Insights into Mathematics | Q Series via Box Arithmetic | Math Foundations 239 | N J Wildberger @njwildberger | Uploaded 9 months ago | Updated 1 day ago
We have a look at the interesting topic of q-series from algebra / analysis / combinatorics / number theory from the point of view of our new "box arithmetic" which prominently utilizes anti-boxes along with boxes. This is a chance to get some more familiarity with this curious new arithmetic in which the role of "nothing" is different from what we are used to.

To interpret Euler's pentagonal formula we introduce an unbounded extension of the current Box arithmetic.

This new way of thinking appears to have obvious computational advantages, in that the notation is capturing some of the arithmetic more efficiently. It also finesses the need for philosophical discussions about "variables".

Video Contents:
00:00 Euler's Pentagonal Number theorem
3:10 Box Arithmetic
7:18 More arithmetic with boxes
10:51 Unbounded extensions
15:10 An identity of Euler
21:44 Notation for multiplicities


Here are the Insights into Mathematics Playlists:

youtube.com/playlist?list=PL55C7C83781CF4316
youtube.com/playlist?list=PL3C58498718451C47
youtube.com/playlist?list=PL5A714C94D40392AB
youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
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youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
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Here are the Wild Egg Maths Playlists (some available only to Members!)

youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
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youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C
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