Here is an even more expanded gigantic map of the formal, natural, and applied sciences with additional topics: Formal Sciences (Language of Patterns) 1. Mathematics a. Algebra - Linear Algebra - Matrix Theory - Vector Spaces - Multilinear Algebra - Abstract Algebra - Group Theory - Ring Theory - Field Theory - Galois Theory - Universal Algebra - Lattice Theory - Variety Theory - Clone Theory - Homological Algebra - Lie Algebras - Representation Theory b. Geometry - Euclidean Geometry - Plane Geometry - Solid Geometry - Trigonometry - Non-Euclidean Geometry - Hyperbolic Geometry - Elliptic Geometry - Absolute Geometry - Differential Geometry - Riemannian Geometry - Symplectic Geometry - Gauge Theory - Algebraic Geometry - Commutative Algebra - Scheme Theory - Birational Geometry - Discrete Geometry - Convex Geometry - Computational Geometry c. Topology - Algebraic Topology - Homotopy Theory - Homology Theory - Cohomology Theory - K-Theory - Geometric Topology - Manifold Theory - Knot Theory - Low-Dimensional Topology - Differential Topology - Morse Theory - Floer Homology - Contact Topology - General Topology - Pointless Topology d. Analysis - Real Analysis - Measure Theory - Integration Theory - Fourier Analysis - Functional Analysis - Complex Analysis - Holomorphic Functions - Riemann Surfaces - Conformal Mappings - Several Complex Variables - Functional Analysis - Banach Spaces - Hilbert Spaces - Operator Theory - Spectral Theory - Harmonic Analysis - Abstract Harmonic Analysis - Noncommutative Harmonic Analysis - Time-Frequency Analysis - Nonlinear Analysis - Variational Analysis - Stochastic Analysis e. Number Theory - Analytic Number Theory - Prime Number Theory - Diophantine Approximation - Arithmetic Functions - Zeta Functions - Algebraic Number Theory - Algebraic Integers - Class Field Theory - Cyclotomic Fields - Diophantine Equations - Computational Number Theory - Primality Testing - Integer Factorization - Elliptic Curve Cryptography - Modular Forms - Combinatorial Number Theory - Transcendental Number Theory - Arithmetic Geometry f. Combinatorics - Enumerative Combinatorics - Permutations & Combinations - Partitions - Generating Functions - Polya Theory - Analytic Combinatorics - Complex Analysis Methods - Saddle Point Method - Singularity Analysis - Mellin Transforms - Extremal Combinatorics - Ramsey Theory - Turán-type Problems - Szemerédi's Theorem - Discrepancy Theory - Algebraic Combinatorics - Topological Combinatorics - Probabilistic Combinatorics g. Logic - Propositional Logic - Boolean Algebra - Intuitionistic Logic - Many-Valued Logic - Relevance Logic - First-Order Logic - Model Theory - Proof Theory - Recursion Theory - Constructive Logic - Higher-Order Logic - Type Theory - Lambda Calculus - Topos Theory - Categorical Logic - Modal Logic - Temporal Logic - Deontic Logic - Epistemic Logic - Dynamic Logic - Paraconsistent Logic - Fuzzy Logic - Quantum Logic h. Set Theory - Axiomatic Set Theory - Zermelo-Fraenkel Set Theory - Von Neumann-Bernays-Gödel Set Theory - Morse-Kelley Set Theory - Constructive Set Theory - Descriptive Set Theory - Borel Sets - Analytic Sets - Projective Sets - Determinacy - Combinatorial Set Theory - Large Cardinals - Forcing i. Category Theory - Abelian Categories - Topos Theory - Monoidal Categories - Enriched Categories - Higher Categories - Categorical Logic j. Graph Theory - Extremal Graph Theory - Turán's Theorem - Ramsey Theory for Graphs - Szemerédi Regularity Lemma - Graph Minors - Spectral Graph Theory - Laplacian Matrices - Expander Graphs - Graph Limits - Random Graphs - Topological Graph Theory - Graph Embeddings - Graph Minors - Robertson-Seymour Theorem - Topological Connectivity - Algebraic Graph Theory - Computational Graph Theory - Probabilistic Graph Theory 2. Computer Science a. Theory of Computation - Automata Theory - Finite Automata - Pushdown Automata - Turing Machines - Cellular Automata - Computability Theory - Recursive Functions - Turing Degrees - Relative Computability - Hyperarithmetical Theory - Computational Complexity Theory - Time Complexity - Space Complexity - Circuit Complexity - Communication Complexity - Formal Languages - Kolmogorov Complexity - Algorithmic Information Theory b. Algorithms & Data Structures - Graph Algorithms - Shortest Path Algorithms - Network Flow Algorithms - Matching Algorithms - Coloring Algorithms - Numerical Algorithms - Matrix Algorithms - Optimization Algorithms - Fast Fourier Transform - Monte Carlo Methods - Approximation Algorithms - Vertex Cover - Set Cover - Traveling Salesman Problem - Knapsack Problem - Parallel Algorithms - Parallel Sorting - Parallel Graph Algorithms - Parallel Matrix Multiplication - Parallel Numerical Methods - Randomized Algorithms - Online Algorithms - Streaming Algorithms c. Programming Languages - Type Theory - Lambda Calculus - Dependent Types - Linear Types - Homotopy Type Theory - Formal Semantics - Operational Semantics - Denotational Semantics - Axiomatic Semantics - Categorical Semantics - Compiler Design - Lexical Analysis - Parsing - Code Generation - Optimization - Programming Language Design - Functional Programming - Logic Programming d. Artificial Intelligence - Machine Learning - Supervised Learning - Unsupervised Learning - Reinforcement Learning - Deep Learning - Natural Language Processing - Syntactic Parsing - Semantic Analysis - Discourse Processing - Machine Translation - Computer Vision - Image Processing - Object Recognition - Scene Understanding - 3D Reconstruction - Robotics - Robot Motion Planning - Robot Manipulation - Robot Perception - Multi-Robot Systems - Knowledge Representation - Ontologies - Semantic Networks - Description Logics - Belief Revision - Reasoning - Search - Planning e. Databases - Relational Databases - Relational Algebra - SQL - Query Optimization - Transaction Processing - NoSQL Databases - Key-Value Stores - Document Databases - Column-Family Databases - Graph Databases - Data Mining - Association Rule Mining - Clustering - Classification - Anomaly Detection - Big Data Analytics - MapReduce - Hadoop - Spark - Stream Processing - Data Warehousing - Information Retrieval - Knowledge Discovery f. Cryptography - Symmetric-Key Cryptography - Block Ciphers - Stream Ciphers - Message Authentication Codes - Cryptographic Hash Functions - Public-Key Cryptography - RSA Cryptosystem - Elliptic Curve Cryptography - Digital Signatures - Key Exchange Protocols - Cryptanalysis - Linear Cryptanalysis - Differential Cryptanalysis - Side-Channel Attacks - Quantum Cryptanalysis - Post-Quantum Cryptography - Lattice-Based Cryptography - Multivariate Cryptography - Code-Based Cryptography - Hash-Based Cryptography - Secure Multi-Party Computation - Zero-Knowledge Proofs - Homomorphic Encryption g. Information Theory - Coding Theory - Error-Correcting Codes - Hamming Codes - Reed-Solomon Codes - LDPC Codes - Data Compression - Huffman Coding - Arithmetic Coding - Lempel-Ziv Algorithms - Burrows-Wheeler Transform - Channel Coding - Convolutional Codes - Turbo Codes - Polar Codes - Sparse Graph Codes - Network Information Theory - Quantum Information Theory - Algorithmic Information Theory h. Software Engineering - Software Design Patterns - Creational Patterns - Structural Patterns - Behavioral Patterns - Architectural Patterns - Agile Methodologies - Scrum - Extreme Programming (XP) - Kanban - Lean Software Development - Formal Methods - Model Checking - Theorem Proving - Symbolic Execution - Abstract Interpretation - Software Testing - Software Architecture - Software Maintenance & Evolution 3. Linguistics & Semiotics a. Syntax - Generative Syntax - Transformational Grammar - Minimalist Program - Head-Driven Phrase Structure Grammar - Lexical-Functional Grammar - Dependency Grammar - Meaning-Text Theory - Word Grammar - Link Grammar - Functional Generative Description - Categorial Grammar - Combinatory Categorial Grammar - Type-Logical