### Map 1 **A Comprehensive Map of Sciences** --- **1. Formal Sciences** - **[[Mathematics]]** - Algebra - Linear Algebra - Abstract Algebra - Group Theory - Ring Theory - Field Theory - Module Theory - Representation Theory - Universal Algebra - Homological Algebra - Analysis - Real Analysis - Complex Analysis - Functional Analysis - Harmonic Analysis - Non-standard Analysis - Geometry - Euclidean Geometry - Non-Euclidean Geometry - Differential Geometry - Algebraic Geometry - Discrete Geometry - Computational Geometry - Topology - Point-set Topology - Algebraic Topology - Differential Topology - Number Theory - Elementary Number Theory - Analytic Number Theory - Algebraic Number Theory - Computational Number Theory - Logic - Set Theory - Axiomatic Set Theory - Descriptive Set Theory - Proof Theory - Model Theory - Computability Theory - Combinatorics - Enumerative Combinatorics - Graph Theory - Design Theory - Matroid Theory - Probability - Theoretical Probability - Stochastic Processes - Martingale Theory - Markov Processes - Statistics - Descriptive Statistics - Inferential Statistics - Bayesian Statistics - Non-parametric Statistics - Multivariate Statistics - Statistical Modeling - Mathematical Physics - Game Theory - Optimization - Cryptography - **Computer Science** - Theoretical Computer Science - Algorithms - Computability Theory - Complexity Theory - Automata Theory - Quantum Computing - Artificial Intelligence - Machine Learning - Deep Learning - Natural Language Processing - Computer Vision - Robotics - Computer Systems - Operating Systems - Distributed Systems - Networking - Parallel Computing - Cloud Computing - Software Engineering - Software Development - Software Testing - Human-Computer Interaction - Programming Languages - Agile Methodologies - Data Science - Data Mining - Big Data Analytics - Predictive Analytics - Business Intelligence - Information Security - Cryptography - Cybersecurity - Information Assurance - **Systems Science** - Systems Theory - Control Theory - Cybernetics - Complexity Science - **Logic** - Mathematical Logic - Philosophical Logic - Modal Logic - Fuzzy Logic - **Statistics and Decision Sciences** - Decision Theory - Operations Research - Actuarial Science - Econometrics --- **2. [[Natural Science]]** - **Physics** - Classical Mechanics - Newtonian Mechanics - Lagrangian Mechanics - Hamiltonian Mechanics - Fluid Mechanics - Acoustics - Thermodynamics and Statistical Mechanics - Thermodynamics - Statistical Mechanics - Chaos Theory - Electromagnetism - Electricity - Magnetism - Optics - Quantum Mechanics - Quantum Field Theory - Quantum Information Science - Relativity - Special Relativity - General Relativity - Condensed Matter Physics - Solid State Physics - Low-Temperature Physics - Nuclear and Particle Physics - Nuclear Physics - Particle Physics - High-Energy Physics - Astrophysics - Stellar Astronomy - Galactic Astronomy - Cosmology - Plasma Physics - Biophysics - Medical Physics - **Chemistry** - Analytical Chemistry - Physical Chemistry - Organic Chemistry - Inorganic Chemistry - Biochemistry - Theoretical Chemistry - Environmental Chemistry - Polymer Chemistry - Electrochemistry - Medicinal Chemistry - Computational Chemistry - Astrochemistry - Supramolecular Chemistry - Green Chemistry - **Earth Sciences (Geosciences)** - Geology - Mineralogy - Petrology - Sedimentology - Stratigraphy - Structural Geology - Volcanology - Seismology - Geophysics - Geochemistry - Oceanography - Physical Oceanography - Chemical Oceanography - Biological Oceanography - Geological Oceanography - Atmospheric Sciences - Meteorology - Climatology - Atmospheric Chemistry - Atmospheric Physics - Soil Science - Glaciology - Paleontology - Paleobiology - Paleoclimatology - Hydrology - Environmental Science - **Astronomy** - Observational Astronomy - Theoretical Astronomy - Planetary Science - Stellar Astronomy - Galactic Astronomy - Extragalactic Astronomy - Cosmology - Astrobiology - **Biology** - Botany - Plant Physiology - Plant Ecology - Plant Pathology - Zoology - Entomology - Ornithology - Herpetology - Ichthyology - Mammalogy - Microbiology - Bacteriology - Virology - Mycology - Parasitology - Molecular Biology - Cell Biology - Genetics - Genomics - Epigenetics - Population Genetics - Evolutionary Biology - Evolutionary Developmental Biology - Phylogenetics - Ecology - Behavioral Ecology - Conservation Biology - Ecosystem Ecology - Landscape Ecology - Physiology - Human Physiology - Comparative Physiology - Neurophysiology - Developmental Biology - Marine Biology - Neuroscience - Cognitive Neuroscience - Computational Neuroscience - Neuroinformatics - Biophysics - Bioinformatics - Systems Biology - Synthetic Biology - Immunology - Pharmacology - Biochemistry - **Materials