Algebra in Context : Introductory Algebra from Origins to Applications /

"This book's unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of every...

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Detalles Bibliográficos
Autores principales: Shell-Gellasch, Amy (Autor), Thoo, J. B. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Baltimore : Johns Hopkins University Press, 2015.
Colección:Book collections on Project MUSE.
Temas:
Algebra.
algebra.
Algebre > Histoire.
Algebre.
Algebra > History.
History.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: pt. I Numeration Systems
  • 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. 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
  • pt. II Arithmetic Snapshots
  • 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
  • pt. III Foundations
  • 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. 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. Sieve of Eratosthenes
  • 17.6.2. Fundamental Theorem of Arithmetic
  • 17.6.3. Perfect Numbers
  • 17.6.4. Friendly Numbers
  • 18. Exercises
  • pt. IV Solving Equations
  • 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
  • 20.1.2. Arabic
  • 20.1.3. Indian
  • 20.1.4. 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. Number #x1B;(Sz#x1B;(B
  • 21. Cubic Equations and Complex Numbers
  • 21.1. Complex Numbers
  • 21.2. Solving Cubic Equations and the Cubic Formula
  • 22. Polynomial Equations
  • 22.1. Relation between Roots and Coefficients
  • 22.2. Viete and Harriot
  • 22.3. Zeros of a Polynomial
  • 22.3.1. Factoring
  • 22.3.2. Descartes's Rule of Signs
  • 22.4. Fundamental Theorem of Algebra
  • 23. Rule of Three
  • 23.1. China
  • 23.2. India
  • 23.3. Medieval Europe
  • 23.4. 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.

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