Mathematics

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Mathematics by Mind Map: Mathematics

1. Pure Math

1.1. Structure

1.1.1. Algebra

1.1.1.1. Order of operation

1.1.1.1.1. PEMDAS

1.1.1.2. Pre algebra

1.1.2. Linear algebra

1.1.3. Number theory

1.1.4. Combinatronics

1.1.4.1. Trees

1.1.4.2. Graph theory

1.1.4.3. Partition theory

1.1.5. Group theory

1.1.5.1. Permutation group

1.1.6. Order theory

1.2. Space

1.2.1. Geometry

1.2.1.1. Pythagoras

1.2.2. Trigonometey

1.2.3. Fracral geometey

1.2.4. Topology

1.2.4.1. Mobius strip

1.2.5. Measure theory

1.2.6. Differential geometry

1.3. Changes

1.3.1. Calculus

1.3.1.1. Integrals

1.3.1.2. Differentials

1.3.1.3. Gradient

1.3.1.4. Areas

1.3.1.5. Differential equation

1.3.2. Vector calculus

1.3.3. Dynamical system

1.3.4. Chaos theory

1.3.4.1. Butterfly effect

1.3.5. Complex analysis

1.4. Number system

1.4.1. Natural numbers

1.4.1.1. Arithmetic

1.4.2. Integers

1.4.3. Rational numbers

1.4.4. Real numbers

1.4.5. Complex numbers

2. Applied Math

2.1. Mathematical physics

2.1.1. Theoretical physics

2.2. Theoretical physics

2.3. Mathematical chemistry

2.4. Biomathematics

2.5. Engineering

2.5.1. Control theory

2.6. Numerical analysis

2.7. Game theory

2.8. Probability

2.9. Statistic

2.10. Mathematical Finance

2.11. Optimization

2.12. Computer Science

2.12.1. Machine learning

2.12.1.1. Linear algebra

2.12.1.2. Optimization

2.12.1.3. Dynamical system

2.12.1.4. Probability

2.13. Economics

2.14. Cryptography

2.14.1. Combinatory

2.14.2. Number theory

3. Foundation of mathematics

3.1. Fundamental rules

3.2. Mathematical logic

3.3. Set theory

3.4. Category theory

3.5. Godels incompleteness theorem

3.6. Theory of computation

3.6.1. Complexity theory

4. Basic laws of mathematics

4.1. Commutative law of addition

4.2. Commutative law of multiplication

4.3. Associative law of addition

4.4. Associative law of multiplication

4.5. Distributive law

4.6. Zero properties