Mathematics: The Next Generation - Professor Peter Cameron скачать в хорошем качестве

Mathematics: The Next Generation - Professor Peter Cameron

Mathematics is important to us all. So it is important to enable young mathematicians, clear-thinking and passionate about their subject, to contribute at the highest level. Peter Cameron will talk about his experience designing and presenting a course for first-semester university students aiming to produce mathematicians. This is the 2013 joint London Mathematical Society / Gresham College lecture recorded live on 14 May 2013. The transcript and downloadable versions of this event by Professor Peter Cameron are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and... Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/ Chapters 0:00 Introduction 0:14 A mathematics lecture 4:58 Oxford College, Emory University 8:03 The problem 11:47 The specification (extract) 12:41 What was in the course? 13:54 Supplementary material 17:00 Details 19:31 Tutorials 23:24 Re-inventing the wheel? 25:44 Entering a mathematics department 28:04 Sets and functions 29:39 Natural numbers 31:17 Integers and rational numbers 35:33 Real numbers 36:28 Reasoning and logic 37:51 Implication 39:19 A problem revisited 41:24 Proof by contradiction 42:13 Euclid's proof 44:41 A proof is a convincing argument 47:14 Why is it true? 50:03 Tutors' comments