Insights into Mathematics Courses

Three Variable Boole - Mobius Transform - N J Wildberger

Exploring the Boole-Mobius transform for three variables, extending from Boolean functions to Boole polynumbers. Introduces binary indexing and reveals a remarkable 8x8 matrix T_3.

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

The Boole Mobius Transform - MathFoundations - N J Wildberger

Explore the Boole-Mobius transform, connecting Boolean functions and polynomials through linear algebra. Learn about binary representations and their relation to set theory in this mathematical deep dive.

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

Addition and Cascading With Open Numbers - Elem Mathematics Explained

Explore a novel approach to elementary arithmetic using open numbers, focusing on addition and cascading. Learn a logical, systematic method that simplifies complex calculations and connects to real-world applications.

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

Boole Reduction - A Challenge for Programmers - MathFoundations - N J Wildberger

Exploring challenges in implementing Boole reduction for circuit analysis, including programming strategies and SAT solver development in the Algebra of Boole context.

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

Trying to Sidestep the SAT Problem - N J Wildberger

Explores the SAT problem in Boolean algebra and logic circuits, introducing the Algebra of Boole approach as an alternative for analyzing smaller circuits and potentially addressing larger-scale issues in integrated circuit design.

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

How the Algebra of Boole Simplifies Circuit Analysis - MathFoundations - N J Wildberger

Exploring Boole's algebra for circuit analysis, covering logic gates, negations, and practical examples. Provides a unique approach to understanding and simplifying complex circuits.

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

Open Numbers - Elementary Mathematics Explained - N J Wildberger

Explore open numbers, a money-like alternative to Hindu-Arabic numerals. Learn conversion techniques, practice with Monopoly money, and discover simplified addition methods in elementary mathematics.

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

How Chromogeometry Transcends Klein's Erlangen Program for Planar Geometries - N J Wildberger

Discover chromogeometry's three-fold symmetry in planar geometry, unifying Euclidean and relativistic geometries. Explore rational trigonometry, colored Pythagoras theorems, Euler lines, and novel perspectives on conic sections.

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

Introducing Arithmetic Sequences - Elementary Mathematics Explained

Explore arithmetic sequences, their patterns, and applications in elementary mathematics. Practice adding sequences systematically to improve number skills and solve interesting puzzles.

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

Strengthening Addition Skills - Elementary Mathematics Explained

Explore fun puzzles and techniques to strengthen addition skills, focusing on complementary numbers, the addition table, and wrapping around 10. Develop a deeper understanding of arithmetic fundamentals.

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

Puzzles Using Arithmetic - Elementary Mathematics Explained

Engaging arithmetic puzzles for young learners, focusing on powers of two, triangular numbers, and geometric rearrangements to improve problem-solving skills and mathematical thinking.

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

Arithmetic with Money - Elementary Mathematics Explained

Explore arithmetic using money to connect math with the real world. Learn a novel number representation system and understand the "Problem of Carrying" in traditional numerals.

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

Cooking and Baking With Basic Arithmetic - Elementary Mathematics Explained

Explore how basic arithmetic and measurement skills can be developed through cooking and baking activities, while emphasizing kitchen safety and practical applications for young learners.

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

Volumes and Capacities - Elementary Mathematics Explained

Explore volumes and capacities through hands-on activities, learning both metric and imperial systems while strengthening arithmetic skills and understanding numerical concepts.

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

Weighing with Grams and Ounces - Elementary Mathematics K-6 Explained

Explore weight measurement using grams and ounces through hands-on activities with household items. Learn about kitchen scales, pan balances, and standardized weights while practicing counting and ordering.

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