Difference between revisions of "Games and mathematics MA375S12Walther" - Rhea

Revision as of 14:49, 2 February 2012

Fun and Challenging Games Directly Related to Discrete Mathematics

For interactive games relating to our Discrete Mathematics class, check out these games that may help in understanding some of the chapters within our book, coming from our book, Discrete Mathematics and Its Applications: See Interactive Demonstration Applets for more games. For example: In Chapter 10, we see the below picture helps demonstrate concepts involving the Shortest Path Algorithm (Dijkstra's).

There are a variety of interactive games for Chapters 1,3,8,10, and 11 to help learn different discrete mathematics concepts while playing these interactive games!

In addition to computer interactive games, there are other ways to work our brains. An article from the publishers of the book we use in class, McGraw-Hill, points out the common mistakes made in Discrete Mathematics. The article starts out saying, In this section of the Guide we list many common mistakes that people studying discrete mathematics sometimes make. The list is organized chapter by chapter, based on when they first occur, but sometimes mistakes made early in the course perpetuate in later chapters. Also, some of these mistakes are remnants of misconceptions from high school mathematics (such as the impulse to assume that every operation distributes over every other operation). In most cases we describe the mistake, give a concrete example, and then offer advice about how to avoid it. To continue reading and working the brain to figure out why these mistakes occur, the link is: Common Mistakes in Discrete Mathematics. Examples of the common mistakes usually made are listed:

• Overusing the term “by definition” in justifying statements in a proof. For example, Franklin Roosevelt was not the President of the United States at the start of the country’s entry into World War II in December, 1941, “by definition”; he was the President because he had been inaugurated as such early in 1941 and had not died or left office. • Incorrectly starting a proof by assuming what is to be proved. A common occurrence of this in an earlier course is trying to prove trigonometric identities by starting with the identity and using algebra to reach A = A; this is not valid. Similarly, if we are trying to prove a set identity in Chapter 2, such as A ⊆ A ∪ B , it would be invalid to start with the statement A ⊆ A ∪ B . • Failing to change the variable in a power series when necessary. For example, if a power series has xk−1 and you need it to be xk , you can replace k by k + 1 throughout the summation (including the limits) and simplify algebraically: 􏱘∞k=1 k xk−1 = 􏱘∞k+1=1(k + 1) x(k+1)−1 = 􏱘∞k=0(k + 1) xk .

On a different note, for those of you who believe Self-Assessments are fun, there are multiple self-assessment quizzes available to you from Discrete Mathematics and Its Applications Seventh Edition - Kenneth H. Rosen

Slightly Easier Games:

For those of you majoring in Mathematics Education or would just like slightly easier games, here is a website which contains games for students all the way from kindergarden to eight grade. Math Playground Games For middle school and high school students, try this site for games. HotMath Games

An interesting article I found while researching was called Odds on: the maths behind game shows published by ABC Science. This article discusses how mathematics could be used on everyday game shows to put the odds of winning closer to your favor. Although it is an opinion piece, which quotes Simon Singh, about how math strategies are better than your chance instincts it shows different ways to better win prizes on game shows by switching to his methods. Game shows such as Deal or No Deal and Let's Make a Deal which were popular and are popular shows on television today are discussed.

Also, sticking with the same game show theme, John A. Rock wrote an article called Mathematics Behind Game Shows: The Best Way to Play in May 2008. There are many problems for practice involving all types of mathematics, focusing on probability mostly. The author makes the problems fun by using well known subjects in the problems; for example, The Price is Right, Jeopardy, Dodgeball, Find the Fake, Coin Flip, etc. These problems can be done by anyone for fun on your own or in group activities in a classroom.

If there are any requests for certain types of games or anything else, please let me know! Thanks, Carolyn Hanes

Opportunities Involving Math Games/Activities

Also, if anyone is interested in a fun math event to help out with then this event is for you! The Math Counts Competition is coming to Purdue and they are looking for some volunteers. Here is some information about what Math Counts is and how to get involved:

On Saturday, February 11, Purdue will be hosting the MathCOUNTS Regional competition here at Purdue University, and we are looking for volunteers to help out with the event. MathCOUNTS is a national middle school competition for students who excel in mathematics. MATHCOUNTS emphasizes fun and excitement through its signature competition program, which is entering its 29th year. Since 1983, over 6 million students have participated in MATHCOUNTS, and compiled data indicates that there is a strong correlation between participation and higher SAT scores, selection of STEM majors in college, and selection of STEM careers after college. The regional competition is a fun day where some of the brightest mathematics students in the region/state get to compete for a place in the national competition.

Volunteers will be needed from 8am to about 1pm. A volunteer can work all or a portion of the time. Their basic duties could include: helping with set-up and check-in, helping administer the tests; or help scoring the tests. Here is the schedule for the day. Volunteers will receive a free lunch and are invited to stay for the afternoon countdown round and awards. 8:30 a.m. Registration 9:00 Welcome and Introductions (10 min.) 9:10 Sprint Round (40 min.) 9:50 Break (15 min.) 10:05 Target Round (45 min.) 10:50 Break (10-15 min.) 11:00 Team Round (20 min.) 11:30 Lunch (provided - 1.5 hour) 1:00 p.m. Count Down (1 hour) in Class of 1950 Building Lecture Hall 2:00 Awards (following countdown)

Anyone who is interested in volunteering or has questions can contact Jerry Woodwar (jwoodwar@purdue.edu) or Vince Drnevich (drnevich@purdue.edu), Professor Emeritus, Civil Engineering, Purdue University.

The Math Club here at Purdue has speakers come and give talks about interesting topics related to Mathematics, check them out as well. Don't forget to participate in Project Euler if interested, which is the game posted below that was added! Thanks - Carolyn --Chanes 19:45, 2 February 2012 (UTC)

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Thanks for sharing info Carolyn.

I only want to add a little "game" I am beginning to play this semester- Project Euler. It is a small project initiated by Colin Hughes in which he and his peers posted mathematical challenges of all level, from novice (e.g. Problem 1:"Add all the natural numbers below one thousand that are multiples of 3 or 5." to extremely difficult (Problem 368: Kepmner Like Series).

What is interesting about project Euler is that it is like an Massive Multiplayer Online gaming experience for incredibly nerdy types (me, included)- you create an account, level up by solving more and more problems, score achievements, and share your answer to another user through problem-specific forums. Solving the problem alone is only marks the entrance to the Project Euler; the real challenge begins when you share your answer with other users to search for the most elegant (and therefore, beautiful) solution. For instance, I answered problem number 3 by writing a brute force program, thereby taking ~4-5 seconds to get my answer (any program that I write that takes more than a second to execute is an ill-written program). But I found another user who wrote a more efficient program that could do the same task in less than fraction of a second because he actually used his brain to recognize and craft a more efficient approach to the solution.

My aim is to solve at least one problem per week, starting tomorrow 23 January. This pace will certainly slow down as the difficult of the problem increases, and for anyone who wants to play the game together, please let me know at lee832 at purdue dot edu