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Subjects
Mathematics
Real Numbers

Free Online

Real Numbers Courses and Certifications

Explore the foundations of real numbers, limits, and infinite decimals through rigorous mathematical analysis. Access in-depth video tutorials on YouTube covering Cauchy sequences, decimal representations, and measurement theory, plus structured courses on Coursera and OpenLearn for systematic learning.

148 courses

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Insights into Mathematics
The Magic and Mystery of Pi - Real Numbers and Limits

Explore the history, formulas, and philosophical implications of pi, from ancient calculations to modern computations, challenging traditional views on its nature and role in mathematics.
- YouTube
- 42 minutes
- On-Demand
- Free Video
Fields Institute
Numerical Computation of Monodromy Action Over R

Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.
- YouTube
- 37 minutes
- On-Demand
- Free Video
Hausdorff Center for Mathematics
Tame Topology in NTP2 Structures

Explore the connection between NTP2 theory and topological tameness, focusing on expansions of ordered real and p-adic fields that define finite Boolean combinations.
- YouTube
- 51 minutes
- On-Demand
- Free Video
Insights into Mathematics
Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations
1 review

Explores logical issues with the modern theory of limits in mathematics, examining the formal definition and its problems through examples and historical context.
- YouTube
- 36 minutes
- On-Demand
- Free Video
Introduction to Real Numbers - Lecture 1

Discover the foundational concepts of real numbers and mathematical proof techniques in this introductory analysis lecture from MIT's rigorous mathematics curriculum.
- YouTube
- 1 hour 6 minutes
- On-Demand
- Free Video
Insights into Mathematics
Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 121

Explores flaws in axiomatics for real numbers, examines rational number structure, and introduces the least upper bound property, challenging conventional mathematical foundations.
- YouTube
- 28 minutes
- On-Demand
- Free Video
Insights into Mathematics
Difficulties with Dedekind Cuts - Real Numbers and Limits in Mathematics

Explores challenges in Dedekind's approach to real numbers, questioning the effectiveness of cuts in establishing a logical foundation for real number theory and arithmetic.
- YouTube
- 40 minutes
- On-Demand
- Free Video
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 Video
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 Video
Insights into Mathematics
The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations

Explore the Stern-Brocot tree's matrix and geometric representations, including wedges, for a deeper understanding of fractions and their relationships in mathematics.
- YouTube
- 34 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations

Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.
- YouTube
- 36 minutes
- On-Demand
- Free Video
Michael Penn
The Best Proof That the Real Numbers Are Uncountable

Discover the most elegant and compelling proof demonstrating why real numbers cannot be countable in this mathematical exploration of Cantor's diagonal argument.
- YouTube
- 14 minutes
- On-Demand
- Free Video
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 Video
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 Video
Insights into Mathematics
What Is a Sequence? - Real Numbers and Limits in Mathematics

Explore the mathematical concept of sequences, from basic definitions to complex examples. Learn about natural numbers, primes, and rational numbers in sequence form, with insights on specification and description.
- YouTube
- 27 minutes
- On-Demand
- Free Video

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