7/7/22

Great little book that clearly explains the 'why' behind Maths that many teachers (at least mine) seem to skip. Each chapter uses real world examples to illustrate the purpose of the mathematics that can describe it. Arithmetic, geometry, algebra, calculus and trigonometry are all covered. Successive chapters often build on what has gone before, so by the end a lot of the detailed calculus and trig gets quite tricky. But I was only reading it as a kind of reminder of some fundamentals so began to skip pages towards the end as I doubt I will ever need to design a tunnel or an electric motor. But if in the unlikely event, I would turn first to this book perhaps.

My book is an old Pelican 1944 reprint of the original published in 1943, hence there are lots of military and war references that give the book a real sense of time. ( )

Indeholder "Part 1: The approach to Mathematics", " 1. The Dread of Mathematics", " Imitation Subjects", " 2. Geometry - The Science of Furniture and Walls", " Some Experiments connected with Geometry", " 3. The Nature of Reasoning", " Reasoning in Mathematics", " Reasoning and Imagination", " Stages of Abstraction", " The Mechanical View of Life", " Euclid's Straight Lines", " The Mathematicians on the Second Floor", " Practical Conclusions", " 4. The Strategy and Tactics of Study", " The Removal of Fear", " The General Plan of this Book", " Reading with a Purpose", " Books on the History and Teaching of Mathematics", "Part 2: On Certain Parts of Mathematics", " 5. Arithmetic", " Decimals", " Negative Numbers", " Working With Negative Numbers", " Imaginary Numbers, or Operators", " Exercises", " Questions of Pattern", " Two Questions for Research", " 6. How to Forget the Multiplication Table", " How Logarithms are Calculated", " How Logarithms were Invented", " A Musical Slide-Rule", " Exercises", " 7. Algebra - the Shorthand of Mathematics", " The Cakes and Buns Problem", " Examples", " 8. Ways of Growing", " The Simplest Form of Growth", " The Size of Cinema Screens", " Powers of x", " Exponential Functions", " The Calculus of Finite Differences", " Binomial Coefficients", " Exercises", " 9. Graphs, or Thinking in Pictures", " The Uses of Graphs", " Graphs as a Record of Trade", " Graphs Used to detect Under-Nourishment", " Mathematicians and Graphs", " Examples", " Minus Numbers on Graphs", " 10. Differential Calculus - the Study of Speed", " The Basic Problem", " Signs for Speed", " The Importance of y' and y''", " Other Useful Subjects", " Triangle of Forces", " Co-ordinate Geometry", " Conclusion", " Examples", " 11. From Speed to Curves", " The Case of Steady Movement", " The General Case", " An Example", " Rolling a Cricket Pitch", " The Use of Rough Ideas", " Some Examples of Rough Ideas", " The Cartwheel Problem", " Illustrations and Experiments", " 12. Other Problems of Calculus", " Differentiation of a Sum", " Differentiation of a Product", " Differentiation of a Quotient", " Function of a Function", " Integration", " The Method of Rough Ideas", " Ways of Seeing Integration", " A Shorter Method", " Differential Equations", " Examples", " 13. Trigonometry, or How to Make Tunnels and Maps", " The Measurement of Angles", " Sines and Cosines", " The Formulae of Trigonometry", " The Explorer's Journey", " Pythagoras' Theorem", " The Cosine Formula", " The Addition Formulae", " Other Formulae", " Differentiating Sines and Cosines", " Movement in a Circle", " Exercises", " 14. On Backgrounds", " Geometrical Progressions", " Other Series", " The Dangers of Series", " The Background of e^x", " Minus Numbers", " Change of Scale", " The Graph y = a^x", " Logarithms", " The Number e", " The Series for e^x", " The Applications of e^x", " 15. The Square Root of Minus One", " What is i?", " The Operators 1, 2, 3 ...", " Addition", " The Operator i", " Addition", " Complex Numbers and Electricians", " The Further Study of i", "Index".

På side 100 er der en sød lille udregning. Start med 5 tal
a, b, c, d, e
Differencerne er så
b-a, c-b, d-c, e-d
Fortsæt:
c-2b+a, d-2c+b,e-2d+c
d-3c+3b-a, e-3d+3c-b
e-4d+6c-4b+a
Vi ser tydeligt hvor binomialkoefficienterne kommer fra. Sødt!

Hele teksten kan findes på nettet og de store afsnit om logaritmer er ikke interessante i dagens computerverden. ( )

W. W. Sawyer is one of the best -- possibly THE best -- writer of mathematics in a "popularizing" vein. He is [was, I should say] a real teacher at heart, but every inch a true mathematician who knows all of the technical nuances as well. I strongly recommend EVERYTHING this man has written. ( )