley or Scratch Method11. Casting Out Nines12. Finding Square Roots12.1. Heron of Alexandria12.2. Theon of Alexandria12.3. Bakhshalı Manuscript12.4. Nicolas Chuquet13. ExercisesPart III14. Sets14.1. Set Relations14.2. Finding 2n14.3. One-to-One Correspondence and Cardinality15. Rational, Irrational, and Real Numbers15.1. Commensurable and Incommensurable Magnitudes15.2. Rational Numbers15.3. Irrational Numbers15.4. I Is Uncountably Infinite15.5. card(Q), card(I), and card(R)15.6. Transfinite Numbers16. Logic17. The Higher Arithmetic17.1. Early Greek Elementary Number Theory17.1.1. Pythagoras17.1.2. Euclid17.1.3. Nicomachus and Diophantus17.2. Even and Odd Numbers17.3. Figurate Numbers17.3.1. Triangular Numbers17.3.2. Square Numbers17.3.3. Rectangular Numbers17.3.4. Other Figurate Numbers17.4. Pythagorean Triples17.5. Divisors, Common Factors, and Common Multiples17.5.1. Factors and Multiples17.5.2. Euclid's Algorithm17.5.3. Multiples17.6. Prime Numbers17.6.1. The Sieve of Eratosthenes17.6.2. The Fundamental Theorem of Arithmetic17.6.3. Perfect Numbers17.6.4. Friendly Numbers18. ExercisesPart IV19. Linear Problems19.1. Review of Linear Equations19.2. False Position19.3. Double False Position20. Quadratic Problems20.1. Solving Quadratic Equations by Completing the Square20.1.1. Babylonian201.2. Arabic201.3. Indian20.1.4. The Quadratic Formula20.2. Polynomial Equations in One Variable20.2.1. Powers20.2.2. nth Roots20.3. Continued Fractions20.3.1. Finite Simple Continued Fractions20.3.2. Infinite Simple Continued Fractions20.3.3. The Number21. Cubic Equations and Complex Numbers21.1. Complex Numbers21.2. Solving Cubic Equations and the Cubic Formula22. Polynomial EquationsRelation between Roots and CoefficientsViète and Harriot22.3. Zeros of a Polynomial22.3.1. Factoring22.3.2. Descartes's Rule of Signs22.4. The Fundamental Theorem of Algebra23. Rule of Three23.1. China23.2. India23.3. Medieval Europe23.4. The Rule of Three in False Position23.5. Direct Variation, Inverse Variation, and Modeling24. Logarithms24.1. Logarithms Today24.2. Properties of Logarithms24.3. Bases of a Logarithm24.3.1. Using a Calculator24.3.2. Comparing Logarithms24.4. Logarithm to the Base e and Applications24.4.1. Compound Interest24.4.2. Amortization24.4.3. Exponential Growth and Decay24.5. Logarithm to the Base 10 and Application to Earthquakes25. ExercisesBibliographyIndex

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. Mathematical Association of America 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. Mathematic Teacher