<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <title>Jeff's Math Web Page </title> <link type= "text/css" rel="stylesheet" href="mystyle.css"></link> </head> <body> <h1> Mathematics </h1> <div id="text"> <p> Mathematics at Mass Academy is considered to be a "Math Modeling Course," where seemingly complicated problems are solved through modeling and conjecturing. </p> <p> In this course, we often use a powerful mathematics program called "Mathematica." The input into this program is much like programming and I find it very difficult to use, yet I haven't found anything in Mathematics that it cannot do. The trick is finding a way to get Mathematica to like the code you put in. Here is a very small examples of what Mathematica can do with: <a href="PDF/AsessmentofMathematica.pdf">Scatter Plots</a>. Mathematica is very difficult to write in, but the output is rather amazing. </p> <p> We also commonly work on problems for Homework for exactly one week. These problems are thus aptly named POWs (no, not prisoners of war) or Problem Of the Week. Personally, I have not done very well on many of the POWs, but I am improving. They are usually problems that are slightly more difficult than normal and on is required to type up one of these papers for each one. The first POW I felt was easier than most. It involved meeting a set of conditions to find a group of numbers. Here is my <a href="PDF/POW1.pdf">First POW</a> so you can see for yourself. Another one of my better POWs was the second one. Here one had to find methods of counting the squares on a checkerboard (assuming they can overlap)Here is my <a href="PDF/POW2.pdf">Second POW</a>. This was one of the easier ones, but it required a number of simplifying assumptions. </p> <p> After completeing Junior Year and looking back, Math class was one our hardest classes. Compared to other clases there was not more homework, but it was far more difficult. One of teh interesting POWs we worked on was the <a href="PDF/ratpow.pdf">Rat Population Growth POW</a>. In this problem, which we worked on while studying recursive systems, envolved exploring a nonrestricted growth pattern. If an even amount of male and female rats were produced per litter, the females could only reproduce after being a certain number of days old,and none of the rats died, how many would there be after one year? Although the recursive from of the function is not extremely hard to understand, it is nearly impossible to find an explicit form of this equation. In fact, I never developed a true explicit form, but we were taught how to do so afterwards. Another POW that I found interesting was one relating to a card trick. Essentially a person takes a deck of cards, looks at the first card, and counts up a number the number of cards up to twelve(or puts it back in the middle of the pile if the card he or she looks at is a face card is a face card). This process is repeated until there are not enough cards. Then another person can guess the value of the sum of all the cards that the person looked at (the top of the pile) simply from knowing how many are left over and how many piles there are. If you have any interest in looking into it, <a href="PDF/cardpow.pdf">this card POW</a> is very entertaining. </p> </div> <div id="menu"> <ul> <li><a href="index.html">Home</a></li> <li><a href="pl.html">Personal</a></li> <li><a href="cs.html">Computer Science</a></li> <li><a href="rs.html">Research Seminar</a></li> <li><a href="hm.html">Humanities</a></li> <li><a href="ph.html">Physics</a></li> <li><a href="sw.html">Technical Science Writing</a></li> <li><a href="fr.html">French</a></li> <li><a href="en.html">Engineering</a></li> </ul> </div> </body> </html>