Mathematics 16
Collected Lectures on Calculus of Variations
A compact study list, grouped by level and type, with freely accessible material for studying Calculus of Variations.
Collected Lectures on Complex Analysis
A compact study list, grouped by level and type, with freely accessible material for studying Complex Analysis.
Collected Lectures on Functional Analysis
A compact study list, grouped by level and type, with freely accessible material for studying Functional Analysis.
Collected Lectures on Harmonic Analysis
A compact study list, grouped by level and type, with freely accessible material for studying Harmonic Analysis.
Collected Lectures on Measure Theory
A compact study list, grouped by level and type, with freely accessible material for studying Measure Theory.
Collected Lectures on Ordinary Differential Equations (ODE)
A compact study list, grouped by level and type, with freely accessible material for studying Ordinary Differential Equations (ODE).
Collected Lectures on Partial Differential Equations (PDE)
A compact study list, grouped by level and type, with freely accessible material for studying Partial Differential Equations (PDE).
Collected Lectures on Real Analysis
A compact study list, grouped by level and type, with freely accessible material for studying Real Analysis.
Ebooks on Combinatorics
Metric $k$-center
General $k$-center problem statement: Let \((X, d)\) be a metric space where \(X\) is a set and \(d\) is a metric. A set \(V \subseteq X\) is provided together with a parameter \(k\). The goal is to find a subset \(C \subseteq V\) with \(|C| = k\) such that the maximum distance of a point in \(V\) to the closest point in \(C\) is minimized. The problem can be formally defined as follows: Input: a set $V \subseteq X$, and a parameter $k$. Output: a set $C \subseteq V$ of $k$ points. Goal: Minimize the cost $r^C(V) = \max_{v \in V} d(v, C)$ The k-Center Clustering problem can also be defined on a complete undirected graph $G = (V, E)$ as follows:
Mathematics - Algebra
Major branches: Elementary algebra Linear algebra Abstract algebra Group theory Ring theory Field theory
Mathematics - Combinatorics
Related fields: Combinatorial optimization Coding theory Discrete and computational geometry Combinatorics and dynamical systems Combinatorics and physics
Mathematics - Mathematical analysis
Main branches: Calculus Real analysis Complex analysis Functional analysis Harmonic analysis Differential equations Measure theory Numerical analysis Vector analysis Scalar analysis Tensor analysis Other branches (small or related): Calculus of variations Geometric analysis Clifford analysis p-adic analysis Non-standard analysis Computable analysis Stochastic calculus Set-valued analysis Convex analysis Idempotent analysis Tropical analysis Constructive analysis Intuitionistic analysis Paraconsistent analysis
Mathematics for Computer Science
Reading list & mathematics resources.
Math Reading List
Mathematics
Study Mathematics # Master of Science in Mathematics @ HCMUS Branches of Mathematics # 1. Foundation of Mathematics # Transition To Pure Rigour Math Set Theory Logic Category Theory Type Theory Homotopy Type Theory Surreal Numbers 2. Number Theory # Algebraic Number Theory Analytic Number Theory 3. Algebra # Abstract Algebra Group Theory Linear Algebra Ring Theory Galois Theory Lie Algebras 4. Combinatorics # Probabilistic methods in Combinatorics Algebraic Combinatorics Graph Theory 5. Geometry Topology # Differential Geometry Algebraic Geometry Algebraic Statistics Topology Algebraic Topology 6. Mathematical analysis # Real Analysis Harmonic Analysis Complex Analysis Functional Analysis Measure Theory ODE PDE Variational Analysis Calculus of Variations Calculus (Single/ Multi-variables) Optimization & Operation Research Dynamical Systems Set-valued Analysis 7. Probability and Statistics # Probability Theory Statistics Statistical Learning Stochastic processes 8. Numerical Analysis # 9. Signal Processing # 10. Mathematics for Computer Science # 11. Mathematical Physics #