Insights into Mathematics channel
Norman Wildberger has more than 500 videos, 35,000 subscribers and 5 million views on his YouTube channel Insights into Mathematics, with user: njwildberger. Playlists include Differential Geometry, Math Foundations A, Math Foundations B, Math Foundations C, Wild LInear Algebra, Wild Trig, Famous Math Problems, Universal Hyperbolic Geometry A, Universal Hyperbolic Geometry B, Algebraic Topology, History of Mathematics
Differential Geometry (35 videos) A novel beginner's course going back to Euler, Monge, Dupin, Gauss and others with a visual algebraic approach minimizing the role of all but basic calculus with GeoGebra. The geometrical side includes projective geometry. Topics include classical curves and surfaces, parametrized and algebraic, projective geometry, and curvature using a parabolic approach. There are a variety of interesting classical applications and results. Here is a list of videos in this course. 

Math Foundations A (79 videos) MF179
Foundational issues have been finessed by modern mathematics, and this series aims to turn things around. And it will have interesting things to say also about mathematics education. 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. A key Playlist for all serious students of mathematics! Here is a list of videos in this course. 

MathFoundations B (70 videos) MF80149
Foundational issues have been finessed by modern mathematics, and this series aims to turn things around. And it will have interesting things to say also about mathematics education. 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. A key Playlist for all serious students of mathematics! Here is a list of videos in this course. 

MathFoundations C (70 videos) MF 150 present Foundational issues have been finessed by modern mathematics, and this series aims to turn things around. And it will have interesting things to say also about mathematics education. 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. A key Playlist for all serious students of mathematics! Here is a list of videos in this course. 

Wild Linear Algebra
This course presents a geometrical view to Linear Algebra, with a focus on applications. We look at vectors, matrices, determinants, change of bases, row reduction, lines and planes, polynomial spaces, bases and coordinate vectors, and then much more! Here is a list of videos for this course. 

Wild Trig (Course on Rational Trigonometry) (73 videos)
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. With rational trigonometry, we can do make calculations algebraically that formerly required transcendental functions and irrationalities, that run now faster and more smoothly. And all of metrical geometry gets recast in a much more elegant and general framework. Here is a WildTriglist of videos for this course. 

Famous Math Problems (25 videos)
We look at famous math problems, both unsolved and solved. These will span both pure and applied mathematics; some will be ancient problems, others relatively new, but hopefully they will all be interesting. Here is a list of videos for this series. 

Universal Hyperbolic Geometry A (34 videos) UHG132 This series introduce 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. Not only do we get many more beautiful theorems, but the results are much more general than classical hyperbolic geometry: extending beyond the unit circle (or the light cone in relativistic physics), working over finite fields, and in fact generalizing to other quadratic forms as well. Here is a list of videos for this course. 

Algebraic Topology (40 videos)
A first course in Algebraic Topology, with emphasis on visualization, geometric intuition and simplified computations. It introduces us to the sphere, torus, projective plane, knots, Klein bottle, the circle, polytopes and curves in a way that only retains the essence of the shapes of spaces. The course has some novel features, including Conway's ZIP proof of the classification of surfaces, a rational form of turn angles and curvature, an emphasis on the importance of the rational line as the model of the continuum, and a healthy desire to keep things simple and physical. We try to use pictures and models to guide our understanding. Here is a list of videos for this course. 

History of Mathematics (30+ videos)
Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, Stevin's decimal system, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology, the origins of group theory, hyperbolic geometry and much more. This series is meant for a broad audience, and it gives undergraduates a concrete historical framework within which to understand modern mathematics. Sometimes it is a lot easier understanding ideas if we can trace how they developed, and what the pioneers who worked out these theories were motivated by. Here is a list of videos for this course. 

MathTerminology for Incoming Uni students (8 videos)
This is a short course designed for students entering college or university who would like to review some essential high school mathematics, particularly the terminology used to describe key concepts. This is especially useful for students for whom English is not their first language. This course is part of an openlearning MOOC that Norman has put together available for free, with exercises. There are even Chinese subtitles, so check it out! Here is a list of videos for this course. 

Elementary Mathematics K6 (19 videos)
Feel like learning mathematics from the ground up? Here is your chance: K6 mathematics explained intuitively but accurately in a novel way by a professional pure mathematician. We employ a step by step intuitive explanation of the main conceptual hurdles that young children meet when they start to learn mathematics. For teachers, parents, and very bright children. Here is a list of videos for this course. 

Math Seminars
This series consists of mathematical seminars presented by N J Wildberger and perhaps also seminars by colleagues. It will be aimed at undergraduate math majors, PhD students, mathematicians and physicists. Most but not all of these will have been presented to the School of Mathematics and Statistics, UNSW Sydney. Prominent among them is the Resolution of the Goldbach Conjecture, which modern mathematicians will slowly have to try to get their heads around! Here is a list of videos in this series. 
