However with the advent of genome sequencing it was discovered that there was good reason to have more "kingdoms," organized somewhat differently from plants and animals. In fact, it was decided that there should be a category above kingdom, often referred to as a domain. The three domains often now used are Archaea, Bacteria, and Eukary. Archaea were a kind of microbe which seemed to be sufficiently different from other kinds of microbes to warrant special attention.
Thus, in , based on work of Carl Woese and George E. Fox, the traditional system of classification was modified and the "kingdoms" reorganized within the category of the three domains given above. Ecology is the branch of biology which is concerned with how organisms relate to each other and the environments in which they live. Humans share the Earth with many other life forms, as Linnaeus and his successors discovered. Wherever one lives, whether it is New York City or the Amazon, one only sees a small part of the diversity of species that the Earth has.
Curiosity about these life forms is why zoos are so popular. It has also led to using scientific ideas to understand how man interacts with and uses other life forms for food, medicine, etc. And where there is science, there is mathematics. In ecology, as elsewhere, one uses numbers to both count and to measure. When one makes measurements on things, say the weight of elephants in a certain region, investigators usually aim to measure the weight of all the elephants or take a sample of elephants and try to extrapolate from the sample information about the population.
When populations are large, it is hard to take measurements for all of its individuals. On the other hand, when one takes a sample it is often difficult to be "sure" that the sample is representative of the population. Are the elephants in American zoos "typical" or all elephants? In getting understanding of a collection of data, there are two fundamental concepts involved.
One is the notion of a measure of central tendency --a single number that captures the values of one's data set. Common measures of central tendency are the mean the sum of the measurements divided by the number of members in the population , the median after arranging the data in increasing order, a measurement in the middle , and the mode a measurement which occurs most often.
Not surprisingly it is hard to capture a whole population with a single number, since one data set may have nearly all the values very close to say, the mean, while another population may have the same mean as the first population but be "spread out. Another measure of dispersion for a set of data would be the range, the difference between the largest and smallest measurements. Having thought of the range, one might invent the measure of central tendency, the "mid-range" value--the value of the range divided by two.
Population means and standard deviations and sample means and standard deviations are the tools that mathematicians statisticians use to understand what is going on in comparing two populations. The general tools of the statistician are also the tools of the ecologist. Ecologists have invented a variety of "indices" to measure and get insight into living things.
When trying to understand species diversity, if one has two sets of "traps" collection stations and collects from these traps just information about the numbers of species found, one can try to sort out that there may be many species at one trap and fewer at another, but the first trap may have approximately equal numbers of each species that are found, while the other trap may have very disparate values for the species found.
Thus, one trap might have 5 species where the numbers for each of these species vary from 1 to 8 while the other trap may have found 11 species but only 2 or 3 individuals for each of these. The many observational complexities of trying to comprehend biodiversity resulted in a variety of definitions to capture different aspects of biodiversity as well. The complexities show how results might vary from summer to winter and from one geographical region to another. Also, ecological studies for large mammals, birds, insects, and corals present different challenges to scientists.
One reason mathematics is powerful is that often the same mathematical tools can be used in vastly different applied settings. On the other hand, when modeling a problem, as a first approximation one might use the same tools in settings that have some similarities, but one has to be careful that the results found are truly meaningful over similar kinds of situations. In order to give more concreteness to this matter let us imagine that an ecologist is trying to understand the diversity of the species that are in a well-defined geographic area. Abstractly, one might approach this by saying one is going to take several samples in the region involved to measure "species diversity.
Another concern is avoiding injuring the sampled creatures. If you are trying to study the different kinds of trees in a certain area, the procedure used will be quite different from studying rodents, moths or beetles. There are interesting questions related to where you might want to take the samples, given different geographical settings.
Is the "region" a lake, a river, an irregular field, or a rectangular section of a forest? While it is intriguing to contemplate the different mathematical approaches to this relatively circumscribed collection of sampling situations, my goal is to say a bit more about how some simple situations of this kind have generated mathematical ideas which have grown to be useful in a range of settings.
One of the spices of life, wherever you live, whether in a large city, suburb, or rural area, is that you see living things other than other humans. In a large city you see squirrels and pigeons in the "animal" department and various flowers and trees in the "vegetable" department.
In rural areas you might see deer or foxes. However, the largest reservoir of variety of life forms is found in areas that are not heavily populated by humans or have been set aside as reserves for "wildlife," in the ocean, or "underground. When humans think of biological diversity, they often think of how many species there are. Mathematics has been used in a number of ways to get a comprehensive look into this issue.
