MTH 495

The simple answer to why math graduates are good to hire is that they are excellent problem solvers.  Every math graduate has been tasked to solve hundreds if not thousands of problems that take a high level of thinking.  These problem solving skills can then be applied to almost any line of work.  There are many aspects of problem solving that a math student would need to acquire in order to get their degree.  The aspects that I will further discuss are persistence towards a solution, knowing when to try something else, using all tools given, and giving structure and clarity within the solution. If someone with a math degree has ever faced a difficult math problem, then they most likely know the meaning of persistence.  Working at a single problem for hours on end can be something that isn't unusual when tasked with a difficult proof or problem.  I know that this has been the case in my experience.  Battling through frustration and growing certainty that there is no solution ca

I was thinking about how puzzles work and the nature of solving puzzles and I came to a couple of conclusions.   Generally, the way you go about solving any sort of puzzle is looking for a logical way to make some sort of progress, whether that be figuring out one number in a Sudoku puzzle or putting two physical puzzle pieces together.   If a puzzle allows all logical conclusions to yield significant progress then it is not a good puzzle because it fails to give the solver any sort of mental challenge.   There are many ways that a puzzle could be good.   One of them is having the first few logical conclusions be easily discovered, and then the final few would come with much more difficulty.   This would give the solver some hope before sprinkling in a little frustration.   Another could be a sort of middle of the road approach, giving relatively equal difficulty to any logical conclusions that could be necessary.   A third way would be to not give any logical conclusions that are easi

The book  e The Story of a Number  by Eli Maor is about the history of many mathematical concepts, including the number e.  Maor introduces each of the concepts he discusses through first describing the works and personality of the famous mathematicians who discovered or invented each of the concepts and then showing how the mathematicians came up with their discoveries.  He relies heavily upon anecdotes about the mathematicians to keep the reader who isn't already absorbed in the math engaged with the text.  Overall Maor's purpose seems to be to show that although e's history isn't widely known, it is related to or rooted in many other topics, some of which have much more extensive histories. If a reader didn't look at the title, he might not know the book is about e until he was over half through it.  This is most likely due to the fact that there isn't a lot of historical material on e as there is, for example, with π.  So Maor begins with the concepts l

The Mayans created a relatively complex numerical system for their time.  This numerical system was heavily intertwined with their astronomy, religion, and day to day transactions.  It was a base 20 system (vigesimal) that has been conjectured to have been created based upon counting toes and fingers.  Another possible explanation is that the number 20 was representative of life or humans and 400 was representative of the year (when dealing with calendars their number normally representing 400 did not mean 400 but it meant 360).  As shown below, the Mayan glyph for "being" (top) is of similar structure to the Mayan glyph for "twenty":  The Mayans were one of the first civilizations to use the number zero.  They utilized it as a placeholder in their number system to help with their calendar.  They had symbols representing zero, one, and five that could be used in association with their base system to represent any number they needed to: Some exam

Math to me is the means of providing the most precise way of representing what everything is and how all things interact.  One way of illustrating this could be to take a normal object such as a baseball and and its interaction of being thrown and then hit by a bat.  The ball is a sphere with 108 stitches, weighing 5 oz., made up of x molecules...  The ball can be thrown at up to about 105 mph at the bat which can be swung at about 100 mph creating a collision of so many Newtons over so many seconds.  Nearly every interaction can be quantified and an attempt to explain it with math can be made. Every object, movement, collision, thought, or decision can be measured in various ways.  We can define things like a bit of information that the brain takes in to the ones it puts out resulting in actions or thought to a rock that is sitting at a bottom of a lake.  The bits can be numbered, paths taken by the bits can mapped out, actions can be measured, and the rock can be weighed, or the pr