Mathematics 153
Notes from April 3, 2020, lecture session

Reminder:
There is a new course directory:
http://math.ucr.edu/~res/math153-2020 
Currently it has some reference folders (braintests, old exams, set-theory, updates2019) as well as folders for week 0 and week 1 of the course.
Announcements:
Due to startup difficulties with Zoom, there is unfortunately no recording of the April 3 class.  Course recordings will begin Monday, when we begin covering course material.   The remarks in the April 1 notes are unchanged:  "Recordings will be posted in iLearn.  Two things are important to recognize:  (1) As a general rule, students should still attend classes.  (2)  These recordings are not meant for distribution beyond those authorized to access them on iLearn without my permission."  
Grading criteria for the course will be determined by the start of Monday's class.  
In addition to the mathematical background files discussed in the lecture 
http://math.ucr.edu/~res/math153-2020/week1/history00a.pdf
http://math.ucr.edu/~res/math153-2020/week1/history00c.pdf
http://math.ucr.edu/~res/math153-2020/week1/history00g.pdf
there is a folder http://math.ucr.edu/~res/math153-2020/set-theory with background in set theory which might be helpful at times.  Basic concepts like unions and intersections are covered in the first three sections of Chapter I I I in these notes, and Chapter V summarizes important properties of the basic number systems in mathematics (the natural numbers, the integers, the rational numbers and the real numbers). 
The file http://math.ucr.edu/~res/math153-2020/week1/history00b.pdf  was not covered in this lecture.  This material provides some useful perspectives on the course and some points which deserve attention.  One should add yet another point:  Several sorts of problems seem to arise in every period of mathematics; some are specific,  and others deal with ways of managing the subject.  It can be worthwhile to think about what sorts of progress was made in each time period.   Examples will be presented as the course progresses.
Regarding elementary geometry as outlined in history00g.pdf, see the folder http://math.ucr.edu/~res/math133-2018/ for more information on the approach to elementary geometry in this course.  In particular, here are the most important filesfor our purposes:
http://math.ucr.edu/~res/math133-2018/geometrynotes00.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes01.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes02a.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes02b.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes03a.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes03b.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes03c.f13.pdf
http://math.ucr.edu/~res/math133-2018/geometrynotes03d.f18.pdf

Student question and response:
Types of documents to be posted.   Since the lectures will be recorded, it is not clear how worthwhile it might be to post PowerPoint lecture summaries, and student feedback on this is welcome.  There will be some postings to note the relative importance of documents in the directory, and again student feedback will figure in my ultimate decisions.  Whatever happens, I intend to continue posting documents like the present one for the class meetings.  Suggestions on how such documents might be improved are of course welcome.  
Final remark:
I appreciate everyone's patience as I tried to get everything up and running properly.