Mathematics 153
Notes from May 6, 2020, lecture session

What was covered:
The material in the main file for Unit 6X,  through the discussions of Chinese mathematics at the beginning and the material on Central American and Japanese mathematics at the end.  
Relevant directory files for Unit 6X:
Here is a listing of files related to the May 6 lecture with comments on their significance.  These links are all clickable.  
http://math.ucr.edu/~res/math153-2020/week5/unit05/history06X.pdf  This is the main file for the subunit 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/week6/unit06/History%20of%20Mathematics_%20China.pdf  This reprinted file contains a fairly detailed outline of the history of Chinese mathematics.   Beginnning with the 15th century, there were steadily increasing influences from outside sources, and the outline ends just before the end of the final imperial dynasty in 1911.
http://math.ucr.edu/~res/math153-2020/week6/unit06/oldmagicsquares.pdf   This is an illustration of the 3x3 magic square which generated considerable interest from Chinese mathematicians.
http://math.ucr.edu/~res/math153-2020/week6/unit06/oldmagicsquares2.pdf   A proof that 3x3 magic squares are essentially unique.  All such squares are given by geometric rotations or reflections of a single example.  A passive understanding of the argument is desirable but will not be required.
http://math.ucr.edu/~res/math153-2020/week6/unit06/moremagicsquares.pdf   This document has a few remarks on larger magic squares and references for further information.
http://math.ucr.edu/~res/math153-2020/week6/unit06/history06c.pdf   This file describes the algebra underlying the solutions to the Chinese Remainder Theorem and gives solutions for several explicit examples.
http://math.ucr.edu/~res/math153-2020/week6/unit06/chinese-remainder.pdf  Yet another solved example.
http://math.ucr.edu/~res/math153-2020/week6/unit06/longdivision.pdf  This file works out a fact about consecutive odd integers which is often useful when solving examples for the Chinese Remainder Theorem.  
http://math.ucr.edu/~res/math153-2020/week6/unit06/homework06x.pdf   AND
http://math.ucr.edu/~res/math153-2020/week6/unit06/homework06xa.pdf  Homework files for the first part of Unit 6X (about Chinese mathematics).
Additional comments:
Information mentioned here and the problems in this file might be on the final exam:
https://www.math.uci.edu/~ndonalds/math184/china.pdf  A pleasant and brief historical survey.   The solutions to the two problems on the last page should be understood well enough for you to explain them to someone else.  There is also considerable information about Chinese numeration systems.