Object-oriented versus expression-oriented mathematics | Arithmetic and Geometry Math Foundations 77

Описание: Twentieth century mathematics has been object oriented. Twenty-first century mathematics, if it gets its act together, will be much more expression oriented. Here we describe the distinction by studying the key example of the unit circle.

This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.

Video Content:
00:00 Intro to distinction between object and expression oriented maths
6:23 The unit circle
11:54 Expression-oriented approach
14:18 A Projective bipolynumber
16:20 Interpretation A
23:49 Interpretation B
29:58 Simple case of a Projective polynumber
33:45 The second most circle
37:41 Interpretation C
42:45 Polar / pole correspondence

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

***********************
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Patreon,   / njwildberger   . Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

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