Data science & ML Video Tutorials Part I - Sets, Tuples, Relations & Functions, Basic Boolean algebra

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 relations that are functions to relations that are not. Binary functions (ternary relations). Boolean functions. Review relations & examples

3A: Mathematical operations & operands. Operation abstraction. Operations are functions and these are subsets of the Cartesian product introduced in session 2. Order of operations (negation, exponent/root, etc.)

3B: Commutative, associative & distributive properties of mathematical operations. Discuss right and left distributive. Properties of the set Cartesian product.

4: Propositions, axioms & identities. The 3 basic Boolean operations. Boolean negation and set complement. Boolean AND/OR AKA conjunction/disjunction. Order of Boolean operations.

Q&A (practice)

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