Lectures related to Separation axiom

Quantum Bits: Illustrations and Postulates

Explores quantum bits, including illustrations, postulates, and examples of quantum systems and Hilbert space.

Segmentation of Lines: Definitions and Notations

Covers the definition of line segments, notations, axioms, and plane separation.

Covers the concept of area, axioms, and the area of rectangles.

Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Plan Separation

Explores the axiom of separating the plane into two half-planes and the concept of interior points.

Vector Spaces: Definition, R2

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.

Introduction to Categories

Introduces the concept of categories essential for understanding group theory.

Axioms of Connection

Introduces the axioms of connection in Euclidean geometry, emphasizing unique lines and non-collinear points.

Quantum Mechanics: Measurement

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Recurrence: Induction

Covers the principle of induction for natural numbers and the importance of caution in its application.

Formal Proofs: Checking Invariants and Bounded Model Checking

Explores formal proofs, satisfiability problems, and inductive invariants using SAT queries in sequential circuits.

Quantum Bits: Axioms and Examples

Explores quantum bits, axioms, examples, Shor algorithm, measurements, Hilbert space, and dynamics.

Vector Spaces: Definitions and Properties

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.

Isometries: Transformations Preserving Distances in the Plane

Introduces isometries as transformations preserving distances in the plane, focusing on symmetry and geometric relationships.

Construction of Real Numbers

Discusses the construction and uniqueness of real numbers from rational numbers.

Propositions and Proofs

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

Ordinary Differential Equations: Definitions and Methods

Explores ordinary differential equations, proof methods, and historical examples from Euclid, emphasizing logical reasoning and step-by-step derivations.

Separation Conditions: Graph and Saturations

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

Real Numbers: Axioms and Bounds

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Sigma Fields: Definition and Examples

Covers the concept of sigma fields and their role in probability theory.