Category Archives: Introductions

Carrie and Bioinformatics

“How might disease spread in populated areas in the event of a bioterrorism incident, and how would it be contained?”

It is questions like the one above that motivated me to become an applied mathematics major. The general definition of Bioinformatics is an interdisciplinary field that develops and improves methods for storing, retrieving, organizing and analyzing biological data. The part that I am interested in is the study of disease. One part of bioinformatics involves taking the data collected from studies to form a complete picture for interpretation and analysis.

In the Journal for Cancer Research, “Serum Protein Fingerprinting Coupled with a Pattern-matching Algorithm Distinguishes Prostate Cancer from Benign Prostate Hyperplasia and Healthy Men” (http://cancerres.aacrjournals.org/content/62/13/3609.full#sec-2) is an article that uses a decision tree algorithm. This is a powerful tool for classification and prediction. It is a classifier in a tree form having a

  • Decision node: specifies a test on a single attribute
  • Leaf node: indicates the value of the target attribute
  • Arc/edge: split of one attribute
  • Path: a disjunction of test to make the final decision

Source: www.cse.ust.hk/~twinsen/Decision_Tree.ppt

I think that bioinformatics is a huge and very important tool in mathematics that I hope to be apart of one day.

Samantha Intro For Funsies

I am Samantha (obviously). I am only three and a half semesters away from graduating with my Math Ed degree. Many of my current classes are not “new” to me. We are working on more of the teaching aspect. However, I am in Calc 3, that stuff is new. I love Calculus. I would rather not teach it, but I love working out the problems. Currently we are working with Integrals again. Integrals would be in my list of “Favorite Math Topics”. If you would like to know all about integrals, Wikipedia knows it!….: http://en.wikipedia.org/wiki/Integral
This is what they look like:
$\int_a^bf(x)dx$
In Calc three we are working with multi-variables, so they look like this:
$\int_a^b\int_c^dF(x)dxdy$

Fun, right?!

Murphy and Fermat’s Last Theorem

My name is Tyler Murphy and I love puzzles.   Currently, my favorite puzzle is Fermat’s last Theorem.   I find it very fascinating that this one conjecture confounded the greatest mathematical minds in the world for over 300 years.  It’s even more fascinating that the math required to prove the theorem ($\nexists  a,b,c,n \in \mathbb{Z}/\{0\} \mid a^n+b^n=c^n, n>2$) didn’t exist for 250 years after Fermat made the claim that he had proven the conjecture.

I also love that most people think mathematics is a stale field with nothing more to discover.  Fermat’s Last Theorem is proof against that.  I love that this was proved in my lifetime.  To me it represents the continually changing and dynamic world of mathematics.  It’s like having special eyesight that allows me to see into a special and private world that permeates every aspect of our lives which most people will never glimpse or understand.

Today, most mathematicians believe that Fermat could not have had a viable proof.  Even once the conjecture was proven in 1995 by Andrew Wiles, the search for a proof didn’t end.   Today, the search is for a more concise proof, as Wiles’ proof was over 100 pages long.   The current search is trying to find a proof for a theorem about numbers that only talks about numbers.

Here’s an interesting article about the most recent advancement in Fermat’s Last Theorem as well as some historical context.

Arthur, Interdependent Complexity

My name is Arthur and my favorite aspect of mathematics is not a particular field of theory, but rather how the fundamentals are used to describe systematically more complex applications of those core concepts. Two of the founding principles in mathematics come in the form of operations, one being the Symmetric Operation, and the other being the Inverse Operation. Continue reading

Square root of 2 is irrational?

My name is Farighon. I have a deep interest in the field of Combinatorics and Number Theory although I do like to take time to study Complex Analysis when I do have some free time. Since the inception of my interest in mathematics, I have always been interested and fascinated by proofs for theorems, lemmas, and propositions. But I would be lying if I said that I understood each proof that I have come across. However, there is one proof that has made perfect sense. It is none other than the proof for the square root of 2.

The proof for the square root of 2 being irrational has been one of the primary interests of ancient mathematicians starting with the Babylonian’s. Then the ancient Indians. Although later on it was proven by a simple yet elegant proof that square root of 2 is irrational, the hunt for determining the square root of 2 to as many decimal places as possible is an ongoing task for mathematicians teamed up with Computer Scientists. After all, who can expect a mathematician to be ever satisfied when perfection is what shapes and disciplines them?

The article for the proof of $\sqrt(2)$ can be found at the following article for the curious reader: http://en.wikipedia.org/wiki/Square_root_of_2.

 

Marc on why Calculus is the Bomb

My name is Marc and I am a math student at Boise State University in Boise, Idaho which is best known for its potatoes as well as recreational opportunities. One area of mathematics that I enjoy learning and studying about is calculus. Calculus is the study of limits, derivatives, and integrals which are useful in studying continuous functions. Limits play a massive role in a variety of fields ranging from economics to engineering, and limits help to define derivatives. Derivatives are functions that describe the slope of a continuous function. The opposite of a derivative, an integral, can be used to find areas under curves in two dimensions as well as volumes in three dimensions. All of these tools can be used for optimization purposes which are significant in practically any field.

For more information about calculus, you can visit the Wikipedia page here.

Because the derivative represents the slope of a function,  the derivative of a function is thus calculated with this idea of change in distance in mind. The equation associated with the derivative is:

$m=\lim_{h\to 0 }\frac{f(a+h)-f(a)}{h}$

Notice that this equation represents a change in distance on a graph. Slopes are meant to represent changes of functions and functions represent a variety of trends! For example, the derivative of a position function in physics would produce a velocity graph which represents speed, or how the distance is changing over time. The derivative of a velocity function would give an acceleration function which reveals how the speed is changing over time. Pretty cool, isn’t it!?

Jordan: Euclidean Geometry

My name is Jordan and a sub-topic of mathematics that I enjoy would be Euclidean Geometry. I like this topic because  with just 5 axioms and 5 common notions, many theorems can be proved. When looking through Euclid’s first book of elements there are many postulates with proofs from these axioms and notions. While the first 4 axioms seem to be very simple and almost common sense, the 5th axiom is more complicated and has had many people try to disprove it. Continue reading

Kenny and Epidemic Models

My name is Kenny. I’m an Applied Mathematics student at Boise State University, with other interests in Computer Science and programming.

An area of math that I’m interested in is differential equations and modeling. Using differential equations we can model a number of natural phenomenons. Namely, predator-prey, competing predator-predator, mass on  spring, and epidemic models. The last one may be modeled, simply, by the system of differential equations:

\begin{align*}
\frac{dS}{dt} &= -\beta{}SI \\
\frac{dI}{dt} &= \beta{}SI-\gamma{}I \\
\frac{dR}{dt} &= \gamma{}I
\end{align*}
Where $S(t)$ is a function of individuals not yet infected, $I(t)$ a function of infected individuals, $R(t)$ a function of recovered individuals and $\beta{}$ and $\gamma{}$ are constants of infection and recovery, respectively.

You can read more about Differential Equations on the Wikipedia page. You can also find more information about epidemic models.