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MOOC

Analysis I (part 1): Prelude, basic concepts, real numbers

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Lectures in this MOOC (36)

The Greatest Common Divisor MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the greatest common divisor, Euclidean algorithm, Joseph Stein's algorithm, and practical examples.

Open and Closed Sets MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the concepts of open and closed sets in real numbers.

Composition of Functions MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explores the composition of functions, defining new functions by combining existing ones and showcasing the associative property of function composition.

Proposition: Demonstration by Absurd Reasoning MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explores the proposition that X² is not equal to 2 using absurd reasoning.

Restriction, Prolongement et Graphe d'une Fonction MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Infimum MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the concept of infimum in real numbers and its properties.

Mathematical Induction: Principle and Example MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Introduces the principle of mathematical induction through an example.

Bijective Functions MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers bijective functions, establishing one-to-one correspondences between sets and the importance of reducing domain and codomain for injectivity and surjectivity.

Q as Subset of R MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the concept of Q as a subset of R and their properties.

Pairs of Functions MOOC: Warm-up for EPFL MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Discusses reciprocal functions and their graphs, including x² and √x, e^x and ln(x), and tangent and arc tangent.

Counterexample to Induction Theorem MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explores a counterexample to the induction principle, demonstrating a property of natural numbers.

Basic Notions MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the basic concepts of sets, functions, and number systems.

Prelude: Linking Mathematics and Course Content MOOC: Warm-up for EPFL MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Introduces the course content by linking familiar mathematics with upcoming topics.

Discussion of Surjectivity MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Discusses the concept of surjectivity in functions and its implications.

Analyse 1: Introduction MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers MOOC: Analysis I (part 3) : Real number sequences I and II MOOC: Analysis I (part 4) : Limit of a function, continuous functions MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function MOOC: Analysis I (part 6) : Study of functions, limited developments

Untitled MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

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MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Introduces the EPFL MOOC Analyse 1, emphasizing understanding over memorization.