Real Numbers Courses and Certifications

Wrath of Math

Density of Rational Numbers in Real Numbers - Rudin's Proof Explained

Explore Walter Rudin's proof demonstrating that rational numbers are densely distributed within real numbers, using the Archimedean property from Baby Rudin's analysis text.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Introduction to Real Numbers - Lecture 2

Explore the completeness property of real numbers and discover why rational numbers are insufficient for mathematical analysis through the least upper bound principle.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

The Bourgain Projection Theorem Part 1 - Over the Real Numbers - Lecture 14

Explore Bourgain's projection theorem, a fundamental result in projection theory, focusing on its formulation and applications over the real numbers in advanced mathematical analysis.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Rational Numbers and Terminating Decimals

Learn how rational numbers relate to terminating decimals, using long division and converting decimal forms back to simplest fractions.

• CodeSignal
• 1 hour
• Self-Paced
• Free Certificate

Mastery of Repeating Decimals

Learn bar notation for repeating decimals and use algebraic methods to convert pure and mixed repeating blocks into exact fractions.

• CodeSignal
• 1 hour
• Self-Paced
• Free Certificate

Algebra: Elementary to Advanced - Equations & Inequalities

655 ratings at Coursera

Build an algebraic foundation: work with real numbers and their properties, solve linear equations and inequalities, and handle polynomials, rational expressions, radicals, exponents and quadratics.

• Coursera
• 5 weeks, 2 hours a week
• Self-Paced
• Paid Course

Imaginary Numbers Are Real

An accessible journey from imaginary numbers and the complex plane to complex multiplication, functions, and Riemann surfaces.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Revisión de Aritmética

19 ratings

Repasa los fundamentos de aritmética necesarios para tener éxito en el estudio del álgebra.

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

Common Core Math Grade 8 - The Number System: Standards

Learn how rational and irrational numbers fit within the eighth-grade Common Core number system standards.

• Study.com
• 40 minutes
• Self-Paced
• Paid Course

Michael Penn

Beyond Real Numbers - Solving X + 1 = 0 in Different Number Systems

Explores how x² + 1 = 0 behaves across different number systems, including why its solutions require going beyond the reals.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Michael Penn

Real Analysis - The Countability of the Rational Numbers

A proof that the rational numbers are countable by representing them as a countable union of disjoint finite sets.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations

Explore how 2×2 matrices and planar wedges reveal new ways to generate and visualize the Stern–Brocot tree of rational numbers.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Fractions and the Stern-Brocot Tree - Real Numbers and Limits Math Foundations

Explore the Stern-Brocot tree as a binary representation of fractions, generated by the mediant operation and connected to Ford circles and Farey sequences.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Math with Mr. J

Basic College Math - Comprehensive Review of Arithmetic, Fractions, Decimals, Integers, and Geometry

1 rating

Master fundamental arithmetic operations, fractions, decimals, integers, geometry basics, and coordinate plane concepts through step-by-step explanations and practical examples.

• YouTube
• 7 hours 19 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Arithmetic and Geometry Math Foundations

Explore fundamental mathematical concepts from arithmetic and geometry to abstract algebra, challenging conventional approaches with rational number systems and innovative geometric frameworks.

• YouTube
• 4 days 1 hour 49 minutes
• Self-Paced
• Free Video