Mathematics 153
Notes from May 8, 2020, lecture session

What was covered:
The material in the main file for Unit 6X  about mathematics in India up to the time of the ultimate British subjugation of India in 1858.  
Relevant directory files for Unit 6X:
Here is a listing of files related to the May 8 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-of-Mathematics_India.pdf  This reprinted file contains a fairly detailed outline of the history of Indian mathematics.   It is less detailed and verifiable than the corresponding file for Chinese mathematical history, but it also discusses one important  point that probably should have been coveed in the lecture; namely, the Indian notation for writing fractions, which evolved into the present day notation.
http://math.ucr.edu/~res/math153-2020/week6/unit06/map-India-British.pdf   A map of British India before the parition which created Pakistan in the 1940s (and the subsequent separation of Bangladesh from the latter in 1972).  This map is useful for locating centers of ancient locations relevant to this history of mathematics, many of which are now part of Pakistan.
http://math.ucr.edu/~res/math153-2020/week6/unit06/history06b.pdf   A method for creating infinitely many new solutions to Pell's equation (for a fixed primt p) from old ones.
http://math.ucr.edu/~res/math153-2020/week6/unit06/history06d.pdf   Comments on the "paradoxical" fact that the product of two negative numbers is positive.
http://math.ucr.edu/~res/math153-2020/week6/unit06/map-India-Current.pdf  One reason for including this map is that it depicts the state of Kerala, which was the center of Indian mathematical activity from the 13th century until the British conquest.   It is important to note that the status of Jammu and Kashmir is still a major source of conflict between India and Pakistan (both of which have nuclear weapons), and Pakistan has occupied portions of this area for many decades.
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 remaining part of Unit 6X (about Indian mathematics).
Additional comments:
Information mentioned here might be on the final exam:
https://www.math.uci.edu/~ndonalds/math184/india.pdf  A pleasant and brief historical survey that should be read.   There are details about the evolution of Hindu-Arabic numbers. and also a section with specific information on one example of altar construction from the Vedic Sulbasutras.    This example illustrates the complexity of such altar descigns and illustrates the level of geometric knowlede implicit in their construction.