• ## Symmetry in Fractals

Fractals lead to a new notion of symmetry. Fractal is a mathematical name used to describe the patterns of scale-self similarity which occur nearly the same at different levels. To elaborate, it is used when a specific and detailed pattern is seen to repeat itself.

Fractals are different from other geometric figures for in fractals, even though one sees one-dimensional lengths doubled, the corresponding spatial content of the fractal scales by a power that is not necessarily double also or even an integer (this spatial content of the fractal scale is referred to in the video as mass, example given is the Sierpinski triangle). This power-exponents are called fractal dimensions or scale dimensions.

The general consensus is that theoretical fractals are infinitely self-similar, iterative and detailed mathematical constructs having fractal dimensions. There may not be an agreed upon definition, different kinds of examples and applications about this have been formulated and studied in great depth.

Reference: http://www.mdpi.com/journal/symmetry/special_issues/symmetry_fractals

• ## Fourier Transform on measuring temperature

The Fourier transform converts a set of time domain data vectors into a set of frequency (or per time) domain vectors.

To know about changes in soil temperature, we can measure the temperature of soil accordingly at different time of the day, every day for a year. We would then have a list of real numbers representing the soil temperatures.

By plotting these readings on a line graph with the vertical y axis labelled as temperature and the horizontal x axis labelled time, we get a so called “time domain” graph. The graph that we created is then the sum of two  sinusoids or sine waves. The first sinusoid is with a frequency of one day as the temperature varies between day and night. The other sinusoid is with a frequency of one year as the temperature varies with the seasons.

The Fourier Transform provides a means of manipulating or transforming this raw data into an alternative set of data, the magnitude of which can be plotted on a graph with differently labelled axis. Disregarding the y axis label for now, the x axis would be labelled ‘frequency’. This is in the frequency domain graph.

This second graph looks very different than the first because it will consist of two vertical lines rising from the frequency axis, one at a frequency (or period) of one day, the other at a frequency of one year. Thus by using Fourier Transform on the raw data we have, we then extracted the most interesting facts from it – days are warmer than nights and summer is warmer than winter.

Reference: http://nptel.ac.in/courses/117101055/cdeep%20demo%20ppt/application%20of%20fourier%20transforms.html

• ## Vector Analysis on Pathogens

A pathogen or infectious agent is a biological agent that causes disease or illness to its host. Vector analysis can track a possible bioterrorism by knowing where it started, a probable point of release. It can also be used to track the links between victims and to predict the spread of the illness. Tracking such can be complicated for it is a multi-variable problem. It takes complex statistical analysis and graph theory.
Not everyone that gets exposed gets sick.

The data of such  can be discovered with the use of a Geographic Information System  which allows mathematicians to map victims and potential disease clusters with real-time data. Working hand-in-hand  with G.I.S is the Susceptible Infectious Recovered (SIR) model is a differential equation model  which identifies the independent and dependent variables. Namely, the independent variable is time t, measured in days while the two related sets of dependent variables are 1.) the number of people in each of the groups of susceptible, infected and recovered individuals and 2.) the fraction of the total population in the same mentioned 3 categories . These G.I.S and S. I.R model are the two things that allows us to know what is the source or is it a person or a place.

Sources: http://www.springfieldspringfield.co.uk/view_episode_scripts.php?tv-show=numb3rs&episode=s01e03

• ## Start of an Epic Journey

Week 1: Introduce yourself

Arlan Vincent D. Uy

What were your thoughts when you enrolled in this course?

My thoughts are the following:

• This class might be the most fun class in Math that I will ever take
• How come Math 55 became a prerequisite for this class? What particular topics in Math 55 are needed for this course.
• I just want to graduate on time as much as possible (This is why I’m taking this subject as early as possible)

How comfortable are you with math?

Oftentimes, I enjoy math and all its little eccentricities and because of this I learn Math not just for purpose of being a required subject but also for fun. In other times, however, I just make comments about it using an angery emoticon. This is because sometimes it fools me that I know in depth one of its certain topic even though I really am just on the tip of the iceberg. Nevertheless, both enjoying studying Math and making angery comments towards Math made me know this subject more and I am just really thankful for this kind of relationship I have with Math

What’s your dominant feeling right now?

Happy because Sir Paul is my professor and thankful that I have one more opportunity to strengthen my relationship with Math

• #### Paul Rossener 3:52 pm on February 22, 2017 Permalink | Reply

Hi Arlan! I can’t remember all the topics in Math 55, but I think later on in the course, we’ll be dealing with series.

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