Sunday, October 18, 2015

The Joy of X: A Guided Tour of Math, from One to Infinity

I recently just finished reading The Joy of X: A Guided Tour of Math, from One to Infinity, by Steven Strogatz. Strogatz is an applied mathematician, but he knows that some people may not understand math right away. While reading his book he takes you on a journey through the progression of math as you would learn it as a student. He breaks the book down into six parts.

1. Numbers - what are they? how do we use them? and why they are important.
2. Relationships - algebra, functions, story problems
3. Shapes - triangles, pi, trigonometry
4. Change - calculus, e, vectors
5. Data - normal distribution
6. Frontiers - primes, group theory, sequences.

Throughout these sections he gives multiple examples to help explain the concept and what is going on. He does this in a manner that everyone can understand. The his creative imagines he uses throughout the book and his sense of humor it is an easy read for even a non-mathematician to enjoy.

Even has a person whom has studied math for now 17 years, I learned some new ways to explain some math concepts that others cannot wrap their mind around. For example, why is a negative times a negative positive? This is how he showed it:

-1 x 3 = -3
-1 x 2 = -2
-1 x 1 = -1
-1 x 0 = 0
-1 x -1 = ?

If you follow the pattern on the right hand side, it is counting up by one so the ? would be a positive 1. I have never thought about a way to explain this to others that didn't believe this. However, I now have some what of a reasoning to show them why this is true. 

Overall, this book was an easy read and I would recommend this book to anyone who would like to know a little bit more behind how math works. He gives great examples that will stick with you. And you will sure get a kick out of his humor throughout the book. 

Some of my favorite quotes from the book:

"...math always involves invention and discovery..." -pg 5

"...even wrong answers can be long as you realize they're wrong." -pg 63

"Proofs can cause dizziness or excessive drowsiness. Side effects of prolonged exposure may include night sweats, panic attacks, and, in rare cases, euphoria. Ask you doctor if proofs are right for you." -pg 93

Saturday, October 10, 2015

Is Math a Science? Is Math an Art?

This is a question that has been debated for while. Everyone has a different perspective, opinion, and thought about the way they look at math as a subject matter. In order to answer these questions I feel like we need to define math, science, and art. According to the following are the definitions:

Mathematics: the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.

Science: a branch of knowledge dealing with a body of facts or truths systematically arranged and showing the operation of general laws.

Art: the quality, production, expression, or realm, according to aesthetic principles, of what is beautiful, appealing, or of more than ordinary significance.

Besides from looking up the definitions of the three words of interest, I researched others opinions and thoughts on the two questions, and also conducted a short poll (from my friends, not random!).  

Looking straight from the definitions I would say math is science and not art. This is because of the word systematically stands out in both definitions for me. Both science and math have a very systematic approach you take to solve a problem. For example, the scientific method is a systematic way carry-out an experiment and the order of operations is a systematic way to solve an equation. 
Art and math do not seem to line up, according to the definitions. In the definition of art, it seems to be expressing how art looks once it is done. Although I do not agree with this definition 100%, I had to be on fair playing field and grab them from the same resource. Therefore, comparing definitions I do not see a link between math and art. 

The results are in.....

Is Math Science?
Is Math Art?

I asked 5 of my friends both questions. Only one person said that math is art, which I found interesting. And it was almost a 50/50 split for if math is science. 

In my research online, I found that many other people who answer these questions are drawn down the middle as well. And almost all responses said it determines on how you think about math and how you define science and art. It's a tough question to tackle and come to a hard-set conclusion. 

Here is my opinion: 
Math is science because we follow laws, theorems, and other properties of mathematical concepts. 

Math is art because as a mathematician you have to use your imagination, creativity, and recognizance to see how to solve a problem. To help support this claim, I will provide you with the definition of art from the Merriam-Webster: "Something that is created with imagination and skill and that is beautiful or that expressed important ideas or feelings."

An example is proving a theorem. You have to first have the will, imagination, and creative thinking skills to work your way through the problem and then you then must also follow all the rules of math and other proven properties to finish the proof properly. And finally, once the proof is written formally with all justifiable reasoning, on clean-crisp paper, you can say that you have now created a beautiful piece of work that took skills and systematic methods. 

Now lets take a poll again....Is Math Science and/or Art?