Monday, October 19, 2015

The Number Mysteries: A mathematical Odyssey Through Everyday Life

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    You want to be a teacher? You want to be able to answer that annoying question of "Where will I ever use this?" This book is an interesting read that will help you answer your students. It will help you see where these topics show up in the world and how they are important they are to what we know today.

   Not only did this book explain out the thinking behind the topics and cover in detail different examples but it gave online resources for you to continue your learning of the topics that you didn't understand. The five chapters in this book relate to:
  1. The Curious Incident of the Never-ending Primes
    1. Fibonacci number
    2. Golden ratio
  2. The Story of the Elusive Shape
    1. Finding length of coast line
    2. Snow flakes 
  3. The Secret of the Winning Streak
    1. Rock paper Scissors
    2. Lottery
  4. The Case of the Uncrakable Code
    1. Morris Code
    2. Semaphore
  5. The Quest to Predict the Future
    1. What hits the ground first a feather or a soccer ball
    2. Chaos vs Laminar Flow
    It is a very interesting they way that so many seeming unrelated topics are actually all interconnected is a very cool way to look at math and I think that it would be awesome to incorporate this into our everyday teaching method. If we get our students to be interested then we will see them understanding and actually enjoying what they are learning more.

   Marcus Du Sautoy the Author is an experienced mathematician and for many different topics one of the most known is his work with group theory and number theory. He put this book together and it shows that math is a very deep part of what our lives are and what we do on a daily basis. 

Book Notes: The Number Mysteries.

This book was broken into five chapters each covering one of the million dollar math problems. The topic of each:

  1. The Curious Incident of the Never-ending Primes 
  2. The Story of the Elusive Shape
  3. The secret of the Winning Streak 
  4. The  Case of the Uncrackable code
  5. The Quest to Predict the Future
Within each of these chapters there are activities that are online that connect you to concepts that are being discussed in the section. I found these as very good activities to understand what he was talking about.

In chapter one the million dollar question is called Riemann hypothesis.

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All the examples that I worked on in this chapter were related to how numbers build and will continue to add up in a never ending pattern. 

Chapter 2 
What is the shape of our universe? Seems like a question we get asked in science but this is actually related to math because we have to think about it in a logical way because we can only guess with science. 
This problem was solved but the mathematician  that found the answer didn't accept the million dollars he just likes doing the problem.

Chapter 3
Strategy to beat Rock Paper Scissors .....Where was this when i was growing up??? There are many things in this chapter that I never would have thought of and how it is explains them helped my understanding of things that I learned without having a real understanding of. To start the chapter it asks you to pick five numbers between 1-49 and then it ends with the Winning numbers....I failed but it was an interesting way to get interaction. The final problem is the Traveling sales men which is a type of question I remember getting asked in 341 class. 

Chapter 4
Code breaking....What kid doesn't have dreams about being a spy?
There are many types of codes that are based in math and even if you don't think its based on math i bet you would be interested in that there is some form of math hidden inside your codes. This really was interesting in how to read codes and write them. kinda makes me feel like a spy. 

Chapter 5
Thinking about the Cubs this year makes me wonder if Doc. Brown actually came to the future and found that they would win.....What is chaos? how would we predict chaos? I didn't understand this chapter as much as the others it was a stretch for me to understand where they were going and what they were doing.  

Sunday, October 11, 2015

Math VS. Science

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Is math a part of science, is science a part of math, or are they related at all?
   This is the question that brings us here today. I think there are many ways that this idea can be looked at and approached. Now I am going to show why I think math and science are related by explaining science and showing the math within and analyzing math and showing the science inside.

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    When we work in science we follow the steps above and we reach a point in the processes that we have to take what we have found and interpret what the data has given us. In many if not all cases this data has some numerical data weather it be height, temperature, etc. This isn't the only time math shows up in science experiments, anytime you need to use a formula to find missing values you are using math in science. There you are using mathematical formulas to find out aspects of science you couldn't find before. Not only that but you also can use the data to find patterns in science to predict how future data would proceed.
   If we now look for science in math we see that math is the process of working with numbers and logic so once we have our answers from given formulas we can then make sense of the data. This step of applying a meaning to data is doing science and then understanding the math that comes out of it.
  Next by looking at both of them we can observe some very interesting overlap:

  •     Tables
    • What is the best way to show numerical data in a table? What do both scientists and mathematicians use to present there data? The answer is tables because it gives all the desired data in one neat form. Tables are used in other areas of study where they are showing data but other areas of study that use tables are taking data that was derived from either mathematical data or scientific research 
  •     Communication 
    • The ideas are meant to be shared with the public and have to be understandable by the general public. This means that their ideas have to be stated in ways that everyday people can understand. 
  •     Proof
    • For the topics to be believed by many others you have to have evidence proving that it is true. This is true in both math and science in both areas you have to be able to prove you reasoning and show that there is always a way to reproduce it. 
   If were to play devils advocate and had to defend why I thought that math and science weren't related I would have to bring up the idea of how you can work on just pure math problems that have no connection to any story. This is like when you work on non-story problems when it's just working through a problem. Science is a different story though I don't believe that you can do pure science without having math show up at some point in the experiment. So my devils advocate would be that you can have just math or science with a hint of math, because you have can't have science without math.
   I know that Science vs. Math is a personal question and we all have our own views on it but this post gives my views on why I think that they are codependent of each other. As you can see, the evidence that both math and science are heavily related is strong and stands for itself in many areas therefore it should be agreed with.