Fields

Category: 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
13. Laser Physics
14. Imaging
15. Statistical Physics
16. Statistical Mechanics
17. Solid State Physics
18. Condensed Matter Physics
19. Cosmology
20. 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
13. Accelerator Physics
14. Applied Physics
15. Atmospheric and Oceanic Physics
16. Atomic and Molecular Clusters
17. Atomic Physics
18. Biological Physics
19. Chemical Physics
20. Classical Physics
21. Computational Physics
22. Data Analysis, Statistics and Probability
23. Fluid Dynamics
24. General Physics
25. Geophysics
26. History and Philosophy of Physics
27. Instrumentation and Detectors
28. Medical Physics
29. Optics
30. Physics and Society
31. Physics Education
32. Plasma Physics
33. Popular Physics
34. Space Physics
35. 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

10. 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

11. Data Analysis

    1. Visualization
    2. Data Storage Systems
    3. Machine Learning

12. Data Structures

13. Algorithms

    1. Machine Learning
    2. Graph Algorithms
    3. Approximation Algorithms
    4. Randomized Algorithms
    5. Distributed Algorithms

14. Networking

    1. Cloud Computing
    2. Mobile Computing
    3. Network Protocols

15. Programming Languages

    1. Type Systems
    2. Syntax / Semantics
    3. Abstraction Mechanisms

16. Compilers

    1. Interpreters

17. 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

Related Links, Source Documents

• OECD Standard
• Open Syllabus Galaxy
• Harvard Concentrations
• SEAS
• MIT Subject Listing
• Stanford Majors
• Wikipedia Outline of Academic Disciplines

Possible Additions

• Complex Systems
• Game Theory / Economics added to technical fields?
• Cognitive Psychology?
• Chemical Engineering

Non-Technical

Social Sciences

1. Economics
2. Social Studies
3. Government
4. History
5. Linguistics
6. Philosophy
7. Psychology
8. Sociology
9. Anthropology

Humanities

1. Art, Film, Visual Studies
2. Classics
3. Comparative Literature
4. English
5. Mythology & Folklore
6. Music
7. Religion

Graduate Study

Major

1. Law
2. Medicine
3. Business
4. Education

Source: Original Google Doc