Grammar - Abstract Categorial Grammar - Pregroup Grammar - Construction Grammar - Functional Grammar - Cognitive Grammar b. Semantics - Formal Semantics - Montague Grammar - Discourse Representation Theory - Dynamic Semantics - Game-Theoretical Semantics - Lexical Semantics - Componential Analysis - Prototype Theory - Generative Lexicon - Frame Semantics - Discourse Semantics - Rhetorical Structure Theory - Segmented Discourse Representation Theory - Centering Theory - Coherence Relations - Cognitive Semantics - Distributional Semantics - Conceptual Semantics c. Pragmatics - Speech Act Theory - Illocutionary Acts - Perlocutionary Acts - Indirect Speech Acts - Politeness Theory - Relevance Theory - Cognitive Principle - Communicative Principle - Explicatures & Implicatures - Procedural Meaning - Conversation Analysis - Turn-Taking - Repair - Preference Organization - Membership Categorization - Discourse Analysis - Presupposition & Implicature - Reference & Anaphora Resolution d. Phonology - Segmental Phonology - Distinctive Features - Phonemes - Allophones - Phonological Rules - Suprasegmental Phonology - Syllables - Stress - Tone - Intonation - Phonological Theory - Optimality Theory - Government Phonology - Dependency Phonology - Articulatory Phonology - Prosodic Phonology - Laboratory Phonology - Computational Phonology e. Morphology - Inflectional Morphology - Verbal Inflection - Nominal Inflection - Adjectival Inflection - Agreement - Derivational Morphology - Affixation - Compounding - Conversion - Reduplication - Morphological Typology - Isolating Languages - Agglutinative Languages - Fusional Languages - Polysynthetic Languages - Morphological Theory - Computational Morphology - Experimental Morphology 4. Game Theory & Decision Theory a. Cooperative Game Theory - Coalitional Games - Shapley Value - Core - Bargaining Theory b. Non-Cooperative Game Theory - Nash Equilibrium - Subgame Perfect Equilibrium - Bayesian Nash Equilibrium - Correlated Equilibrium c. Evolutionary Game Theory - Evolutionarily Stable Strategies - Replicator Dynamics - Adaptive Dynamics - Evolutionary Algorithms d. Behavioral Game Theory - Bounded Rationality - Prospect Theory - Quantal Response Equilibrium - Level-k Thinking e. Multi-Criteria Decision Analysis - Analytic Hierarchy Process - ELECTRE Methods - PROMETHEE Methods - TOPSIS Method f. Utility Theory - Expected Utility Theory - Subjective Expected Utility - Multi-Attribute Utility Theory - Rank-Dependent Utility Theory g. Social Choice Theory h. Mechanism Design i. Optimal Stopping Theory 5. Statistics & Probability Theory a. Bayesian Statistics - Bayesian Inference - Markov Chain Monte Carlo - Bayesian Networks - Empirical Bayes Methods b. Frequentist Statistics - Hypothesis Testing - Confidence Intervals - Maximum Likelihood Estimation - Generalized Linear Models c. Nonparametric Statistics - Kernel Density Estimation - Splines - Wavelets - Bootstrapping d. Multivariate Analysis - Principal Component Analysis - Factor Analysis - Discriminant Analysis - Canonical Correlation Analysis e. Stochastic Processes - Markov Processes - Poisson Processes - Brownian Motion - Lévy Processes f. Measure-Theoretic Probability Theory - Probability Spaces - Random Variables - Expectation - Conditional Probability g. Statistical Learning Theory h. Actuarial Science i. Econometrics 6. Systems Theory & Cybernetics a. Dynamical Systems Theory - Ordinary Differential Equations - Partial Differential Equations - Bifurcation Theory - Chaos Theory b. Control Theory - Linear Control Systems - Nonlinear Control Systems - Optimal Control - Adaptive Control c. Information Theory - Shannon Entropy - Mutual Information - Channel Capacity - Rate-Distortion Theory d. Complex Systems Theory - Self-Organization - Emergence - Swarm Intelligence - Network Science e. Cybernetics f. Synergetics g. Autopoiesis h. Second-Order Cybernetics Natural Sciences (Localizing Patterns in the Physical Universe)