Lectures related to Partial Ordering: Relations, Sequences, Summation

Functional Analysis I: November 18, 2021

Covers partially ordered sets, maximal elements, upper bounds, and the Zorn lemma in functional analysis.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

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Total Order Relation: Properties of Real Numbers

Covers the concept of total order relation and properties of real numbers.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Relations and Sequences: Well-ordered Sets and Geometric Series

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.

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Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Introduction to Real Numbers

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.