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# Fields

Category: [[technical|Technical]]

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The Knowledge

Technical Fields
A minimal comprehensive map of technical knowledge.

Fundamental
Mathematics
Physics
Chemistry
Biology
Engineering
Applied Mathematics
Mechanical Engineering & Materials Science
Electrical Engineering
Computer Science
Bioengineering
Environmental Science & Engineering
Bibliography & Decisions

________________

Fundamental
Mathematics
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
3. Topology
4. Foundations
   1. Logic
   2. Set Theory
   3. Category Theory
   4. Model Theory
   5. Representation Theory
5. Geometry
6. Number Theory
7. Discrete Mathematics
   1. Combinatorics
   2. Graph Theory
8. Trigonometry
9. Optimization
10. Probability & Statistics

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

Resources:
* How to Become a Pure Mathematician
* Math I Ought to Learn
* How to Go About Learning Mathematics
* Mathematical Reading List (Cambridge)
* Princeton Companion to Mathematics

Physics

Major Topics

1. Mechanics
2. Electromagnetism
   1. Circuits
   2. Electrodynamics
3. Thermodynamics
   1. Energy
   2. Heat
   3. Work
   4. Temperature
   5. Entropy
4. Quantum Mechanics
   1. Quantum Field Theory
   2. Quantum Information
   3. Quantum Optics
   4. Quantum Theory of Solids
5. Relativity
   1. General Relativity
   2. Special Relativity
6. Particle Physics
7. Atomic Physics
8. Elasticity
9. Fluids
10. Diffusion
11. Waves
12. Optics
   1. Laser Physics
13. Imaging
14. Statistical Physics
15. Statistical Mechanics
16. Solid State Physics
17. Condensed Matter Physics
18. Cosmology
19. String Theory

Physics Research Frontier

1. Astrophysics 
   1. Astrophysics of Galaxies; Cosmology and Nongalactic Astrophysics; Earth and Planetary Astrophysics; High Energy Astrophysical Phenomena; Instrumentation and Methods for Astrophysics; Solar and Stellar Astrophysics
2. Condensed Matter 
   1. Disordered Systems and Neural Networks; Materials Science; Mesoscale and Nanoscale Physics; Other Condensed Matter; Quantum Gases; Soft Condensed Matter; Statistical Mechanics; Strongly Correlated Electrons; Superconductivity
3. General Relativity and Quantum Cosmology
4. High Energy Physics - Experiment
5. High Energy Physics - Lattice
6. High Energy Physics - Phenomenology
7. High Energy Physics - Theory
8. Mathematical Physics
9. Nonlinear Sciences
   1. Adaptation and Self-Organizing Systems; Cellular Automata and Lattice Gases; Chaotic Dynamics; Exactly Solvable and Integrable Systems; Pattern Formation and Solitons
10. Nuclear Experiment
11. Nuclear Theory
12. Physics
   1. Accelerator Physics
   2. Applied Physics
   3. Atmospheric and Oceanic Physics
   4. Atomic and Molecular Clusters
   5. Atomic Physics
   6. Biological Physics
   7. Chemical Physics
   8. Classical Physics
   9. Computational Physics
   10. Data Analysis, Statistics and Probability
   11. Fluid Dynamics
   12. General Physics
   13. Geophysics
   14. History and Philosophy of Physics
   15. Instrumentation and Detectors
   16. Medical Physics
   17. Optics
   18. Physics and Society
   19. Physics Education
   20. Plasma Physics
   21. Popular Physics
   22. Space Physics
13. Quantum Physics

Resources
* How to Become a Good Theoretical Physicist
* Susan Fowler’s Physics Reading List
* Leonard Sussman’s Reading List
Chemistry

Major Topics

1. Inorganic Chemistry
2. Organic Chemistry
3. Physical Chemistry
4. Nuclear Chemistry
5. Biochemistry
6. Materials Chemistry
7. Neurochemistry
8. Catalysis
9. Theoretical & Quantum Chemistry
Biology

Major Topics

1. Molecular Biology
2. Cellular Biology
3. Evolutionary Biology
4. Synthetic Biology
5. Genetics / Genomics
6. Neuroscience
7. Microbiology
8. Zoology
9. Anatomy & Physiology
10. Systems Biology
11. Biochemistry
12. Biophysics

Biology Research Frontier

* Animal Behavior and Cognition
* Biochemistry
* Bioengineering
* Bioinformatics
* Biophysics
* Cancer Biology
* Cell Biology
* Clinical Trials*
* Developmental Biology
* Ecology
* Epidemiology*
* Evolutionary Biology
* Genetics
* Genomics
* Immunology
* Microbiology
* Molecular Biology
* Neuroscience
* Paleontology
* Pathology
* Pharmacology and Toxicology
* Physiology
* Plant Biology
* Scientific Communication and Education
* Synthetic Biology
* Systems Biology
* Zoology

