Cauchy Sequences Courses and Certifications

Insights into Mathematics

Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations

Explores challenges in defining real numbers using Cauchy sequences, discussing convergence concepts and visualizing sequences in the plane. Highlights issues in establishing arithmetic for real numbers.

• YouTube
• 29 minutes
• On-Demand
• Free Online Course

statisticsmatt

Sequences and Series of Real Numbers and Functions

Comprehensive exploration of real number sequences and series, covering convergence, limits, and advanced mathematical concepts for a deep understanding of analysis fundamentals.

• YouTube
• 4 hours 30 minutes
• On-Demand
• Free Online Course

The Bright Side of Mathematics

Real Analysis

Comprehensive exploration of real analysis, covering sequences, limits, series, functions, continuity, differentiation, integration, and fundamental theorems of calculus.

• YouTube
• 10 hours
• On-Demand
• Free Online Course

The Bright Side of Mathematics

Functional Analysis

Comprehensive exploration of functional analysis, covering metric spaces, Banach spaces, Hilbert spaces, operators, and spectral theory, with detailed examples and key theorems.

• YouTube
• 4 hours 30 minutes
• On-Demand
• Free Online Course

Sequences

Explore fundamental concepts of sequences, including limits, convergence, and advanced topics like limsup and the Bolzano Weierstraß Theorem. Gain a deep understanding of mathematical analysis.

• YouTube
• 10 hours
• On-Demand
• Free Online Course

Insights into Mathematics

Real Numbers as Cauchy Sequences - Limitations and Challenges - Math Foundations 114

Explores logical weaknesses in using Cauchy sequences to define real numbers, challenging traditional approaches and highlighting ambiguities in fundamental mathematical concepts.

• YouTube
• 52 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 113

Explore Archimedean real numbers and Cauchy sequences, examining their definitions, properties, and applications in mathematical analysis and approximation theory.

• YouTube
• 30 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 112

Explores the concept of real numbers, challenging their existence and examining how quantities like length, area, and function values are inherently approximate rather than exact 'real' values.

• YouTube
• 36 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 111

Explores Cauchy sequences of rational numbers as a foundation for real numbers, discussing limits, equivalence classes, and the logical challenges in this approach to constructing the real number system.

• YouTube
• 21 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Dedekind Cuts and Computational Difficulties with Real Numbers - Famous Math Problems 19

Explores the challenges and misconceptions surrounding 'real numbers', examining various approaches like infinite decimals, Dedekind cuts, and Cauchy sequences, while emphasizing the importance of concrete computations in mathematics.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Online Course

Analyse I (partie 3) : Suites de nombres réels I et II

Étude approfondie des suites de nombres réels, leurs limites et propriétés. Exploration des concepts fondamentaux en analyse mathématique, incluant la convergence, les séries numériques et les critères associés.

• edX
• 4 weeks, 4-5 hours a week
• On-Demand
• Free Online Course (Audit)