Science** - Metallurgy - Polymer Science - Ceramics - Nanomaterials - Biomaterials - Electronic and Optical Materials --- **3. Social Sciences** - **Psychology** - Clinical Psychology - Cognitive Psychology - Developmental Psychology - Social Psychology - Evolutionary Psychology - Neuropsychology - Forensic Psychology - Industrial and Organizational Psychology - Educational Psychology - Health Psychology - Sport Psychology - Psychometrics - **Sociology** - Criminology - Demography - Social Stratification - Gender Studies - Rural Sociology - Urban Sociology - Cultural Sociology - Sociology of Education - Medical Sociology - **Anthropology** - Cultural Anthropology - Physical (Biological) Anthropology - Archaeology - Linguistic Anthropology - Forensic Anthropology - **Economics** - Microeconomics - Macroeconomics - Development Economics - Behavioral Economics - International Economics - Econometrics - Financial Economics - Environmental Economics - Health Economics - Labor Economics - Public Economics - **Political Science** - Comparative Politics - International Relations - Political Theory - Public Administration - Public Policy - Political Economy - Political Methodology - **Human Geography** - Economic Geography - Cultural Geography - Political Geography - Urban Geography - Environmental Geography - Population Geography - **Education** - Curriculum Studies - Educational Technology - Special Education - Adult Education - Educational Psychology - **Law** - Criminal Law - Civil Law - International Law - Environmental Law - Intellectual Property Law - Human Rights Law - **Communication Studies** - Media Studies - Journalism - Public Relations - Advertising - **Linguistics** - Phonetics - Phonology - Morphology - Syntax - Semantics - Pragmatics - Sociolinguistics - Psycholinguistics - Computational Linguistics - Applied Linguistics - **History** - Social History - Economic History - Military History - Cultural History - History of Science and Technology - **Demography** - **Information Science** - Library Science - Archival Science - Knowledge Management - Information Architecture --- **4. Applied Sciences** - **Engineering** - Mechanical Engineering - Automotive Engineering - Aerospace Engineering - Marine Engineering - Mechatronics - Electrical Engineering - Electronics Engineering - Telecommunications Engineering - Power Engineering - Control Engineering - Civil Engineering - Structural Engineering - Environmental Engineering - Geotechnical Engineering - Transportation Engineering - Chemical Engineering - Process Engineering - Biochemical Engineering - Petroleum Engineering - Materials Engineering - Computer Engineering - Hardware Engineering - Network Engineering - Software Engineering - Biomedical Engineering - Bioinstrumentation - Biomaterials - Biomechanics - Rehabilitation Engineering - Environmental Engineering - Industrial Engineering - Manufacturing Engineering - Systems Engineering - Operations Research - Nuclear Engineering - Agricultural Engineering - Petroleum Engineering - Optical Engineering - Nanotechnology - **Medicine and Health Sciences** - Medicine - Anatomy - Physiology - Pathology - Pharmacology - Surgery - Psychiatry - Radiology - Oncology - Pediatrics - Obstetrics and Gynecology - Neurology - Cardiology - Endocrinology - Dermatology - Epidemiology - Public Health - Nursing - Dentistry - Veterinary Medicine - Pharmacy - Occupational Therapy - Physical Therapy - Speech-Language Pathology - Audiology - Biomedical Sciences - Immunology - Microbiology - Neuroscience - Genetics - Health Informatics - **Computer Science (Applied)** - Software Development - Web Development - Mobile Computing - Game Development - Information Systems - Database Management - Cybersecurity - **Agricultural Sciences** - Agronomy - Horticulture - Animal Science - Forestry - Soil Science - Agricultural Economics - Plant Pathology - Entomology - Food Science - **Environmental Science** - Conservation Biology - Ecology - Environmental Chemistry - Environmental Engineering - Climate Science - Waste Management - Renewable Energy - Sustainable Development - **Forensic Science** - Forensic Chemistry - Forensic Biology - Digital Forensics - Forensic Anthropology - Forensic Psychology - **Business and Management** - Business Administration - Marketing - Finance - Accounting - Human Resource Management - Operations Management - Strategic Management - Entrepreneurship - Supply Chain Management - **Information Science** - Information Systems - Information Management - Data Management - Knowledge Management --- **5. Interdisciplinary Sciences** - **Biophysics** - **Biochemistry** - **Geochemistry** - **Astrobiology** - **Environmental Science** - **Cognitive Science** - **Neuroscience** - **Behavioral