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Author:   Amy Shell-Gellasch (Eastern Michigan University) ,  John Thoo
Publisher:   Johns Hopkins University Press
Imprint:   Johns Hopkins University Press
Dimensions:   Width: 17.80cm , Height: 3.70cm , Length: 25.40cm
Weight:   1.293kg
ISBN:  

9781421417288

ISBN 10:   1421417286
Pages:   552
Publication Date:   10 December 2015
Recommended Age:   From 17
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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. Bakhshali 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

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. Mathematical Association of America

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 *

Author Information

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.

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