However, given that the world is a dynamic place, the issue of even counting species is not a total "triviality. What is the distribution of large mammals in terms of temperature zones? One might intuitively think there would be more large mammals in the tropics than in the cold regions near the poles. What can one learn from collecting data? What about the spread of trees and flowering plants as one moves from the equator towards either the North or South Poles?
Is there more diversity of life in the oceans or on land? How are insects distributed across the different temperature zones? Perhaps the simplest way to analyze species diversity is to count species. However, this is not as simple as it might appear because telling species apart is not all that easy. It may not be hard to tell a tiger from an elephant but at a given time or location it is easier to tell the presence or absence of a species if one knows what one is looking for and can tell apart the things that one actually sees! To many people lots of different kinds of beetles look alike.
How do you measure how many different birds a country has since many bird species do not spend their whole lives within one country's borders? Some countries have very few lakes and rivers and so don't have many marine species. The regions of a large country may take pride in the number of different species present in those regions e. Leaving aside many of the subtle questions hinted at above, how does one "measure" the number of species present in a particular locale?
Perhaps the simplest such measure is to count the number of species--take a census. However, we know from counting humans that the problem of counting humans, no less squirrels in NY State, is not an easy task. Not surprisingly, one turns to statistics as a tool for using partial information samples to get information about the populations involved.
One might try to answer questions about presence or absence of species by employing collection stations. Mathematics might be involved in where to place the collection stations for the study. Placing them close to each other might not show the full "range" of diversity of species but stations which are close to each other might help "sort out" the consistency with which species appear in a particular locale.
There are other placement issues depending on the nature of what is being counted. To understand marine diversity in a lake which is approximately circular, what mixture of collection stations near the shore versus the interior of the lake should be used? At what depth in the water should stations be placed since different marine life may be present at different depths? So for simplicity let us imagine that the non-obvious places to put two traps to look for "creatures" fish, eels, etc.
To get you thinking about some of the issues the following artificial example shows the results of setting two collection stations, one in the East E and one in the West W of a certain region and obtaining counts of animals say, rodents encountered and the species they belong to. What one notices immediately is that some species don't occur at one of the two collection stations and that when there is a species that appears at both stations, it may appear at one collection station much more often than at the other collection station.
One sees that there is a large difference in the "sample" numbers found in the two collection stations--one collected 10 more items than the other. While there were 11 species represented in the two collection stations, one station found 8 species and the other only 5 but that was the station that collected fewer animals. So what concepts might we use to get insight? One might just count how many species one finds. Many sections of the Wolf River are protected and accessible only by non-motor powered boats.
The entire Wolf River is a Class I stream which means there is no whitewater. Each year we have paddled the majestic Ghost River section. Announcements for the trips are sent out to faculty and students in biomath related courses each fall. Contact Prof. Bodine if you are interested in participating. Skip to main navigation. What is Biomathematics? Swiler is as dedicated to her responsibilities as a wife and mother as she is to her commitment as a mathematician and mentor. However, Swiler has served as a living testament to the ability of the modern day woman to be both focused in her career and engaged with her children, which is no small feat.
Although some academic fields seem stacked against women because the childbearing years coincide with what are usually the years of peak productivity, Swiler has demonstrated that women do not have to choose between their family lives and their careers. It is apparent that Swiler has never allowed herself to be discouraged by the dearth of women in mathematics. Her profound appreciation of and delight in the power and elegance of mathematics has driven her to pursue her dream of effecting change through mathematics without regard to perceived gender limitations.
Though she grapples with uncertainty on a daily basis, one thing there is no uncertainty about is Dr. I am actively involved in school organizations and my community, including our school newspaper, tennis team, speech and debate team and community service club. I am genuinely fascinated and delighted by mathematics and have eagerly pursued it both through my academic coursework I am taking AP Calculus BC and through tutoring younger students in math. To me, math is a splendid way to exercise my problem solving skills nothing really compares to the satisfaction of finally solving a difficult problem and has helped me understand that there are usually several different approaches to solving the same problem.
In my free time, I enjoy running, drawing and reading especially National Geographic. I hope to have the opportunity to further pursue my passion for math and science through university and beyond. Stevenson is the daughter of a mathematician and a social worker, and she never imagined she would be either; today, she is both.
Growing up, Stevenson had little interest in the latter and only a vague curiosity for math. Her passion for mathematics blossomed during her undergraduate years at Mount Holyoke. As one of just two thousand students, Stevenson received considerable encouragement, which prompted her interest in further mathematical study. Before graduate school, Stevenson spent a summer working for a primary dealer in United States government securities, to assure herself that she would not rather bring her education to a close and start working. By the end of the summer, she was sure.
