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1. Mathematics makes the invisible visible

1.1. Daniel Benoulli

1.1.1. Uses Calcules

1.1.2. Discovered the what's lets you see the invisible

1.2. Netown

1.2.1. Uses Calculus

1.3. Calculus

1.3.1. Works by making visible infinitesimally small

2. When Seeing is Discovering

2.1. Study of complex dynamical systems

2.1.1. Pierre Fatou and Gaston Julia

2.2. Real soap film

2.2.1. A minimal surface is the mathematical equivalent of an infinite soap film

2.3. Without its algebraic symbol

2.3.1. Large parts of mathematics simply would not exist

2.3.2. This linguistic aspect of mathematics is often overlooked

3. The hidden beauty in the symbols

3.1. Cold and austere

3.2. The science of patterns

3.2.1. Physical

3.2.2. Biological

3.2.3. Socialogical

3.3. Physical Domain

3.3.1. Mathematics greatest succes

3.3.2. Where the subject is rightly referred to as both the queen and the servant of the natural sciences

3.4. Mathematics is Finding new locks to turn

3.4.1. Todays age. dominated by information communication and computaion

4. Its not just numbers

4.1. Egyptian and Babylonia, Arithmethic

4.2. Ancient Greece, Greek Mathemics

4.3. Thales, Could be logically proved by a logical argument

5. The Science Of Patterns

5.1. Abstract patterns

5.2. Numerical patterns

5.3. Patterns of shape

5.4. Patterns of motion

5.5. Patterns of behaviour

5.6. Voting Patterns in a population

5.7. Patterns of repeating chance events

5.8. Modern mathematics

5.8.1. Abstact notation

5.8.2. Algebraic expressions

5.8.3. Complicated-looking foromulas

5.8.4. Geometric Diagrams

6. Mathematics In Motion

6.1. No major changes in the nature of mathematics

6.2. Newton and Leibinz

6.2.1. Invented Calculus

6.3. Study of physics

7. The invisible universe

7.1. Technological society

8. Symbols of progress

8.1. Diophantus

8.1.1. Fist systematic algebraic notation

8.1.2. Used special symbols to denote the unknown in an equation

8.1.3. Employed symbols for subtraction and equality

8.2. To appreciate mathematics

8.2.1. To sight-read the symbols

8.2.2. Can be seen with the eyes of the mind