Science** - **Computational Science** - Computational Biology - Computational Chemistry - Computational Physics - **Nanotechnology** - **Systems Biology** - **Bioinformatics** - **Quantum Information Science** - **Network Science** - **Complex Systems** - **Econophysics** - **Sociophysics** - **Cognitive Neuroscience** - **Cybernetics** - **Artificial Intelligence** - **Robotics** - **Human Factors and Ergonomics** - **Data Science** --- This extensive map categorizes a vast array of scientific disciplines across the formal, natural, social, applied, and interdisciplinary sciences. Each field branches into specialized subfields, reflecting the complexity and interconnectivity of modern scientific inquiry. This structure not only illustrates the breadth of human knowledge but also highlights the interdisciplinary nature of contemporary research, where collaboration across different scientific domains leads to innovation and advancement. ### Map 2 ### [[Natural science]] 1. **[[Physics]]** - Classical Mechanics - Quantum Mechanics - Thermodynamics - Electromagnetism - Astrophysics - Nuclear Physics - Particle Physics - Condensed Matter Physics - Acoustics - Optics 2. **Chemistry** - Organic Chemistry - Inorganic Chemistry - Physical Chemistry - Analytical Chemistry - Biochemistry - Theoretical Chemistry - Environmental Chemistry - Industrial Chemistry 3. **Biology** - Molecular Biology - Microbiology - Botany - Zoology - Genetics - Evolutionary Biology - Ecology - Marine Biology - Physiology 4. **Earth Sciences** - Geology - Meteorology - Oceanography - Geophysics - Environmental Science - Paleontology - Hydrology - Soil Science - Climatology 5. **Astronomy** - Observational Astronomy - Theoretical Astronomy - Cosmology - Planetary Science - Astrobiology ### [[Social science]] 1. **Psychology** - Clinical Psychology - Cognitive Psychology - Developmental Psychology - Experimental Psychology - Industrial-Organizational Psychology - Social Psychology - Educational Psychology 2. **Sociology** - Social Theory - Social Research - Cultural Sociology - Political Sociology - Economic Sociology - Industrial Sociology - Criminology 3. **Economics** - Microeconomics - Macroeconomics - Developmental Economics - International Economics - Labor Economics - Environmental Economics - Behavioral Economics 4. **Political Science** - Comparative Politics - International Relations - Political Theory - Public Administration - Public Policy - Political Economy 5. **Anthropology** - Cultural Anthropology - Physical Anthropology - Archaeology - Linguistic Anthropology - Social Anthropology 6. **Geography** - Physical Geography - Human Geography - Geographical Information Systems (GIS) - Urban Geography - Regional Geography 7. **History** - Ancient History - Medieval History - Modern History - Art History - Economic History - Cultural History ### [[Formal science]] 1. **[[Mathematics]]** - Algebra - Calculus - Geometry - Statistics - Applied Mathematics - Pure Mathematics - Number Theory - Topology 2. **[[Computer science]]** - Theoretical Computer Science - Software Engineering - Artificial Intelligence - Computer Systems and Networks - Human-Computer Interaction - Data Science 3. **Logic** - Mathematical Logic - Philosophical Logic - Computational Logic - Modal Logic 4. **Statistics** - Descriptive Statistics - Inferential Statistics - Probability Theory - Biostatistics - Econometrics - Applied Statistics ### [[Applied science]] 1. **Engineering** - Mechanical Engineering - Electrical Engineering - Civil Engineering - Chemical Engineering - Aerospace Engineering - Biomedical Engineering - Environmental Engineering - Software Engineering 2. **Medicine** - General Practice - Surgery - Psychiatry - Pediatrics - Oncology - Neurology - Cardiology - Radiology 3. **Agriculture** - Agronomy - Horticulture - Animal Science - Aquaculture - Soil Science - Agricultural Economics - Plant Pathology 4. **Architecture** - Building Architecture - Landscape Architecture - Urban Design - Interior Design - Sustainable Design ### [[Humanities]] 1. **Philosophy** - Metaphysics - Epistemology - Ethics - Aesthetics - Logic - Philosophy of Science 2. **Literature** - Fiction - Non-Fiction - Poetry - Drama - Comparative Literature - Literary Theory 3. **Linguistics** - Syntax - Phonetics - Phonology - Semantics - Sociolinguistics - Psycholinguistics 4. **Art** - Painting - Sculpture - Photography - Film - Digital Arts - Performance Arts 5. **Music** - Music Theory - Composition - Performance - Musicology - Ethnomusicology ### [[Interdisciplinarity]] - Environmental Studies - Gender Studies - Urban Studies - Cognitive Science - International Studies - Bioinformatics - Neurosciences This list provides a broad overview of the major fields of science and their