What are the branches of Mathematics?

arithmetic
algebra
calculus
differential equations
statistics
probability
numerical analysis
trigonometry
geometry

thats only I know...

1 Areas of basic mathematics
Outline of discrete mathematics
List of calculus topics
List of geometry topics
List of topics in logic
List of trigonometry topics
Outline of trigonometry
List of trigonometric identities
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2 Areas of advanced mathematics
2.1 Pure mathematics
→ 2.1.1 Algebra
→ 2.1.2 Calculus and analysis
→ 2.1.3 Geometry and topology
→ 2.1.4 Combinatorics
→ 2.1.5 Logic
→ 2.1.6 Number theory

2.2 Applied mathematics
→ 2.2.1 Dynamical systems and differential equations
→ 2.2.2 Mathematical physics
→ 2.2.3 Computing
→ 2.2.4 Information theory and signal processing
→ 2.2.5 Probability and statistics
→ 2.2.6 Game theory
→ 2.2.7 Operations research