Real Analysis Courses and Certifications

Real Analysis Midterm Review - 18.100B

Master key concepts and problem-solving techniques for MIT's real analysis midterm through comprehensive review of sequences, limits, continuity, and differentiation.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Wrath of Math

Uniform Continuity Explained - Real Analysis

Dive into uniform continuity in real analysis, exploring its definition, examples, proofs, and related theorems. Gain insights into its distinction from standard continuity and its application to compact sets.

• YouTube
• 13 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Big, Bigger, and Biggest Five of Reverse Mathematics Part I - Real Analysis

Explore reverse mathematics of real analysis, uncovering equivalences between second-order Big Five and third-order theorems for discontinuous functions and new classification systems.

• YouTube
• 1 hour 6 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

Understanding Limits in Real Numbers - Math Foundations

Simplified definition of limits for rational polynumber sequences, challenging traditional epsilon-delta approach. Introduces scale and start numbers for bounding differences, offering a more intuitive understanding of limits.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Wrath of Math

So, There Are Basically No Fractions - The Measure of Rational Numbers is Zero

Discover why almost all real numbers are irrational by exploring measure theory and proving that rational numbers have zero measure on the number line.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Michael Penn

How to Take a Walk and Miss Every Rational Number

Explore the mathematical concept of creating a path that avoids all rational numbers, using clever techniques from real analysis and number theory.

• YouTube
• 14 minutes
• On-Demand
• Free Video

IIT Bombay;  NPTEL

Basic Real Analysis

Comprehensive exploration of real analysis fundamentals, covering sequences, series, continuity, derivatives, integrals, and multivariable calculus, with applications and theoretical foundations.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Dibrugarh University;  CEC

Real Analysis

Explore analytical aspects of real numbers, sequences, series, and functions. Gain essential knowledge for pure and applied mathematics, focusing on convergence and fundamental theorems.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

NPTEL;  IIT Palakkad

Real Analysis I

Explore foundational concepts of real analysis, from set theory to calculus theorems. Develop rigorous mathematical thinking and gain deeper insights into advanced mathematical topics.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Commercial Real Estate Analysis and Investment

Master financial analysis techniques to identify profitable commercial real estate investments and manage property portfolios using economic principles and data-driven strategies.

• GetSmarter
• 6 weeks, 8 hours a week
• 15th Jul, 2026
• Paid Course

Sustainable Real Estate: Analysis and Investment

Explore green building practices, ESG principles, and investment strategies to make informed sustainable real estate decisions while addressing climate challenges.

• GetSmarter
• 6 weeks, 5 hours a week
• 6th May, 2026
• Paid Course

The Banach Contraction Mapping Theorem - Oxford Mathematics 1st Year Lecture

1 review

Explore the Banach contraction mapping theorem in this Oxford Mathematics lecture, focusing on guaranteeing convergence of fixed point iterations in one dimension.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Insights into Mathematics

Inequalities and Limits in Real Numbers - Math Foundations 107

Simplified epsilon-delta limit definition for rational polynumbers, with visual interpretation and practical examples. Comprehensive review of inequalities for natural numbers, integers, and rational numbers.

• YouTube
• 35 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Stone-Weierstrass Theorem

Explore the Stone-Weierstrass theorem, a fundamental result in functional analysis and approximation theory.

• YouTube
• 31 minutes
• On-Demand
• Free Video