Topics In Applied Math

We continue building the knowledge required for basic probability theory and statistics (needed for data science & ML). The videos in this post are about set algebra and algebraic structures like groups, rings & fields. It includes an introduction to identity, inverse and idempotent elements. We'll see that Boolean conjunction and disjunction can be seen as multiplication and addition and investigate possible additive and multiplicative identities and inverses. This is followed by power sets and basic operations on elements of power sets (union, intersection, complement, difference). All concepts are then combined in a discussion of algebraic structures including groups, rings and fields. We end with Boolean rings and describe set algebra as an example Boolean ring. In the review session we complete an example proof from CH1 of W. Rudin's Principles Of Mathematical Analysis using the axioms of a field. Introduction to part II. The main subject of the sessions of Par

What follows is part I of a series of short instructional videos in mathematics. The videos cover concepts needed for analysis & probability theory. The part I video sessions are embbeded in order below: Intro: Introduction to Part I of a course in mathematics for probability, statistics, data science and machine learning. 1A: The basic concepts of set algebra. Set builder notation, common sets of numbers (natural numbers, whole numbers, rational number, real numbers), subset, superset, universal set & complement. This session is part of a series of math tutorials for statistics, data science & machine learning( ML ). 1B: Introduce tuples, the set Cartesian product, Cartesian triple product and set cardinality. 2A: Define a mathematical relation as a subset of the Cartesian product. Define the inverse relation. Example relations. Position and function input. Continuation of session 1A. 2B: Definition of a function as a special case of a relation. Compare relati