sub-disciplines. Each field continues to grow and evolve, and new subfields are constantly emerging. #### Anki **Advanced Mathematics** --- **Front:** What is the statement of the Atiyah–Singer Index Theorem? **Back:** The Atiyah–Singer Index Theorem states that for an elliptic differential operator \( D \) on a compact manifold, the analytical index (the difference between the dimension of the kernel and the dimension of the cokernel of \( D \)) equals the topological index computed using topological data from the manifold and the symbol of \( D \). --- **Front:** Explain the Riemann Hypothesis. **Back:** The Riemann Hypothesis posits that all non-trivial zeros of the Riemann zeta function \( \zeta(s) \) lie on the critical line in the complex plane where the real part of \( s \) is \( \frac{1}{2} \). It has profound implications for the distribution of prime numbers. --- **Front:** What is the Jacobian Conjecture in algebraic geometry? **Back:** The Jacobian Conjecture asserts that any polynomial mapping \( \mathbb{C}^n \to \mathbb{C}^n \) with a non-zero constant Jacobian determinant is invertible and that its inverse is also a polynomial mapping. --- **Front:** Define the concept of a Lie Group. **Back:** A Lie Group is a group that is also a smooth manifold where the group operations (multiplication and inversion) are smooth (differentiable). Lie groups are used to study continuous symmetries in mathematics and physics. --- **Front:** What is the Hodge Conjecture? **Back:** The Hodge Conjecture proposes that certain types of differential forms (called Hodge classes) on a non-singular projective algebraic variety are linear combinations of classes of algebraic cycles. It connects algebraic geometry and topology. --- **Advanced Physics** --- **Front:** State the principle of gauge invariance in quantum field theory. **Back:** Gauge invariance is the principle that certain physical laws are invariant under local transformations of the gauge fields. This symmetry leads to the conservation laws and necessitates the existence of gauge bosons, mediating fundamental interactions. --- **Front:** Explain the concept of spontaneous symmetry breaking. **Back:** Spontaneous symmetry breaking occurs when the underlying laws are symmetric, but the system's ground state is not. In physics, this mechanism explains how particles acquire mass (Higgs mechanism) and leads to phenomena like superconductivity. --- **Front:** What is the Heisenberg Uncertainty Principle? **Back:** The Heisenberg Uncertainty Principle states that one cannot simultaneously know the exact position and exact momentum of a particle. The uncertainties are inversely proportional, with \( \Delta x \Delta p \geq \frac{\hbar}{2} \). --- **Front:** Describe the significance of the Dirac Equation. **Back:** The Dirac Equation is a relativistic wave equation that describes spin-½ particles, like electrons, consistent with both quantum mechanics and special relativity. It predicted the existence of antimatter and provided a foundation for quantum electrodynamics. --- **Front:** What is the Casimir Effect? **Back:** The Casimir Effect is a physical force arising from a quantized field between two uncharged, parallel conducting plates in a vacuum. It's due to the restriction of vacuum fluctuations, resulting in an attractive force between the plates. --- **Advanced Computer Science** --- **Front:** What is the P vs NP problem? **Back:** The P vs NP problem asks whether every problem whose solution can be verified in polynomial time (NP) can also be solved in polynomial time (P). It's one of the most important open questions in theoretical computer science. --- **Front:** Explain the concept of a Turing Machine. **Back:** A Turing Machine is an abstract computational model that manipulates symbols on an infinite tape according to a set of rules. It's used to model algorithmic processes and define the limits of what can be computed. --- **Front:** Define NP-completeness. **Back:** A problem is NP-complete if it's both in NP and as hard as any problem in NP, meaning any NP problem can be reduced to it in polynomial time. Solving an NP-complete problem efficiently would solve all NP problems efficiently. --- **Front:** What is the Halting Problem? **Back:** The Halting Problem is the question of determining whether an arbitrary computer program will eventually halt (stop running) or continue to run indefinitely. Alan Turing proved that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. --- **Front:** Describe the concept of Quantum Computing. **Back:** Quantum Computing utilizes principles of quantum mechanics, such as superposition and entanglement, to perform computations. Qubits can represent 0 and 1 simultaneously, potentially solving certain problems