Insights into Mathematics Courses

Alternating and Symmetric Polynumbers - A Missing Chapter of Algebra - Math Foundations 234

Explore symmetric, alternating, and central polynumbers in algebra. Discover their relationships, product formulas, and significance in mathematics and physics.

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

The Curious World of Integral Polynumbers - Math Foundations 233

Explore integral polynumbers through particle physics concepts, expanding arithmetic to include integers as coefficients and exponents, and viewing polynomials as algebraic objects rather than functions.

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

Chords and the Mathematical Fretboard - Exploring Guitar Music Theory

Explore the mathematical structure of guitar chords and fretboards, focusing on triads and tetrads. Learn to navigate the instrument using the 12-tone chromatic scale for a deeper understanding of music theory.

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

New Directions for Mathematics Education and Research - Channel Trailer 2023

Exploring innovative approaches to mathematics education and research, challenging traditional concepts, and advocating for a stronger logical structure in mathematical understanding.

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

Arithmetic with Negative Multisets and Integral Polynumbers - Math Foundations 232

Explores advanced arithmetic using negative msets and anti-objects, introducing integral polynumbers and Laurent polynomials in a pure algebraic context, revolutionizing traditional algebra understanding.

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

Negative Numbers from Antimultisets - Math Foundations 231

Explore negative numbers through antimultisets, drawing parallels with particle physics concepts. Discover a new arithmetic perspective based on elementary principles.

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

Multiset Arithmetic via Trees - Math Foundations 230

Explore multiset arithmetic using rooted trees, offering a visual representation for counting functions and new arithmetic operations. Gain insights into this alternative approach with concrete examples and useful notations.

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

Equality in Computer Science - Sociological and Mathematical Perspectives

Exploring fundamental issues in programming and mathematics related to equality, assignment, and conversion, with insights on how computer science can provide solid foundations for pure mathematics.

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

Clock Mathematics and the 12-Tone Chromatic Scale - Connecting Music Theory and Mod 12 Arithmetic

Explores the connection between mathematics and music through the 12-tone chromatic scale, clock geometry, and mod 12 arithmetic, offering a fresh perspective on music theory and mathematical notation.

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

Formal Power Series and the Miraculous Relation Between E (exp) and L (log)

Explore formal power series as a powerful alternative to traditional analysis, focusing on the miraculous inverse relationship between exp and log polyseries variants E and L.

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

Go Lesson 13: Honinbo Sansa vs Rigen - Classic Game Analysis from 1600s Japan

Explore a classic Go game from 1600s Japan between Honinbo Sansa and Rigen. Learn strategic moves, fierce battles, and beautiful play as the commentary focuses on beginner-friendly insights.

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

The Impossibility of a Pythagorean Scale and Square Root of 2 in Music Theory

Explores the mathematical challenges in creating a perfect musical scale, linking the cycle of fifths, chromatic scale, and the irrational nature of sqrt(2) to reveal fundamental connections between music theory and arithmetic.

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

Barycentric Coordinates and Subtractive Arithmetic of Vectors - Algebraic Calculus and dCB Curves 9

Explore barycentric coordinates and vector arithmetic in affine geometry, enhancing understanding of de Casteljau Bezier polygons and curves. Gain insights into advanced mathematical concepts and their applications.

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

Archimedes' Area Formula for Archimedean de Casteljau Bezier Cubics - Lecture 8

Discover a new cubic version of Archimedes' Parabolic Area Formula for special de Casteljau Bezier curves. Explore the Archimedean condition and its fascinating geometric connections.

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

Divide Like a Babylonian - Centimal Arithmetic and Old Babylonian Division Techniques

Explore the Old Babylonian approach to division using base 100 arithmetic. Learn about centimal reciprocal tables, regular numbers, and combined multiplication/division tables for a fresh perspective on mathematical operations.

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