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njwildberger

Insights into mathematics

2,866 subscribers
683,892 video views

MathHistory7a: Analytic geometry and the continuum 2,213

by njwildberger 8 months ago

Featured Playlists

WildTrig An introduction to Rational Trigonometry and Universal Geometry: simpler and more powerful for calculations, easier to learn, more general, and a richer theory of Euclidean geometry leading to many new discoveries. Also the basis for Universal Hyperbolic Geometry.      Play all 72 videos Play all(72)
WildLinAlg (full lectures) The WildLinAlg course on Linear Algebra by N J Wildberger, here presented in full 50 minute lectures      Play all 23 videos Play all(23)
Universal Hyperbolic Geometry A new, completely algebraic approach to hyperbolic geometry using the ideas of Rational Trigonometry. This makes the subject much simpler, more logical, more general and more beautiful.      Play all 33 videos Play all(33)
MathHistory: A course in the History of Mathematics Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, and hyperbolic geometry. Meant for a broad audience, not necessarily mathematics majors.      Play all 18 videos Play all(18)
Algebraic Topology (full lectures) A first course in Algebraic Topology, with emphasis on visualization, geometric intuition and simplified computations. Given by Assoc Prof N J Wildberger at UNSW. The really important aspect of a course in Algebraic Topology is that it introduces us to a wide range of novel objects: the sphere, torus, projective plane, knots, Klein bottle, the circle, polytopes, curves in a way that disregards many of the unessential features, and only retains the essence of the shapes of spaces. What does this exactly mean? That is a key question... The course has some novel features, including Conway's ZIP proof of the classification of surfaces, a simplified form of turning angles and curvature, and an emphasis on the importance of the rational line as the model of the continuum. The course will be continued past Lecture 25 in fall 2012.      Play all 26 videos Play all(26)
Elementary Mathematics (K-6) Explained Feel like learning mathematics from the ground up? Here is your chance: K-6 mathematics explained intuitively but accurately in a novel way by a professional pure mathematician.      Play all 6 videos Play all(6)
MathFoundations Does mathematics make logical sense? The answer is no. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. Aimed for a general audience, interested in mathematics, or willing to learn.      Play all 79 videos Play all(79)
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