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Wednesday, April 10, 2019

50 Mathematical Ideas You Really Need To Know




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Mathematics is a vast subject and no one can possibly know it all. What one can do is explore and find an individual pathway. The possibilities open to us here will lead to other times and different
cultures and to ideas that have intrigued mathematicians for centuries.

Mathematics is both ancient and modern and is built up from widespread cultural and political influences. From India and Arabia we derive our modern numbering system but it is one tempered
with historical barnacles. The ‘base 60’ of the Babylonians of two or three millennia BC shows up in our own culture – we have 60 seconds in a minute and 60 minutes in an hour; a right angle is still
90 degrees and not 100 grads as revolutionary France adopted in a first move towards decimalization.

The technological triumphs of the modern age depend on mathematics and surely there is no longer any pride left in announcing to have been no good at it when at school. Of course school mathematics is a different thing, often taught with an eye to examinations. The time pressure of school does not help either, for mathematics is a subject where there is no merit in being fast.
People need time to allow the ideas to sink in. Some of the greatest mathematicians have been painfully slow as they strove to understand the deep concepts of their subject.

There is no hurry with this book. It can be dipped into at leisure. Take your time and discover what these ideas you may have heard of really mean. Beginning with Zero, or elsewhere if you wish,
you can move on a trip between islands of mathematical ideas. For instance, you can become knowledgeable about Game theory and next read about Magic squares. Alternatively you can move
from Golden rectangles to the famous Fermat’s last theorem, or any other path.

This is an exciting time for mathematics. Some of its major problems have been solved in recent times. Modern computing developments have helped with some but been helpless against others. The Four-colour problem was solved with the aid of a computer, but the Riemann hypothesis, the final chapter of the book, remains unsolved – by computer or any other means.

Content:-
Introduction
01. Zero
02. Number systems
03. Fractions
04. Squares and square roots
05. π
06. e
07. Infinity
08. Imaginary numbers
09. Primes
10. Perfect numbers
11. Fibonacci numbers
12. Golden rectangles
13. Pascal’s triangle
14. Algebra
15. Euclid’s algorithm
16. Logic
17. Proof
18. Sets
19. Calculus
20. Constructions
21. Triangles
22. Curves
23. Topology
24. Dimension
25. Fractals
26. Chaos
27. The parallel postulate
28. Discrete geometry
29. Graphs
30. The four-colour problem
31. Probability
32. Bayes’s theory
33. The birthday problem
34. Distributions
35. The normal curve
36. Connecting data
37. Genetics
38. Groups
39. Matrices
40. Codes
41. Advanced counting
42. Magic squares
43. Latin squares
44. Money mathematics
45. The diet problem
46. The travelling salesperson
47. Game theory
48. Relativity
49. Fermat’s last theorem
50. The Riemann hypothesis
Glossary
Index

Author Details
"Tony Crilly"




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