Insights into Mathematics Courses

Inconvenient Truths About the Square Root of 2 - Real Numbers and Limits

Explores the concept of sqrt(2), its historical significance, and modern approaches, challenging traditional views on irrational numbers and highlighting logical issues in mathematical analysis.

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

Calculus on the Unit Circle - Arithmetic and Geometry Math Foundations 78

Explore algebraic calculus on unit circles, covering subderivatives, Taylor expansions, tangents, and 3D visualizations. Gain insights into foundational mathematics with a unique approach to this fundamental topic.

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

Lines and Parabolas - Quadratic Polynomials and Geometric Relations

Explore advanced parabola concepts: algebraic calculus, subderivatives, tangent lines, Taylor expansions, and geometric relations. Learn to analyze and graph parabolas using completing the square method.

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

Graphing Polynomials - Arithmetic and Geometry Math Foundations

Learn to graph polynomials using integer and rational points, explore quartic polynomials, and understand the foundations of mathematical graphing. Gain insights into Cartesian coordinates and tangent lines.

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

Tangent Lines and Conics of Polynomials - Math Foundations 71

Explore tangent lines and conics of polynomials using polynumbers. Learn to define tangents, compute approximations, and understand Taylor expansions in this advanced mathematical exploration.

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

Calculus with Integral Polynumbers - Arithmetic and Geometry Math Foundations 70

Explore calculus with integral polynumbers, covering Pascal's Array, Taylor polynumbers, derivatives, and subderivatives. Learn alternative approaches to traditional calculus concepts and their applications.

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

Visualizing Decimal Numbers and Their Arithmetic - MathFoundations 67

Explore decimal numbers as special rational numbers, their visualization on a number line, and arithmetic operations. Learn precise definitions and unique properties of decimals in mathematics.

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

Laws of Arithmetic Using Geometry - Elementary Mathematics Explained - Lecture 5

Explore geometric interpretations of arithmetic laws using translations and reflections in the grid plane, enhancing understanding of commutativity in addition and multiplication.

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

Fundamental Group of Surfaces - Multiplication and Properties

Explores fundamental group of surfaces, proving loop multiplication forms a group. Covers torus and projective plane, with examples and a problem on describing fundamental groups.

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

Knots and Surfaces - Seifert Surfaces in Algebraic Topology - Lecture 2

Explore Seifert surfaces, their construction for knots like the trefoil, and learn about Euler numbers for surfaces with boundaries in this advanced algebraic topology lecture.

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

Sphere Geometry and Complex Analysis - Algebraic Topology Lecture 4

Explore advanced concepts in sphere geometry, including inversive geometry, Riemann sphere, complex analysis, and projective lines, enhancing understanding of algebraic topology.

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

The Geometry of Surfaces - Algebraic Topology Lecture 20

Explore the connection between 2D surfaces and classical geometries, focusing on isometries and introducing hyperbolic geometry through circle inversions in the Beltrami Poincare disk model.

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

Classification of Combinatorial Surfaces - Lecture 2

Explores the classification of two-dimensional surfaces using polygon reduction techniques. Covers cutting, pasting, and creating crosscaps and handles to achieve standard forms in algebraic topology.

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

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

Introduces a new rational definition of polytope curvature, using turn-angle to connect curvature with Euler number. Explores opposite cones and applies Harriot's theorem on spherical triangles.

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

Duality for Polygons and the Fundamental Theorem of Algebra - Algebraic Topology Lecture 12

Explore duality in polygons and a rational proof of the Fundamental Theorem of Algebra using winding numbers. Gain insights into algebraic topology concepts and their applications.

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