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--- title: "Fields" visibility: public --- # Fields Category: [[technical|Technical]] [Read the original document](https://docs.google.com/document/d/13s1ZC1kCFGn26OL1quIwGz0fLibaVpkDZ9RxEbNzb3U/edit?usp=sharing&sa=D&ust=1596495076370000&usg=AOvVaw1BLJZ3__v6uTZUGgOtylgd) <!-- gdoc-inlined --> --- 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 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](https://docs.google.com/document/d/13s1ZC1kCFGn26OL1quIwGz0fLibaVpkDZ9RxEbNzb3U/edit?usp=sharing&sa=D&ust=1596495076370000&usg=AOvVaw1BLJZ3__v6uTZUGgOtylgd)*