Mathematics Hub

Mathematics provides the formal language and foundational structures for science, engineering, and computing. This hub organizes Wikantik's mathematical content, ranging from the absolute foundations of set theory to the specialized tools used in modern machine learning and physical simulation.

Foundations and Logic

The bedrock of mathematical reasoning and the formal systems that underpin computation.

• Set Theory and Logic — ZFC axioms, cardinality, and the standard foundation of modern math
• Propositional Logic — The logic of "and", "or", and "not"; the basis of digital circuits
• Predicate Logic — First-order logic, quantifiers, and the foundation of relational databases
• Infinity Mathematics — Comparing different sizes of infinity and the continuum hypothesis
• Symbolic Logic — Formal manipulation of symbols and its role in automated reasoning
• Temporal Logic — Reasoning about propositions qualified in terms of time; critical for system verification
• Modal Logic — The logic of necessity and possibility

Algebra

The study of mathematical structures and the rules for manipulating symbols within those structures.

• Abstract Algebra — Groups, rings, and fields: the math behind cryptography and error correction
• Linear Algebra — Vectors, matrices, and linear transformations; the computational engine of ML and graphics
• Number Theory — Properties of integers, primality, and modular arithmetic
• Category Theory — The "math of math"; high-level abstractions used in functional programming
• Group Theory and Symmetry — Formalizing symmetry and its applications in physics and chemistry

Analysis and Calculus

The mathematics of change, limits, and continuous spaces.

• Applied Math Survey — A high-level map of the mathematical tools used in science and engineering
• Calculus Refresh for CS — Targeted calculus for software engineers and ML practitioners
• Differential Calculus — Rigorous study of derivatives, Taylor series, and multivariable analysis
• Real Analysis — The rigorous foundation of calculus and the properties of real numbers
• Complex Analysis — Calculus extended to complex numbers; essential for signal processing
• Functional Analysis — Vector spaces with infinite dimensions and their operators
• Measure Theory — Generalizing the concept of "size" or "volume"; the foundation of modern probability

Geometry and Topology

The study of shape, space, and properties that are preserved under continuous deformation.

• Differential Geometry — Calculus on curved spaces and manifolds; the math of general relativity
• Topology Mathematics — Properties of spaces like compactness and connectedness

Probability and Statistics

Reasoning about uncertainty and analyzing data.

• Probability Theory — Sample spaces, random variables, and the laws of probability
• Bayesian Reasoning — Updating beliefs based on new evidence; the foundation of many AI techniques
• Markov Chain Fundamentals — Stochastic processes that transition between states with the memoryless property

Information and Complexity

• Information Theory — Entropy, mutual information, and the limits of communication

Discrete and Applied Mathematics

Topics with direct applications in algorithms, optimization, and system design.

• Combinatorics Refresher — Counting, permutations, and combinations
• Numerical Methods — Solving continuous math problems using discrete computer arithmetic
• Optimization Algorithms — Gradient descent, Adam, L-BFGS, and the engines of ML training
• Chaos and Dynamical Systems — Systems that evolve over time and the emergence of chaotic behavior
• Game Theory Fundamentals — Strategic decision-making in competitive environments
• Discrete Match Refresher — Mathematical matching problems and their algorithmic solutions
• Fuzzy Logic — Reasoning with degrees of truth rather than binary true/false
• Integer and Combinatorial Optimization — Finding the best solution in a discrete search space
• Linear Programming Foundations — Optimizing linear objectives subject to linear constraints

Adjacent Hubs

• ML Hub — The application of these mathematical tools to machine learning
• Software Engineering Practices Hub — Applying rigorous logic to code and system design