## 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