Mathematics 133
Notes from October 7, 2020, lecture session

The recording for this lecture is available online as 
 http://math.ucr.edu/~res/math133-2020/Oct07.mp4 .
Please note that this file is quite large, so downloading might take some time and there might be storage problems on your devices.

 Relevant directory files:
Here is a listing with comments on their significance.  These links are all clickable.
http://math.ucr.edu/~res/math133-2020/week1/geometrynotes01.f13.pdf   The first chapter of the course notes.   The lecture covered Sections I.2 and I.3  with a very brief peek at Section I.4.
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-1.png  Edited version of a whiteboard created during the lecture.  It describes the associative law of multiplication, which holds for may algebraic systems including the real and complex numbers and matrix algebras file.  However, it does not hold for the 3 – dimensional vector cross product.   
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-2.png  Edited version of a whiteboard created during the lecture.  It illustrates a standard method for remembering how to work with the 3 – dimensional vector cross product.
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-3.png  Edited version of a whiteboard created during the lecture.  This file poses a basic question motivating the material in Section I.4.
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-4.png  Edited version of a whiteboard created during the lecture.  This file suggests how one might consider the question in the preceding document for the special case of lines. 
https://math.ucr.edu/~res/math133-2020/week1/flatness.pdf   Drawings to illustrate a key step in the proof of Theorem I.3.8 (p. 28).     
https://math.ucr.edu/~res/math133-2020/week1/examples0103.pdf   Worked out examples which illustrate the method of elimination for solving systems of linear equations.  This is included for review purposes.