About Mathematics

Description

Mathematics is an essential component of the educated mind. It has two important roles to play: as queen of the sciences (providing the logical structure that holds science together) and as handmaiden to those sciences (carrying out the computations that apply scientific concepts.) Unfortunately, a gulf exists between science and the humanities and our text, About Mathematics, seeks to bridge that gap, to serve humanities students just as humanities texts are offered to inform science students. In doing so, unlike most math texts, we avoid the usual focus on detailed technique to expose instead some of the important concepts and values of mathematics.

CHAPTER 1: Getting Started

• 1.1 Demonstrations
• 1.2 Recent Computing History
• 1.3 Order and disorder

CHAPTER 2: Algorithms, Functions and Equations

• 2.1 An unexpected algorithm
• 2.2 An old school algorithm
• 2.3 Functions
• 2.4 How computers solve equations

CHAPTER 3: Dimensional Analysis

• 3.1 Using dimensions in converting units
• 3.2 Using dimensions in calculations
• 3.3 Length, area and volume
• 3.4 Measurement precision and scientific notation

CHAPTER 4: Money Matters

• 4.1 Interesting interest
• 4.2 Amortization
• 4.3 A detour through sequence sums
• 4.4 Deriving the amortization formula
• 4.5 Savings
• 4.6 Credit cards
• 4.7 At the casino
• 4.8 Edge

CHAPTER 5: The Science of Secrecy

• 5.1 Secret communication
• 5.2 Substitution ciphers
• 5.3 Edgar Allen Poe: an early cryptologist
• 5.4 The de Vigenère cipher
• 5.5 Modular arithmetic
• 5.6 The RSA code
• 5.7 Why RSA Coding is such a breakthrough

CHAPTER 6: Calculus: The Smallest Pebble on the Beach

• 6.1 Calculus: a perfect title
• 6.2 Slope and velocity
• 6.3 The derivative
• 6.4 The integral calculus
• 6.5 The definite integral and area
• 6.6 The remarkable connection
• 6.7 The indefinite integral
• 6.8 Tying up loose ends
• 6.9 Discrete Mathematics

CHAPTER 7: Mathematical Models

• 7.1 Random number functions
• 7.2 Do we need computer-chosen random numbers?
• 7.3 Probability
• 7.4 Expectation
• 7.5 The St. Petersburg paradox
• 7.6 Monte Carlo simulations
• 7.7 Approximating by modeling

CHAPTER 8: Arithmetic

• 8.1 Counting
• 8.2 Addition
• 8.3 Subtraction
• 8.4 Multiplication
• 8.5 Division

CHAPTER 9: Powers, Logarithms and Exponential Change

• 9.1 Integer powers
• 9.2 Square Root
• 9.3 Rational and real powers
• 9.4 Logarithms and Exponents
• 9.5 An Important Equation
• 9.6 Logistic growth

CHAPTER 10: Alternative Geometries

• 10.1 Triangle area formulas
• 10.2 Euclid’s Elements
• 10.3 Problems with Euclid
• 10.4 Geometry on the Earth
• 10.5 Where am I?
• 10.6 Distance and direction on a sphere
• 10.7 The other alternative to Postulate 5

INDEX AND PANEL LISTING

Matthews, James_About Mathematics_Sample chapter (May 03, 2021)