DueDate: 0504 23:30PM Beijing time; a minimum of 650 words;
Assignment: Maths Game for Fun
Many people who are not professional mathematicians enjoy exploring mathematical problems or puzzles. Write an essay on a mathematical topic that a hobby mathematician would find interesting and stimulating. Your readers do not necessarily have a deep mathematical training. You may assume that they know arithmetic and elementary algebra and geometry, but not much more.
The topic of your essay will be the following game of strategy between two players, whom we will here call A and B. A stack of cards is given initially. It may contain an arbitrary number of cards. A player whose turn comes may take between 1 and 5 cards; how many they take is their choice. Player A begins. The last player who can make a move has won the game. (JUST FOR EXAMPLE)
You can explore some of the following questions: How should the players behave? Is there a strategy by which one of the players can force a win, no matter what the opponent does? How does it depend on the initial numbers of cards? For given numbers of cards, how many rounds must at least be played before the game ends? What is the longest possible game?
This list of questions is intended to stimulate your imagination. Answer some of them or invent others. Pick one or a few problems in this topic that are interesting to you and to your target audience. (You probably should address the question about a winning strategy.) Present ways to address these problems. You will get credit for the solutions you find even if not all solutions are complete. You may describe partial answers and ideas that would allow you to go further, but you should point out any gaps in your argument. You may even point out additional questions that a reader might want to explore.
Make sure to construct a coherent essay with a clear logical structure. Don’t try to work through all the questions – that would produce an essay with many loosely connected pieces.
Make sure that your essay is comprehensible on its own. Your readers won’t have access to this assignment sheet, and you do not need to reference it.
Keep in mind that your intended readers will read your essay for entertainment. Choose your material well and motivate why you find it interesting. Write a lively, engaging prose. Your essay should entice the reader to read on. Find a captivating title. You may even be able to cloak the rules of the game in a captivating story. There’s no reason why the players need to be called A and B; you can change that if you have a better idea!
You may discuss your ideas with your classmates, but you must pick your material yourself and you must write your own essay. You should demonstrate in this assignment that you can tackle a mathematical problem on your own and solve it with original ideas. You are, of course, free to consult any published sources. Remember to cite them properly.
Marking Criteria
This handout provides you with a list of some of the criteria according to which your essays will be assessed. This is not a definitive list, but it gives you an idea of the key points that I will be looking for.
- Content and organization (80% of mark)
_ Does the author raise interesting and challenging problems?
_ Does the author try interesting approaches to solving the problems?
_ Are the solutions correct?
_ Does the essay give a good motivation for studying the topic?
_ Is the level of the presentation appropriate?
_ Is the text clearly structured?
_ Are the relationships among its parts clear?
_ Is the internal organization of paragraphs and sections good?
_ Is there a captivating introduction and a satisfying conclusion?
- Style and layout (20% of mark)
_ Is the writing clear?
_ Is the prose engaging and entertaining?
_ Is the report free of grammatical and spelling mistakes?
_ Is the mathematics typeset correctly (including punctuation)?
_ Are the figures (if any) placed and labelled correctly?
_ Are all sources referenced correctly?
_ Do margins and spacing look good?
Note: Remember to reference all figures that you did not draw yourself. To do that,
include in the caption text like \(Taken from Ref. [2])”
Failure to reference your sources appropriately constitutes academic misconduct.
General Requirement:
Grammar, spelling, formatting, etc. are all very important.
English language using must be very good; all sentences are well organized with strong logic!!! Avoid long sentence in your essay!!!! If the expression or construction is cumbersome or difficult to read, consider rewriting. Not write a sentence for 3 lines without punctuation Please note that clear, concise, and correct writing will be considered in the evaluation, you may lose points for writing that impedes communication: poor organization, weak paragraph development, excessive wordiness, hard-to-follow sentence structure, spelling mistakes and grammatical errors.