Mathematics Book

Mathematics the science of patterns written by keith devlin published by scientific america library
was a refreshing read. At 216 pages it took me about 3 weeks to read on and off although if I calculate total time it took to read this probably happened in a four or five day span. With those days being days of high concentration for this work. This book reminded me of the history of mathematics which was so nessicary in helping me to understand some fundamental concepts that I simply missed in other readings.


The topics in the contents where as such

Preface
Prologue
Counting
Reasoning and Communicating
Motion and Change
Shape
Symmetry and regularity
Position
Postscript
Further Readings
Sources of Illustration
Index.

I think that the artist that did the layout did a good job. Although I would not say that the book was as complete artistically as many roleplaying texts it still was lovely.
Which is something I think one should aspire for in their work is a cohesive tour de force of content and layout with both balancing one another.

The purpose of this text is to give one a sense of the purpose of the study of the science of pattern going into a slurry of topics that shows the connection and the beauty of the study of pattern.

Further the work hopes to describe and works with the idea of abstraction and how evermore the day we abstract some still from the hopes of the infinite region.

Chapter 1 Couting.
Here it recalls the rise of counting and its purpose and how people counted and why.
In the beginning of counting their was set to be a matching system where one would match an object with another object and then compare. Then their was idyllic markings placed in soft clay or on envelopes of tokens to keep track of things. So even then it might be seen that man was cybernetic storing important information outside of themselves.

Then as a subtopic we move to Greek Mathematics.
The description then starts to enter and entertain the possibility that our abstraction grew sometime before this yet it was unknown and although this had occurred we would further abstract previous works.

Area of a truntacated square pyramid
V = 1/3h(a^2 +ab +b^2)


The seven liberal arts where

Quadrivium
Arithmetica(number theory)
Harmonia(music)
Geometria(geometry)
Astrologia(astronomy)

Trivium
Logic
Grammar
Rhetoric

These where necessary of an educated man at the time.
I think that part of the undercurrent and the design of this work is in this vein as well whereas the fellow covers in some degree all of these topics. I wonder if he was speaking out through the ages to times now past to remember and respect these aspects of the mind.

Subtopics of couting
Prime Numbers
Finite Arithmetic
Prime Number Patterns
Message Encryption
Fermat's Last Theorem


Chapter 2 Reasoning and Communication
Greek logic
Venn Diagrams
Booles Logic
Vector Algebra
Propositional Logic
Predicate Logic and Patterns of Language
Abstraction and the Axiomatic Method
Set Theory
Numbers from Nothing
Hilberts Program Godel's Theorem
Proof theory
Model theory
Set theory
Computability theory
Patterns of Language

Motion and Change
Paradox of Motion
Number Patterns in Motion
Infinite Series
Functions
Computing gradients
Gradient of straight line from p to q
((x+h)^2 - x^2) / h
Fathers of calculus
Fourier Analysis
Differential Calculus
Differentional Equations
Integration
Real Numbers
Complex Numbers
Fundamental Theorem of algebra
eulers formula
e^ix = cosx + i sinx
Analytic Number Theory

Shape
Eucilds Axioms
Euclids Elements
The golden ratio
(x+1) / x = x/1
Platos Atomic Theory
Keplers Planetary Theory
Cartesian Geometry
Three Classic Problems
Non Euclidean Geometries
Projective Geometry
Cross Ratio
Dimension

Symmetry and Regularity
Symmetry Groups
Symmetry in greek is ice
Sphere Packing
Wallpaper Patterns
Tiling


Position
Networks
Topology
Classification of Surfaces
Knots
Genetic Knots
Fermat's Last Theorem Again

Postscript
This describes the many things that where not discussed throughout the book which is to say a great many.

Further Reading

Sources of Illustration