The Language of Mathematics
The Stories behind the Symbols
1st Edition
Published on 14. January 2025
280 pages
978-0-691-26368-7 (ISBN)
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Raúl Rojas is professor of mathematics and statistics at the University of Nevada, Reno, and professor emeritus of computer science and mathematics at the Free University of Berlin. A world-renowned expert in artificial intelligence, he is the author of the seminal book Neural Networks and the editor (with Ulf Hashagen) of The First Computers.
Content
- Cover
- Contents
- Acknowledgments
- Symbols and Expressions
- Introduction
- I. The Long History of Mathematical Symbols
- The Birth of Algebra
- How Do We Use Mathematical Symbols?
- The Most Beautiful Mathematical Formulas
- Why Do We Extract Roots?
- II. Numbers and Variables
- Hindu-Arabic Numerals and Mercantilism
- The Greek Alphabet and Its Predecessors
- Zero
- Symmetry of Symbols
- The Variable x
- Absolute Value and the Father of Analysis
- Powers as Superscripts
- Subscripts
- The Decimal Point
- III. Arithmetic Operators
- The Greek Cross of Addition
- Subtraction and Negative Numbers
- According to Adam Ries
- The Cross of Multiplication
- The Division Bar
- Homer, the Obelus, and Division
- IV. Relational and Grouping Operators
- No Two Things Can Be More Equal
- Inequality Symbols
- The Parenthesis versus the Vinculum
- The Comma and the Period
- V. Calculus/Analysis
- Star Wars: Leibniz versus Newton
- The Partial Derivative
- Nabla, the Harp of Assyria
- John Wallis and Infinity
- Delta
- The Notation f (x) and the Concept of a Function
- Epsilons, Deltas, and the Invention of Real Numbers
- Reaching the Limit
- The Mathematical Dart
- VI. Sets and Functions
- The Existential Quantifier
- The Universal Quantifier
- ? Is for Belonging
- The Set of Rational Numbers
- Mathematics and Nothingness
- Union and Intersection
- The Aleph and the Paradise of Infinities
- VII. Constants
- The Power of Imagination
- Pi: The Archimedean Constant and the Ludolphian Number
- Euler's Number and Exponential Growth
- Planck's Constant: The Quantum of Action
- The Speed of Light c
- VIII. Combinatorics
- The Factorial
- Sigma: Notation to Sink Your Teeth Into
- A Floor and a Ceiling for Numbers
- The Binomial Symbol
- IX. Various Topics
- The Invisible Symbol: Einstein's Convention
- The Halmos Box
- Sine of Theta and Trigonometry
- The Symbol of Congruence and Arithmetic in Miniature
- Matrices: The Mother Structure
- Publish or Perish: The First Scientific Journals
- Epilogue
- Bibliography
- Index
