The number theory revival | Math History | NJ Wildberger скачать в хорошем качестве

The number theory revival | Math History | NJ Wildberger

After the work of Diophantus, there was something of a lapse in interest in pure number theory for quite some while. Around 1300 Gersonides developed the connection between the Binomial theorem and combinatorics, and then in the 17th century the topic was again taken up, notably by Fermat, and then by Euler, Lagrange, Legendre and Gauss. We discuss several notable results of Fermat, including of course his famous last theorem, also his work on sums of squares, Pell's equation, primes, and rational points on curves. The rational parametrization of the Folium of Descartes is shown, using the technique of Fermat. We also state Fermat's little theorem using the modular arithmetic language introduced by Gauss. Video Contents: 00:00 The number theory revival 01:05 Fermat 03:40 Diophantus 200-300 AD 05:43 Combinatorics - Binomial theorem 13:40 Some results of Fermat 38:23 Algebraic curves 41:32 Folium of Descartes 47:22 Newton forms for cubics 51:40 Sum of four squares 53:47 Fermat's little theorem ************************ 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.