Selected Topics in Mathematics

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Related lectures (50)

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Total Order Relation: Properties of Real Numbers

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

Complexity of Algorithms: Proofs of Time Complexity

Covers the analysis of worst time complexity for algorithms and time complexity with real numbers and integers.

Cardinality of Sets: Countable and Uncountable

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Mathematical structures: selected topics

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Rational Numbers: Construction and Properties

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Real Numbers: Sets and Operations

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

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.

The Bolzano-Weierstrass Theorem MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Explains the Bolzano-Weierstrass Theorem, stating that every bounded sequence has a convergent subsequence.

Multiplication in Rational Numbers

Covers the extension of addition and multiplication operations in rational numbers.

Complex Numbers: Algebraic Structures and Applications Log in to Mediaspace to watch this video

Covers algebraic structures, real numbers, fields, and the applications of complex numbers in science and engineering.

Introduction to Mathematics for Engineers Log in to Mediaspace to watch this video

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Real Analysis: Basics and Sequences Log in to Mediaspace to watch this video

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Introduction to Analysis Log in to Mediaspace to watch this video

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Introduction to Analysis: Understanding Real Numbers and Proofs Log in to Mediaspace to watch this video

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Real Numbers: Properties and Formulas Log in to Mediaspace to watch this video

Explores real numbers, including supremum, infimum, maximum, and minimum properties.

Linear Algebra: Introduction and Systems of Equations Log in to Mediaspace to watch this video

Covers the basics of linear algebra and systems of equations with exercises and IT tools for support.

Real Sequences: Limits and Properties Log in to Mediaspace to watch this video

Explores real sequences, limits, convergence, divergence, and operations on limits.

Number Theory: Operations and Equivalence Log in to Mediaspace to watch this video

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

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