Mathematics 153
Notes from June 3, 2020, lecture session

What was covered:
The remaining material from Unit 14 and issues involving the midterm and final exams.  The latter has been posted, and a sheet with a correction, other changes and hints has been posted: http://math.ucr.edu/~res/math153-2020/exam2s20add.pdf  
Relevant directory files for Unit 14:
Here is a listing of files from Unit 14 which are related to the June 3 lecture, with comments on their significance.  These links are all clickable. 
http://math.ucr.edu/~res/math153-2020/weekTEN/unit14/history14.pdf  This is the main file for the unit and should ultimately be read from beginning to end.  After doing so one should read the cited sections of Burton.
http://math.ucr.edu/~res/math153-2020/weekTEN/unit14/limit-definition.png   A very brief desciption of the definition for a limit.  
https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit   A fairly thorough but transparent summary of the development and use of the delta-epsilon definition for a limit.
http://math.ucr.edu/~res/math153-2020/weekTEN/unit14/maximality-of-reals.pdf   Frequently in this course we have said that the real numbers form a maximal system containing the rationals and satisfying certain conditions.  This characterization is not easy to find in textbooks, so there is an explanation for the sake of completeness.  This involves material beyond the undergraduate level, so the file is for reference purposes only with no need to understand its contents for the purposes of this course.
Relevant directory files for examinations:
http://math.ucr.edu/~res/math153-2020/exam1s20key.pdf   Solutions to the problems on the exam.
http://math.ucr.edu/~res/math153-2020/exam1s20prob4.pdf  Another solution to this problem; this one corresponds more faithfully to the drawing in the exam.
http://math.ucr.edu/~res/math153-2020/exam1s20comments.pdf   Remarks about common mistakes and omissions in student responses.
http://math.ucr.edu/~res/math153-2020/exam2s20.pdf   The take-home final due next week.
http://math.ucr.edu/~res/math153-2020/exam2s20add.pdf   Remarks, including a typo correction and several hints, for the sixth problem.