Lectures related to Tarski's axioms

Quantum Bits: Illustrations and Postulates

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

Quantum Mechanics: Measurement

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

Segmentation of Lines: Definitions and Notations

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

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Illustration of Quantum Bits

Covers the postulates of Quantum Mechanics and examples with quantum bits, including observables and unitary matrices.

Quantum Entanglement

Delves into quantum entanglement, exploring entangled particles' state, evolution, and measurement.

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.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Formal Proofs: Checking Invariants and Bounded Model Checking

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

Recurrence: Induction

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

Isometries: Transformations Preserving Distances in the Plane

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

Vector Spaces: Definitions and Properties

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

Area: Axioms and Rectangles

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

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.

Plan Separation

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

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.