Engineering
Applied Mathematics

1. Statistics & Probability
2. Optimization
3. Differential Equations
4. Complexity & Nonlinear Dynamics
5. Modeling

Resources:
* Princeton Companion to Applied Mathematics
Mechanical Engineering & Materials Science
1. Mechanics and Materials
2. Dynamics and Control
3. Thermal-Fluids Engineering
4. Thermodynamics
5. Head and Mass Transfer
6. Design
7. Manufacturing
8. Tools for Mechanical Engineering
9. Measurement and Instrumentation
10. Hydrodynamics
11. Product Engineering
12. Aerodynamics
13. Structural Analysis
14. Fluid Mechanics
15. Materials Science
16. Civil Engineering

Applications:
Robotics
Ocean Systems

Mechanical Engineering Research Frontier

1. Biomechanical
2. Design
3. Thermosciences
4. Flow Physics and Computational Engineering
5. Mechanics and Computation
6. Multi-Scale Engeering
7. Computational Engineering
8. Energy

Resources:
* MIT Course 2
Electrical Engineering
1. Power Engineering 
2. Control Theory, Control Engineering
3. Electronic Engineering
4. Microelectronics, Nanoelectronics
5. Signal Processing
6. Telecommunications Engineering
7. Instrumentation Engineering
8. Computer Engineering

Computer Science

Major Fields

1. Systems Programming
2. Data Analysis
3. Data Structures
4. Algorithms
5. Networking
6. Programming Languages
7. Compilers
8. Computer Hardware
9. Artificial Intelligence

1. Systems Programming
   1. Operating Systems
   2. Machine Organization
   3. Assembly
   4. Memory
      1. Caching
      2. Virtual Memory
      3. Dynamic Memory
   5. Concurrency
   6. Threads
   7. Synchronization
   8. Computer Architecture
2. Data Analysis
   1. Visualization
   2. Data Storage Systems
   3. Machine Learning
3. Data Structures
4. Algorithms
   1. Machine Learning
   2. Graph Algorithms
   3. Approximation Algorithms
   4. Randomized Algorithms
   5. Distributed Algorithms
5. Networking
   1. Cloud Computing
   2. Mobile Computing
   3. Network Protocols
6. Programming Languages
   1. Type Systems
   2. Syntax / Semantics
   3. Abstraction Mechanisms
7. Compilers
   1. Interpreters
8. Artificial Intelligence
   1. Machine Learning
   2. Knowledge Representation
   3. Computational Linguistics
   4. Search
   5. Robotics

Minor Fields

1. Cryptography
2. Graphics
3. Computer Vision
4. Graphics

Computer Science Research Frontier

1. Artificial Intelligence
2. Computation and Language
3. Computational Complexity
4. Computational Engineering, Finance, and Science
5. Computational Geometry
6. Computer Science and Game Theory
7. Computer Vision and Pattern Recognition
8. Computers and Society
9. Cryptography and Security
10. Data Structures and Algorithms
11. Databases
12. Digital Libraries
13. Discrete Mathematics
14. Distributed, Parallel, and Cluster Computing
15. Emerging Technologies
16. Formal Languages and Automata Theory
17. General Literature
18. Graphics
19. Hardware Architecture
20. Human-Computer Interaction
21. Information Retrieval
22. Information Theory
23. Logic in Computer Science
24. Machine Learning
25. Mathematical Software
26. Multiagent Systems
27. Multimedia
28. Networking and Internet Architecture
29. Neural and Evolutionary Computing
30. Numerical Analysis
31. Operating Systems
32. Other Computer Science
33. Performance
34. Programming Languages
35. Robotics
36. Social and Information Networks
37. Software Engineering
38. Sound
39. Symbolic Computation
40. Systems and Control

Resources:
* Teach Yourself CS
* Studying Computer Science
* Always Be Coding
Bioengineering
1. Biomedical Engineering
2. Tissue Engineering
3. Genetic Engineering
4. Neural Engineering
5. Pharmaceutical Engineering
6. Clinical Engineering
7. Bioinformatics
8. Biomechanics
9. Biochemical Engineering
10. Bioprocess Engineering
11. Environmental Health Engineering
12. Biomimetics / Biomimicry
13. Biomechanical Engineering
14. Bionics / Biorobotics (Prosthetics)

Environmental Science & Engineering

1. Atmospheric Sciences
2. Ecology
3. Environmental Chemistry
4. Geosciences

Bibliography