After earning her PhD at the University of Pennsylvania, Stevenson traveled to Montreal to brave the freezing winters and study Arithmetic Geometry, which falls in between the fields of Algebraic Geometry and Number Theory. By looking at curves defined over abstract fields, she examined the connections between curves and lines. Her year in Montreal was the penultimate in which she would bear the biting winters of the Northeast, thanks to a chance meeting in Zurich, Switzerland.
At a conference, Stevenson ran into a man demanding that someone wash his shirts. She rolled her eyes, and then fell in love with him. Stevenson spent a year at the University of Southern California, then two as a visiting professor at Cal Tech. To earn teaching credibility for her permanent California job search, Stevenson taught for a year at Pomona College.
She attributed being hired at California State University, Northridge in part to a recommendation from Pomona College. Though she always believed she would carry out her love for teaching at a prestigious university, Stevenson has found her calling at the less well known California State University, Northridge.
But it has been a perfect job for me. Her research extends past pure mathematics to mathematical pedagogy. Stevenson runs a grant from the Bill and Melinda Gates Foundation for general education math courses across the California State University system.
She works to redesign curriculums, secure funding, and coordinate across campuses for the high-failure general education classes that are ignored by many math professors but crucial to the universities. With the grant, she has transformed some entry level pass rates from one-third to three-fourths of students. With about 3, students entering each semester who require remedial math and thirty-five faculty members, Stevenson is the heart of the program.
Is a kid failing because he is sitting in the back of the room and texting all of class? At home, Stevenson is an avid gardener; among her blossoming flowers and trimmed tomato plants, she creates something tangible. Though I have been a year advanced in math since middle school, I have only lately recognized my love for it, in AP Calculus last year and Multivariable Calculus this year. Outside of math and writing, I am interested in international journalism, travel, and perfectly ripe pomegranates. Sadly, this profession has a negative reputation and it is unusual for a child to even dream about pursuing it.
She graduated from the University of Utah with a degree in Economics and then worked in the industry as a software engineer for eight years. After marrying David Evans, a fellow lover of math, she decided to pursue what she loved, followed her dreams, and went back to school to become a mathematician. Following her graduate studies in domains with fractal boundaries in Massachusetts she moved to Utah with her husband and daughter Eleanor to teach at BYU.
Through her experiences as a software engineer and in Economics she has gained a broader perspective as a mathematician. She learned important skills to become a better problem-solver. And, as advisor of the Women-in-Math club at BYU, she has inspired many young college women to follow their dreams.
The best piece of advice that Emily said she could give me was to not make excuses for my innate talents. She said that as women we are apologetic for our choices and talents. But in reality, we should not be ashamed of what we do well. We must embrace our talents, and not make excuses in fear of rejection or in fear of going against the social norm.
Emily learned this lesson the hard way; she made excuses not to pursue mathematics and chose a different path. These decisions shaped her into the mathematician she is today who continues to inspire everyone around her.
Do you need to know math for doing great science? - Scientific American Blog Network
Now living her childhood dream as a Mathematician she enjoys working on three research projects that vary from engineering to biology to pure mathematics. She is truly a Renaissance woman in mathematics! Her first project involves computational mechanics and includes doing mathematical analysis of ships and airplane wings. Together with other engineers and computer-aided design programs, Emily helps link different types of engineering to make new discoveries and advancements.
And if that is not impressive enough, Emily also works with biologists to improve cell motion. They specialize in a slug-like moving cell called amoeboidal cells. With other biologists, Emily has come up with mathematical models to analyze the movement of these cells. Her last but not least project deals with her emphasis during graduate school. She researches domains with fractal boundaries, or shapes with bumpy boundaries and how they relate to their surroundings. Apart from being a successful mathematician, Emily enjoys spending time with her family, hiking, and reading books.
She is living proof that dreams can come to pass despite any detour or challenge you may face. She enjoys many aspects of math including combinatorics and complex analysis, two of the classes she is currently taking. She also really enjoys geometry ever since her 8th grade geometry class. Actuaries, mathematicians who manage risk for insurance companies, have one of the top-ranked professions in the United States, but not everyone realizes the dedication it takes to become one.
To become an actuarial fellow, one must pass a series of very difficult exams. The exam process takes years and to complete it is an impressive feat. To become the head of the actuarial department at a company, or a chief actuary, is even more so. However, Nora talks very candidly and modestly about her success. I called her during a typical Wednesday morning to ask her some questions about her career. She studied at Miami University of Ohio, where she originally planned to get her PhD in mathematics and teach at the collegiate level. She noticed that there was only one female math professor in the department, and that she taught the lowest level courses.
It seemed sexist and political to Nora, so she chose to look into actuarial science. Her father was an actuary and encouraged her to pursue the career. While still in school, she wrote her first exam and passed. She liked that with an actuarial career the exams offered an outside measure of her skill, and no bias could figure into her success. After graduation, Nora began working for Columbus Mutual, a small insurance company. When the company demutualized in , it was acquired by Western and Southern, a larger insurance group, and Nora moved to Cincinnati. Nora says that the jobs were different in nature.
