Amy Kwan

From MathWiki

News Articles

Article #1: Toronto Prof ups the odds for poker

http://www.yorku.ca/yfile/archive/index.asp?IssueDate=9/13/2005&section=York%20in%20the%20Media

This article shows the significance that mathematics has on games like poker (aka Games Theory). As we can see above, one of our very own Professors at York University has used mathematics to developing a “10 Steps to Winning Texas Hold’Em” after “spending years analyzing the statistics for limit Texas Hold’Em cash games”.

Article #2: Obesity link to heart disease confirmed

http://www.canada.com/globaltv/national/story.html?id=5ee25c66-9c9b-4fe7-a05a-be485d60cddc

This article shows how the “mathematics of a human shape” (aka waist circumference measurements) can be a significant indicator of what “healthy versus unhealthy” is. This is one of the many examples that can be viewed as to how mathematics plays a significant role in presenting data (i.e. via statistical analysis and correlation) in determining “healthy ranges”.

Article #3: Bosh hits for 31 in win over Sixers

http://www.thestar.com/NASApp/cs/ContentServer?pagename=thestar/Layout/Article_Type1&c=Article&cid=1142376616699&call_pageid=969907729483&col=970081562040

Mathematics is all over the sports world (via Stats! Stats! Stats!). Sports analysts make many “statistical” references during a single game: from individual stats, to team stats, to even stats and trends for a single game, there is no escaping “mathematics” in the world of sports. As seen below (link), boxscores for games are loaded with statistical breakdowns! http://www.nba.com/games/20060314/TORPHI/boxscore.html


Project: Interview with an Ornithologist

Introduction:

An ornithologist is a scientist who studies the lives and behaviours of birds (http://www.nmnh.si.edu/BIRDNET/Ornith.html). I recently had the privilege to sit down with one of my friends (Elizabeth) who is an ornithologist for an exclusive one-on-one Q&A interview session in order to get a look into how mathematics applies to her profession.

Questions and Answers:

Q. What do you do as an Ornithologist? What types of courses did you have to take?

A. I study birds, and my area of study is mating systems. You need to take biology courses, particularly in ecology and animal biology areas, and basic ornithology courses are good too.

In terms of math courses, I had to take calculus and stats…lots of stats courses! You need to know your stats for ornithology data interpretation.

Q. How long have you been doing this for?

A. Officially as a profession, I have been doing this for 2 years. But I handled my first bird when I was 2 years old – my father studies birds as a hobby and often involved me on his adventures.

Q. Is there a certain season that you work, or is it all year round? How do you study?

A. Studying depends on the breeding system on migratory birds. Depending on the bird, most of the studies are conducted between April and July. We work at field stations and study in the birds in the respective forest/field.

The particular bird that I study is the “Hooded Warbler”.

Q. Can you give me an overview of the types of things you do during your field research…particularly how mathematics is applied to your field of work?

A. Well, one of the basic items we do is we measure the birds – more particularly, we measure their weight, tarsus (leg/foot), and wing cord (wing span). We do this to get an idea of the size to assess and measure against the population.

After we capture the bird, before releasing it, we would “tag” or “mark” them. Most birds are marked after they are caught, but we also tag newborns from their nest.

Q. What information do you obtain from “tagged” birds?

A. We often tag breeding pairs to identify the different territories. We can use this information to calculate the carrying capacity. We can also determine the boarder of the territory by following the birds and observing their behaviour. For example, singing birds usually indicate that they are in the middle of the territory, and are trying to attract their mates. However, birds who are fighting with each other, usually indicates the boarder or edge of the territory, as the act is to defend the edge of their territory (the less birds in a territory, increases the probability of their chances to getting the mate)

We also study the fitness of them and analyze reproductive assessment, i.e. birds that are more “fit” have a higher chance of passing on their genes/finding a mate. This concept relates to reproductive success (sexual selection) – males who are more fit usually have more mates. In the case of females, females can’t nest or would have more difficulty nesting if they are not in good shape.

With respects to mating systems (which is what I study), measuring fitness is primary.

Q. How do you track the reproductive success?

A. We measure blood from the nestlings and compare the DNA. We don’t perform the DNA analysis ourselves. Samples are labeled and sent to a lab where the technicians do their jobs and send us back the data – we are actually expecting our results from this past summer in Pennsylvania soon.

Q. Are there any other activities that you do that require the use of mathematics?

A. Another interesting thing that we did this past summer is called Song Frequency Analysis to see if the more a bird sings correlates with being able to attract more mates. We would follow around a bird for an hour and count how many times they sing in an hour – so there’s a lot of dependence on counting, tracking, and then analysis of data.

Something else we do is count the species and abundance of insects. This relates to analyzing the quality of habitat. For example, to see if survival rates of the birds relates to the quality of the specific territory.

Q. Can you give me one or two mathematical based theorems I can look up that you would use or run into in your field of work?

A. Well, there is the carrying capacity that I mentioned earlier…and also you can look up the Hardy-Weinberg Theorem.

-End of Interview-

Summary of Interview

My short interview with my friend Elizabeth defiantly opened my eyes about how crucial the knowledge of mathematics is. From the beginning to end of the interview, I learned so much about how mathematics is applied to the occupation of an Ornithologist. Elizabeth had made reference from the beginning towards how important stats were in her profession, she gave me the example of like if 25/56 nests had extra pair young - is that result significant? I also learned about how important even basic mathematics was, for example how mathematics and mathematical tools are used to measure the birds in order to obtain data about the bird’s health and physical fitness. There is defiantly a lot of counting and analysis of those results in her profession.

Mathematics is defiantly an important tool to have when applying to scientific studies! Following the interview, I looked up “Carrying Capacity” and the “Hardy-Weinberg Theorem” as examples of mathematical applications used in Elizabeth’s field of study (below).

Carrying Capacity

1. Carrying capacity (K) is the maximum number of individuals of a species that can be supported by environment. 2. When N is small, a large portion of the carrying capacity has not been utilized, but as N approaches K, population growth slows down because (K - N/K) is nearing zero. 3. Examples: over-fishing drives a population into the lag phase; it is best to maintain populations in a growth phase; and reducing crop pests places them in exponential phase again. 4. Farmers can reduce the carrying capacity for a pest by alternating rows of different crops.

Hardy-Weinberg Theorem http://www.mun.ca/biology/scarr/2900_Population_Genetics.htm


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