Mathematicians: Sofya Kowalevskya

I often ask students, if you practice hard enough, will you be able to control a coin-toss? If yes, why is batting order decided by a coin-toss? If not, why not?, is not rigid body dynamics, ruled by Newton’s laws?

A part answer to that comes from the work of Sofya Kowalevskya, from her analysis of the differential equations that govern the rotation of rigid bodies.

What is all the more interesting is that essentially the same equations govern the roll of a dice of spin of a sattelite.

Her work has a quality of “mysterious” about it because she used a conjecture (unproven theorem) to get a set of solvable systems, without actually solving them. Now if the last statement has made you furious, I am sorry, the full story is very long, so some other time and some other place.

hands and height

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Photo by Sharon McCutcheon on Pexels.com

Recently saw a study that connected the size of a hand of a person with his/her height. The regression looked reasonably linear.

There are also studies that show the connection between blood-pressure between two arms of a person and health. That makes me think there might be variety of correlations that we may look at, some simple questions to ask may be,
“Does the shoulder length of a person correlate with height? or weight?”
“How does BMI correlate with height?”
“what about the legth of a person’s foot and height?”
We know there is a correlation but how good is it? It would also be interesting to see is their is something special about the outliers.

Regression: Reading suggestions

In every aspect of practical applications, understanding interpreting and modeling using
data is get getting more and more important. As a part of regression analysis projects, I recommend the following readings for insights into working with data.

1. Process improvement using data: “https://learnche.org/pid/
This is a detailed review discussing various aspects of data analysis. Chapter 4 reviews regression. There is also discussion on chemometrics in the book.

2. SAT scores: There exists variety of documents seeking correlation between the SAT scores and family income, month of birth, college success, etc., take your pick.

3. This research paper provides multiple examples of effective regression:
https://www.pnas.org/content/104/17/7301”.

4. Information on databases can be found on wikipedia or through a simple search.