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Lecture
Sets and Functions
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Related lectures (28)
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Functions and Integers
Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.
Relations and Sequences
Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.
Equivalence Relations: Relations, Sequences and Summations
Explores equivalence relations, functions, subsets, and De Morgan's laws.
Mathematical Analysis: Functions and Composition
Covers the analysis of functions, composition, and mathematical induction.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Introduction to Category Theory: Examples
Introduces the theory of categories through examples and discusses the product of categories.
Sets, Functions and Relations: Summary of Week 4
Covers sets, functions, and relations, including functions' properties and binary relations.
Relational Algebra and SQL: Foundations of Database Management
Introduces the relational model and relational algebra, focusing on SQL and its operations for effective database management.
Cartesian Product and Equivalence Classes
Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.
Differential Equations: Mathematical Complements
Covers the definition of differential equations and their relation to functions and derivatives.