exponentially faster than classical computers. --- **Advanced Engineering** --- **Front:** Explain the concept of control theory in engineering. **Back:** Control theory deals with influencing the behavior of dynamical systems using feedback. It aims to design systems that maintain desired outputs despite external disturbances, ensuring stability and optimal performance. --- **Front:** What is Finite Element Analysis (FEA)? **Back:** Finite Element Analysis is a numerical method for solving complex structural, fluid, and thermal problems by breaking down a large system into smaller, simpler parts called finite elements. It approximates solutions to differential equations over complex domains. --- **Front:** Define the Kalman Filter. **Back:** The Kalman Filter is an algorithm that estimates the state of a dynamic system from a series of incomplete and noisy measurements. It operates recursively, providing estimates of past, present, and even future states. --- **Front:** What is the significance of Shannon's Theorem in communication systems? **Back:** Shannon's Theorem, or the Shannon-Hartley Theorem, defines the maximum data rate (channel capacity) of a communication channel with a specific bandwidth and noise level. It forms the foundation of information theory and digital communications. --- **Front:** Describe the principle of operation of a MOSFET. **Back:** A MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) controls current flow by applying a voltage to the gate terminal, which alters the conductivity of a channel between the source and drain terminals. It's fundamental in digital circuits. --- **Advanced Biology and Chemistry** --- **Front:** Explain the Central Dogma of Molecular Biology. **Back:** The Central Dogma of Molecular Biology describes the flow of genetic information: DNA is transcribed into RNA, which is then translated into proteins. It highlights the unidirectional transfer of information in biological systems. --- **Front:** What is the mechanism of action of CRISPR-Cas9? **Back:** CRISPR-Cas9 is a genome-editing tool where the Cas9 enzyme, guided by a synthetic RNA sequence, introduces double-strand breaks at specific DNA locations. This allows for targeted modifications to the genome, such as gene insertion or deletion. --- **Front:** Define the concept of enzyme kinetics. **Back:** Enzyme kinetics studies the rates of enzymatic reactions, focusing on how factors like substrate concentration affect reaction speed. The Michaelis-Menten equation describes the rate of enzymatic reactions concerning substrate concentration. --- **Front:** What is the Aufbau principle in chemistry? **Back:** The Aufbau principle states that electrons fill atomic orbitals starting with the lowest energy levels before filling higher ones. It's a guideline for determining the electron configurations of atoms in their ground states. --- **Front:** Explain the concept of chirality in organic chemistry. **Back:** Chirality refers to molecules that are non-superimposable on their mirror images, much like left and right hands. Chiral molecules can have different chemical properties, especially in biological systems where they interact with other chiral molecules. --- **Advanced Topics in Statistics** --- **Front:** What is Bayesian Inference? **Back:** Bayesian Inference is a statistical method that updates the probability for a hypothesis as more evidence becomes available. It applies Bayes' Theorem to revise prior probabilities into posterior probabilities based on observed data. --- **Front:** Define the concept of Markov Chain Monte Carlo (MCMC). **Back:** MCMC is a class of algorithms for sampling from probability distributions using Markov chains. It's particularly useful for approximating complex integrals and is widely used in Bayesian statistics to estimate posterior distributions. --- **Front:** Explain the Central Limit Theorem. **Back:** The Central Limit Theorem states that the sum (or average) of a large number of independent, identically distributed random variables tends toward a normal distribution, regardless of the original distribution of the variables. --- **Front:** What is the Curse of Dimensionality? **Back:** The Curse of Dimensionality refers to the exponential increase in volume associated with adding extra dimensions to a mathematical space. It leads to sparsity of data in high-dimensional spaces, making statistical analysis more challenging. --- **Front:** Describe Principal Component Analysis (PCA). **Back:** PCA is a dimensionality reduction technique that transforms data into a new coordinate system. The greatest variance by any projection of the data comes to lie on the first coordinate (principal component), the second greatest on the second coordinate, and so on. ---