Mathematics and Ecology
At Columbus Mutual, insurance was sold regionally and the company would focus on the agents who sold the policies. At Western and Southern, Nora began working with several different companies, distributions, and target markets. She says she enjoyed different aspects of both jobs. Around , she ascended to the position of chief actuary, becoming a woman with authority in an office that was mostly comprised of men.
I wondered about her perspective on being a woman actuary, and she said that when she started her career, being a woman could be used to her advantage. When she was the only female in the room, it made her memorable. However, there were also drawbacks. This pushed her to work hard and be noticed, and the work paid off. I inquired about her favorite part of her job, and she identified two aspects of her job that she particularly loves.
Being part of the big picture and noticing her success has made her rightfully proud, but she also enjoys noticing the success in others. She loves seeing young people learn and pass exams, advancing their own careers as actuaries. Hoping to be a successful actuary myself one day, I asked her what advice she might give to young women in the field today. She advises young actuaries to do whatever it takes to pass exams. In her experience, she has noticed that the longer it takes for someone to get through the exam process, the less likely it is that he or she will finish.
She also believes in lifelong learning. Once someone achieves an FSA, that is the beginning, she says, not the end. I believe Nora offers a great deal of wisdom. Her success is something to be admired and emulated.
- KEEPING MY SECRET SAFE (Domination, Submission and the Violation of Violet West).
- Travels Through Absence, Letters from the European City.
- Barbeque Magic.
- A Good Man.
- Perspectives in Biology and Medicine!
- I Refuse to Die: My Journey For Freedom.
I plan to take her advice as I advance in my own career, remembering that I am extremely fortunate to have the opportunity to become an actuary and to have the support of professionals like Nora along the way. My goal is to become an actuarial analyst. During the summer of , I interned with Great American Insurance Company as an actuarial intern and learned about annuities and financial planning. I have written and passed two actuarial exams, P and FM. Along with my interest in actuarial science, I am also president of Omicron Delta Kappa, a leadership fraternity, and currently involved with planning our All-Campus Leadership Conference.
A List of 25 Research Topics in Mathematics
What makes a person take the road less traveled? He thought I would be a nice nurse or marry well. And yet, while she never saw it as an excuse, there WAS one obstacle she had to overcome: her dyslexia. Her teachers labeled her slow and lazy. School eventually got better because she found ways to compensate, not because it became easier or because her dyslexia went away. She would memorize words and how they were spelled.
She would count the number of students in front of her, find the section she would be asked to read aloud, and then practice that paragraph over and over until it was her turn.
She would create patterns, charts, and tricks to help classify and retain information. She was persistent and worked hard. Perhaps my ability to pull information out of context, concentrating not just on one indicator, but bringing many in laterally, may have been affected by what I learned to do from my struggles with dyslexia. But there were no jobs. She even looked in the obituaries. She found a dead history teacher in New Hampshire and called the school. Well, so much for that! After she was married, she partnered with her husband, Paul, in the securities business as a registered principal.
She continues to do this today. I know what it feels like for something not to make sense.
I try to share what I can with others, breaking down numbers so they can make sense. She likes this label a lot better. She is beautiful and charming, wears fashionable clothing, and loves having fun! She is an accomplished photographer, devoted wife, loving mother, and great friend. She is exactly what math needs as a spokeswoman for its cause and advancement for young girls.
I am proud to say that Mary Judith Gedroiz is my aunt and role model, not just because of the obstacles she overcame, but because she is somebody that one day maybe I could become.
Mathematics and Ecology
I am in 7th grade at St. Cecelia Interparochial School in Clearwater, Florida. My whole life, I have been the worst speller in my grade. At first, everyone thought that it was normal because I was so little. As the years passed, it got worse and worse. But, in 5th grade, I got the news that changed my life. I had dyslexia. My life changed so much that I thought it was ruined, only to find out later that it changed for the better. I realized that just because I have trouble with spelling and reading does not mean that I am bad at everything else, too. I am stronger in things that others are not.
I love math. This summer I will attend a 3-week program at UC Berkeley called Math Zoom, which is a training program for mathematically gifted students. Handmade roller-coasters line the back wall. Papers are dispersed about the room. The board is a canvas of numbers and symbols. Shelves are stocked with crystal-ball-like apparatuses and pressure sensing devices.
Seated around the room are students debating equations and questions and problems, while she smiles on. Jennifer Tillenburg is a unique teacher. She bounces into her classroom every day, ready to take on the challenges of the course.