Book contents
- Frontmatter
- Preface
- Contents
- 1 The Sources of Algebra
- 2 How to Measure the Earth
- 3 Numerical solution of equations
- 4 Completing the Square through the Millennia
- 5 Adapting the Medieval “Rule of Double False Position” to the Modern Classroom
- 6 Complex Numbers, Cubic Equations, and Sixteenth-Century Italy
- 7 Shearing with Euclid
- 8 The Mathematics of Measuring Time
- 9 Clear Sailing with Trigonometry
- 10 Copernican Trigonometry
- 11 Cusps: Horns and Beaks
- 12 The Latitude of Forms, Area, and Velocity
- 13 Descartes' Approach to Tangents
- 14 Integration à la Fermat
- 15 Sharing the Fun: Student Presentations
- 16 Digging up History on the Internet: Discovery Worksheets
- 17 Newton vs. Leibniz in One Hour!
- 18 Connections between Newton, Leibniz, and Calculus I
- 19 A Different Sort of Calculus Debate
- 20 A ‘Symbolic’ History of the Derivative
- 21 Leibniz's Calculus (Real Retro Calc.)
- 22 An “Impossible” Problem, Courtesy of Leonhard Euler
- 23 Multiple Representations of Functions in the History of Mathematics
- 24 The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation
- 25 Finding the Greatest Common Divisor
- 26 Two-Way Numbers and an Alternate Technique for Multiplying Two Numbers
- 27 The Origins of Integrating Factors
- 28 Euler's Method in Euler's Words
- 29 Newton's Differential Equation ẏ/ẋ = 1 − 3x + y + xx + xy
- 30 Roots, Rocks, and Newton-Raphson Algorithms for Approximating √2 3000 Years Apart
- 31 Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras
- 32 Thomas Harriot's Pythagorean Triples: Could He List Them All?
- 33 Amo, Amas, Amat! What's the sum of that?
- 34 The Harmonic Series: A Primer
- 35 Learning to Move with Dedekind
- About the Editors
20 - A ‘Symbolic’ History of the Derivative
- Frontmatter
- Preface
- Contents
- 1 The Sources of Algebra
- 2 How to Measure the Earth
- 3 Numerical solution of equations
- 4 Completing the Square through the Millennia
- 5 Adapting the Medieval “Rule of Double False Position” to the Modern Classroom
- 6 Complex Numbers, Cubic Equations, and Sixteenth-Century Italy
- 7 Shearing with Euclid
- 8 The Mathematics of Measuring Time
- 9 Clear Sailing with Trigonometry
- 10 Copernican Trigonometry
- 11 Cusps: Horns and Beaks
- 12 The Latitude of Forms, Area, and Velocity
- 13 Descartes' Approach to Tangents
- 14 Integration à la Fermat
- 15 Sharing the Fun: Student Presentations
- 16 Digging up History on the Internet: Discovery Worksheets
- 17 Newton vs. Leibniz in One Hour!
- 18 Connections between Newton, Leibniz, and Calculus I
- 19 A Different Sort of Calculus Debate
- 20 A ‘Symbolic’ History of the Derivative
- 21 Leibniz's Calculus (Real Retro Calc.)
- 22 An “Impossible” Problem, Courtesy of Leonhard Euler
- 23 Multiple Representations of Functions in the History of Mathematics
- 24 The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation
- 25 Finding the Greatest Common Divisor
- 26 Two-Way Numbers and an Alternate Technique for Multiplying Two Numbers
- 27 The Origins of Integrating Factors
- 28 Euler's Method in Euler's Words
- 29 Newton's Differential Equation ẏ/ẋ = 1 − 3x + y + xx + xy
- 30 Roots, Rocks, and Newton-Raphson Algorithms for Approximating √2 3000 Years Apart
- 31 Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras
- 32 Thomas Harriot's Pythagorean Triples: Could He List Them All?
- 33 Amo, Amas, Amat! What's the sum of that?
- 34 The Harmonic Series: A Primer
- 35 Learning to Move with Dedekind
- About the Editors
Summary
Introduction
How often do you have to tell your students to brush up on their notation? When they have dropped limit notation, forgotten critical modulus signs, mixed up their integrals, muddled up their derivatives, how do you convey to them the importance of recording it right?
What of your exasperation as they fail to appreciate the precision that mathematical notation affords them—notation which has been developed and refined over centuries, and notation that will continue to be improved for centuries more. Indeed, mathematics is the one subject in which they can really express exactly what they mean. How can we help them appreciate the symbolism they use?
This paper provides a light-hearted look at various notational conventions concerning the derivative. It will briefly cover the various proposals for its symbolic representation over history and the reasons behind the prevalence of the various manifestations over others. The examination of the history of the development of calculus notations is not only fascinating, but suggests a paradigm for the development of future notations. An examination of the reasons behind the failures and successes of past notation can equip one with a certain foresight regarding the future of newly introduced symbols, as particular areas of mathematics expand.
This capsule is intended for undergraduate calculus classes and should ideally be offered directly before or after covering the derivative and its various applications, or indeed right in the middle when the students need a bit of a break from theory and practice! It may also be suitable for higher level secondary school mathematics.
- Type
- Chapter
- Information
- Mathematical Time CapsulesHistorical Modules for the Mathematics Classroom, pp. 151 - 158Publisher: Mathematical Association of AmericaPrint publication year: 2011
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