Rediscovering mathematics : you do the math /

Rediscovering mathematics is an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics.--

Bibliographic Details
Main Author: Simonson, Shai
Corporate Author: Mathematical Association of America
Format: Printed Book
Language:English
Published: United States of America: Mathematiical Association of America, 2011.
Series:Classroom resource materials (Unnumbered)
Subjects:
Mathematics > Problems, exercises, etc.
Problem solving > Study and teaching.
Mathematics > Study and teaching.
Table of Contents:
  • Introduction: How to read mathematics. An example of mathematical writing-the birthday paradox
  • Our reader tackles the birthday paradox
  • Challenges
  • 1. Mathematical discovery in the classroom. A simple lesson
  • The math teacher as conductor
  • The effective teacher
  • Challenges
  • 2. Don't reach for your calendar (Yet). A magic trick
  • Clever calculations
  • Pythagorean triples
  • Challenges
  • 3. Have another piece of pie, Zeno? A simpler way
  • Euclid, proofs, and writing mathematics
  • Challenges
  • 4. Thinking like a mathematician- Lessons from a medieval rabbi. Rabbi Levi ben Gershon and his sums
  • The number of squares and rectangles in a grid
  • The triangle puzzle-a model mathematics problem
  • Challenges
  • 5. What is mathematics good for? Knock hockey
  • Basketball
  • Rates of growth
  • Challenges
  • 6. Three averages. Average I. The Arithmetic Average
  • Average II. The Harmonic Average
  • Average III. The Geometric Average
  • Exploring averages
  • Challenges
  • 7. Algorithms- the unexpected role of pure mathematics. A solution to the two jug puzzle
  • Euclid's Algorithm
  • Other methods for calculating greatest common divisors
  • The efficiency (or speed) of an algorithm
  • The Egyptian Mutliplication Algorithm
  • The fast Modular Exponential Algorithm
  • Greatest Common Divisors, algorithms, and e-commerce
  • E-commerce and cryptography
  • The rest of the story-the RSA Algorithm
  • Challenges
  • 8. Pythagoras' theorem and math by pictures. A proof of Pythagoras' Theorem
  • A personal experience
  • The height of a pyramid
  • Challenges
  • 9. Memorizing versus understanding. Example 1: FOIL
  • Example 2: Square roots
  • Example 3: The quadratic equation
  • A "real life" quadratic equation
  • Challenges
  • 10. Games and gambling. A carnival game
  • Craps
  • The careless casino
  • Challenges
  • 11. Soccer balls and counting tricks. Euler's Formula
  • Platonic solids
  • Counting
  • The puzzle of the soccer ball
  • Challenges
  • 12. Pizza Pi and area. Pi and the bible
  • The area of a circle
  • A hard puzzle involving areas
  • Challenges
  • 13. Back to the classroom. A classroom experience
  • Emphasizing understanding
  • What next?

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