Insights into Mathematics Courses

Modular Arithmetic With Fermat and Euler - Data Structures in Mathematics Math Foundations

Explore Fermat's and Euler's theorems in modular arithmetic, learning to simplify calculations and solve problems like z mod 13 through practical examples and applications.

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

Back to Gauss and Modular Arithmetic - Data Structures in Mathematics Math Foundations

Explore modular arithmetic and its applications in number theory. Learn about congruences, divisibility, and efficient calculation of remainders without long division.

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

Astronomy and Trigonometry in India - Math History

Explore ancient Indian contributions to astronomy and trigonometry, including Brahma Gupta's work and the development of sign tables, in this insightful mathematical history lecture.

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

Divisibility of Big Numbers - Data Structures in Mathematics Math Foundations

Explore divisibility of large numbers, modular arithmetic, and long division techniques. Learn key concepts and practical applications in number theory and mathematical foundations.

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

Arithmetical Expressions as Natural Numbers - Data Structures in Mathematics Math Foundations

Explores the complexities of representing large numbers through arithmetical expressions, discussing limitations, logical issues, and the challenges of creating a coherent system for such representations.

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

A New Look at Hindu Arabic Numbers and Their Arithmetic - Data Structures in Math Foundations

Exploring base-10 arithmetic using vexels, extending from binary to decimal systems. Covers addition, multiplication, and Hindu-Arabic numerals, providing insights into foundational mathematics.

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

Arithmetic With Base 2 Vexels - Data Structures in Mathematics Math Foundations

Explore binary arithmetic using base-2 vexels, a flexible vertical notation system. Learn advantages, conversion methods, and vertical multiplication techniques for a fresh perspective on number systems.

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

The Hindu Arabic Number System Revisited - Data Structures in Mathematics Math Foundations

Explores three approaches to Hindu Arabic numerals, examining their mathematical foundations and practical applications in arithmetic and number representation.

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

Naming and Ordering Numbers for Students - Data Structures in Mathematics Math Foundations

Explores naming, ordering, and using natural numbers, focusing on their fundamental nature as expressions of marks. Discusses counting, cardinal vs ordinal usage, and the successor operation.

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

Multisets and a New Framework for Arithmetic - Data Structures Math Foundations

Explores multisets to redefine natural numbers, offering fresh insights into fundamental arithmetic operations and laws. Presents a simplified, logical approach to basic mathematics suitable for all levels.

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

The Essential Dichotomy Underlying Mathematics - Data Structures Math Foundations

Explore the fundamental dichotomy underlying mathematics, challenging traditional views on natural numbers and geometry to uncover the core essence of mathematical thinking.

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

Ancient Astronomy in Babylon and China - Math History - NJ Wildberger

Explore ancient Babylonian and Chinese astronomy, examining celestial observations, coordinate systems, and angular measurements that laid the foundation for modern astronomical understanding.

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

Hyperoperations and Even Bigger Numbers - Data Structures in Mathematics

Explore hyperoperations and the successor limit hierarchy to extend arithmetic beyond traditional bounds, opening up new realms of mathematical understanding and computation.

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

The Sporadic Nature of Big Numbers - Data Structures in Mathematics

Explores how arithmetic breaks down with large numbers, revealing most "numbers" are invisible to us. Challenges conventional number theory and questions the nature of natural numbers.

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

The Chaotic Complexity of Natural Numbers - Data Structures in Mathematics

Exploring the complex nature of arithmetic with large numbers, focusing on exponential and triangular complexity, and examining the role of powers in mathematical computations.

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