Suggest edit — High Level Understanding Mathematics

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title: "High Level Understanding Mathematics"
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# High Level Understanding Mathematics

Category: [[technical|Technical]]

[Read the original document](https://docs.google.com/document/d/14FjQcA1Z-Nos5sCZ0pt9L6O51cNFKdK1UjbP20cutwk/edit?usp=sharing&sa=D&ust=1596495076372000&usg=AOvVaw1YYVNtVkuWrX-1PQPYRnQA)

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Mathematics

Major Fields

1. Algebra
   1. Linear Algebra
   2. Abstract Algebra
      1. Group Theory
   3. Lie Algebras
      1. Lie Groups
2. Analysis
   1. Calculus
   2. Differential Equations
   3. Real Analysis
   4. Complex Analysis
   5. Topology
3. Foundations
   1. Logic
   2. Set Theory
   3. Category Theory
4. Z d de dar de por favor me avisa cuando r de frente d de de de r d
5.  Y I I para y yd Model Theory
   1. Representation Theory
6. Geometry
7. Number Theory
8. Discrete Mathematics
   1. Combinatorics
   2. Graph Theory
9. Trigonometry
10. Optimization

Lol, so many advanced math courses are just combinations of fundamental courses:

1. Analytic Number Theory
2. Differential Geometry
3. Algebraic Topology
4. Algebraic Geometry
5. Algebraic Number Theory (Number Fields)

Mathematics Research Frontier

1. Algebraic Geometry
2. Algebraic Topology
3. Analysis of PDEs
4. Category Theory
5. Classical Analysis and ODEs
6. Combinatorics
7. Commutative Algebra
8. Complex Variables
9. Differential Geometry
10. Dynamical Systems
11. Functional Analysis
12. General Mathematics
13. General Topology
14. Geometric Topology
15. Group Theory
16. History and Overview
17. Information Theory
18. K-Theory and Homology
19. Logic
20. Mathematical Physics
21. Metric Geometry
22. Number Theory
23. Numerical Analysis
24. Operator Algebras
25. Optimization and Control
26. Probability
27. Quantum Algebra
28. Representation Theory
29. Rings and Algebras
30. Spectral Theory
31. Statistics Theory
32. Symplectic Geometry

Links:

Algebraic Geometry; Algebraic Topology; Analysis of PDEs; Category Theory; Classical Analysis and ODEs; Combinatorics; Commutative Algebra; Complex Variables; Differential Geometry; Dynamical Systems; Functional Analysis; General Mathematics; General Topology; Geometric Topology; Group Theory; History and Overview; Information Theory; K-Theory and Homology; Logic; Mathematical Physics; Metric Geometry; Number Theory; Numerical Analysis; Operator Algebras; Optimization and Control; Probability; Quantum Algebra; Representation Theory; Rings and Algebras; Spectral Theory; Statistics Theory; Symplectic Geometry

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*Source: [Original Google Doc](https://docs.google.com/document/d/14FjQcA1Z-Nos5sCZ0pt9L6O51cNFKdK1UjbP20cutwk/edit?usp=sharing&sa=D&ust=1596495076372000&usg=AOvVaw1YYVNtVkuWrX-1PQPYRnQA)*