Professor Higgins’s Problem Collection 1st Edition by Peter Higgins 0191071973 9780191071973

Professor Higgins’s Problem Collection 1st Edition by Peter M. Higgins – Ebook PDF Instant Download/DeliveryISBN:   0191071973, 9780191071973 

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Product details:

ISBN-10 :  0191071973 

ISBN-13 :  9780191071973

Author:  Peter M. Higgins 

What can you do with your maths? You can use it to thoroughly understand all manner of things that cannot be dealt with in any other way. This book serves up a variety of problems and shows how mathematics answers them. Topics range from cracking codes to the persistence of recessive genes; from logic puzzles to classical geometry; and from planetary motion questions to predicting the market share of competing companies. And there are other problems where the mathematics itself is intrinsically surprising and interesting.

Professor Higgins’s Problem Collection 1st Table of contents:

1. Number
Introduction
Problem 1: What values may primes take?
Problem 1 solution
Problem 2: Hidden binary
Problem 2 solution
Problem 3: How should we write fractions?
Problem 3 solution
Problem 4: Labelling a cube
Problem 4 solution
Problem 5: Map numbering problem
Problem 5 solution
Problem 6: Counting the pennies
Problem 6 solution
Problem 7: Counting solutions
Problem 7 solution
Problem 8: Cracking codes
Problem 8 solution
Problem 9: Logic puzzles
Problem 9 solution
Problem 10: Pigeonhole tricks
Problem 10 solution
Number notes
Integers
Modular arithmetic
Combinations
Complex numbers
Comments on number problems
2. Algebra
Introduction
Problem 11: Trading equations
Problem 11 solution
Problem 12: Frog and toad
Problem 12 solution
Problem 13: Geometric series questions
Problem 13 solution
Problem 14: Summing powers of integers
Problem 14 solution
Problem 15: Roots of equations
Problem 15 solution
Problem 16: Special series
Problem 16 solution
Problem 17: Exact values of trigonometric functions
Problem 17 solution
Problem 18: Cosine questions
Problem 18 solution
Problem 19: How many terms to get close?
Problem 19 solution
Problem 20: Functional equations
Problem 20 solution
Algebra notes
Arithmetic and geometric series
Comments on algebra problems
3. Geometry
Introduction
Problem 21: Goat grazing problems
Problem 21 solution
Problem 22: Compasses and straight edge
Problem 22 solution
Problem 23: Tiny changes mean a lot? Or not?
Problem 23 solution
Problem 24: Golden diagonal
Problem 24 solution
Problem 25: Newton’s ladder problem
Problem 25 solution
Problem 26: How long is a fan belt?
Problem 26 solution
Problem 27: A fifth century trick
Problem 27 solution
Problem 28: At a tangent
Problem 28 solution
Problem 29: Low lights
Problem 29 solution
Problem 30: Rugby place kicking problem
Problem 30 solution
Geometry notes
Triangles
Pythagoras’s theorem
Circle theorems
Sine and Cosine rules
Ellipses and hyperbolas
Volume and surface areas
Comments on geometry problems
4. Chance and combinations
Introduction
Problem 31: Tennis tournaments
Problem 31 solution
Problem 32: Tumbling dice and a tricky toss
Problem 32 solution
Problem 33: Tactile random walks
Problem 33 solution
Problem 34: More amblings
Problem 34 solution
Problem 35: One in a million?
Problem 35 solution
Problem 36: Loyalty versus Switch
Problem 36 solution
Problem 37: Think it’s going to rain today?
Problem 37 solution
Problem 38: Persistence of recessive genes
Problem 38 solution
Problem 39: Counting mappings
Problem 39 solution
Problem 40: Area under the bell curve
Problem 40 solution
Chance and combinations notes
Probability
Comments on chance and combinations problems
5. Movement
Introduction
Problem 41: Cycling questions
Problem 41 solution
Problem 42: On the run
Problem 42 solution
Problem 43: Sam Loyd’s ferry boat problem
Problem 43 solutions
Problem 44: Cylinder problems
Problem 44 solution
Problem 45: Catching The Goblin
Problem 45 solution
Problem 46: Flag in the wind
Problem 46 solution
Problem 47: Planetary motion
Problem 47 solution
Problem 48: Elastic collision
Problem 48 solution
Problem 49: Slip sliding away?
Problem 49 solution
Problem 50: Fermat’s Principle and Snell’s Law of Refraction

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