Math 210: Tentative Syllabus | Spring 2019 |
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This course focuses on the mathematics applications in everyday life. There will be an emphesis on discovery, understanding, and communication. The impact of the Internet cannot be underestimated.
Instead of building a machine, we will primarily investigate some significant examples. Here are some possibilities, each of which are huge areas of study.
Caution: Interpreting misleading data. "Air Travel Surges by 123%!" [New York Times]
Specific applications such as to how Google search works, and how YouTube and NetFlix make their suggestions, and how to rank college football teams when most teams have not played other.Some specific probability and statistics questions
As part of this we will introduce and use some topics from Linear Algebra.
R_{0} : Researchers still aren't sure how contagious COVID-19 is compared to other viruses, but it appears to spread more rapidly than the flu. "In public health we measure something called the R_{0} (pronounced 'R-naught') which is the average number of people infected by a person with the virus," says Dr Brown. He goes on to explain that the R_{0} for influenza is about 1.3, meaning about 1.3 people get the virus from every ten who have the infection. Measles, on the other hand, is extremely contagious, with an R_{0} of 12-18. "We are still not sure what the R_{0} is for coronavirus, but it appears to be about 2.0, which is about the same as SARS," Dr. Brown continues, "These are early estimates though and are likely to change as we get better data."
Thieme "Kermack McKendrick
SIR Model"
Epidemics: SIR Murray,
Epidemics (Fig) Murray,
SEIR Model (Thieme),
Jones-Math-Epmidemics.
Modeling an epidemic
Brauer, Mathematical epidemiology (2017)
Understanding Epidemiology Models ((May 2020) The point of these
models is not really to predict the future but to understand the
problem. For the COVID-19 virus, the current data is way too skimpy
and unreliable to predict anything.
Chasing the Elusive Numbers That Define Epidemics
Wuhan coronavirus 2020,
data?, and
Update Feb. 10, 2020
The Coronavirus, by the Numbers, March 2020
The reproductive number of a disease (video)
January 2021
Hard Lessons of Modeling the Coronavirus Pandemic
The Hard Lessons of Modeling the Coronavirus Pandemic
Predator-Prey Murray, Predator-Prey, Jones
Biodiversity
Viscous fluid in a long pipe Hagen-Poiseuille equation
Blood Flow, Blood Pressure, and Resistance
tectonic plates
SVD Face Recogntion [Nathan Kutz]: Lecture 1, Lecture 2, Lecture 3
Biology [Bingni Wen Brunton]: PCA 1, PCA 2, PCA 3,
To be successful in this course, you should be present for all class meetings and plan to take good notes.