Articles

Mathematics

$$\int_a^b f'(x)\, dx = f(b) - f(a) \qquad\qquad \frac{d}{dx}\!\left(\int_a^x f(t)\, dt\right) = f(x)$$

The integration on forms concept is of fundamental importance in differential topology, geometry, and physics, and also yields one of the most important examples of cohomology, namely de Rham cohomology, which measures precisely the extent to which the fundamental theorem of calculus fails in higher dimensions and on general manifolds.

Terence Tao, Differential Forms and Integration

• (EM-KDS) Abstract Algebra I

  Cyclic Group, Classification of Cyclic Group, Lagrange’s Theorem, Converge of Lagrange’s Theorem
• (EM-KDS) Abstract Algebra II

  Group Action, Cayley Theorem, Normal Subgroups, Normality of the Kernel
• (EM-KDS) Abstract Algebra III

  First Isomorphism Theorem, Second Isomorphism Theorem, Third Isomorphism Theorem
• (EM-KDS) Abstract Algebra to Linear Algebra

  TBA
• (EM-KDS) Advanced Calculus I

  Boundedness, Supremum and Infimum, Least Upper Bound Property, Well-Ordering Principle and Mathematical Induction,Archimedean Property
• (EM-KDS) Advanced Calculus II

  Convergence of Sequences, Inequality Rule for Absolute Values, Limit Theorem (Algebraic Property of Limit of Sequence)
• (EM-KDS) Advanced Calculus III

  Limit of a Function (ε − δ), Continuity of a Function, Monotone Convergent Theorem (MCT), Nested Interval Property (NIP), Bolzano-Weierstrass Theorem, Limit Superior and Limit Inferior
• (EM-KDS) Algebraic Structures

  Group, Ring, Field, Module, Vector Space, Algebra
• (EM-KDS) Linear Algebra I

  Basis, Hamel Basis Theorem (Existence of Basis), Invariance of Basis Cardinality
• (EM-KDS) Linear Algebra II

  Linear Transformation, Classification of Vector Space (up to Isomorphism), Matrix Representation of a Linear Transformation
• (EM-KDS) Linear Algebra III

  TBA
• (EM-KDS) Linear Algebra IV

  TBA
• (EM-KDS) Linear Algebra to Abstract Algebra

  Subgroup,Homomorphism, Isomorphism, Kernel and Image
• (EM-KDS) Set Theory I

  Set, Subset, Power set, Cartesian product, Union, Intersection, Function, Injectivity, Surjectivity, Axiom of Choice
• (EM-KDS) Set Theory II

  Binary relation, Equivalence relation, Union and Intersection of an Indexed Family, Partitions, Equivalence Class
• (EM-KDS) Topology I

  Topology and Topological Space, Open Set, Continuous Mapping, Distance Function and Metric Space, Convergence of Sequences; Continuity of Functions
• One-form

  1-form, integral, FTC
• Riemann–Roch

  riemann-roch, riemann-surfaces, algebraic-geometry, divisors, line-bundles, sheaf-cohomology, serre-duality

Cryptography

$$\operatorname{Adv}^{\mathrm{IND\text{-}CPA}}_{\mathcal{A}}(\Pi) \;:=\; \left|\Pr\!\left[\mathsf{Game}^{\mathrm{IND\text{-}CPA}}_{\Pi,\mathcal{A}}(1^\lambda)=1\right]-\tfrac{1}{2}\right|$$

In modern security definitions, a construction is considered secure if every efficient adversary's advantage in a well-specified experiment is negligible as a function of the security parameter. This viewpoint makes cryptographic claims precise, composable, and testable against explicit threat models.

• Number Theoretic Transform (NTT)
  cryptographymathematics

Programming

$$\text{Program} = \text{Algorithms} + \text{Data Structures}$$

"Programs must be written for people to read, and only incidentally for machines to execute."

Harold Abelson, Structure and Interpretation of Computer Programs

• ARMv8-A vs Cortex-A vs AArch64
  armv8-a
• Neon Programming
  neonprogrammingtechniques

E.T.C.

• Schedule
• TikZ Gallery by J.YH
  study