## What is it?

Since January 2008, the NSML is pleased to begin a program which helps high school students learn to write formal proofs. For those teams who participate in the NSML, this is an excellent way to prepare for the Power Question component of the provincial final. Even if your school does not participate in the NSML (yet), you are more than welcome to try the questions and submit them to us.

At the end of the year, a certificate will be given to the team with the highest overall mark.

## How does it work?

At the start of each month, two questions will be posted via the links below. Students will have one calendar month to work on the questions.

Once solutions have been written for the questions, they can be submitted for marking. Each school may submit two solutions to the address below. It is acceptable to submit the same solution written up by differing groups of students. Each solution will be given a mark out of ten. Please feel free to encourage your students if they are unable to complete the problem but have made a fair amount of progress, to submit their solutions for partial marks.

We encourage working in groups to solve the problems, as this parallels how the power questions are done during the provincial final. If possible, try to limit the number of students working together to four or less.

We will be more than happy to send marked solutions back to the schools. If you would like to have your school's marked solutions sent back to you, please include a stamped, self-addressed envelope with your submission.

## Mailing Address

Please mail completed solutions to:

Meghan Rose Allen

Department of Mathematics and Statistics

Chase Building, Dalhousie University

Halifax, Nova Scotia

Canada B3H 3J5

If you would like to submit electronic copies of your solutions, please send them to ameghan@mathstat.dal.ca

Letters must be postmarked by the last day of the calendar month to be counted in the standings. E-mail submissions must be received before 23.59 of the last calendar day of the month to be counted in the standings.

## Questions/Solutions/Results

Please note that the questions may vary in length and difficulty. This is to help us determine at what level our provincial final power questions should be.

Month |
Questions |
Solutions |
Results |

September | Questions | Solutions | Results |

October | Questions | Solutions | Results |

November | Questions | Solutions | Results |

December | Questions | Solutions | Results |

January | Questions | Solutions | Results |

February | Questions | Solutions | Results |

March | Questions | Solutions | Results |

April | Questions | Solutions | Results |

## Tips On Writing Full Solutions

From Daniel R. Grayson, Professor, University of Illinois Urbana-Champlain:

- Use complete sentences, correct grammar, and correct punctuation.
- Don't submit your first draft. Read it, get someone else to read it, and find out where it's unclear.
- Don't expect mathematical formulas and figures to speak for you. Refer explicitly to each one and tell the reader what you want the reader to get from it.
- Many mathematical adjectives and nouns have precise mathematical meanings, and an English synonym will not serve as a replacement. For example, "element" and "part" are not interchangeable when referring to an element of a set.
- Look at examples of writing proofs well in the book, and try to emulate the style.
- Global organization of a proof is important. Tell the reader what you are about to do, and then do it. Use paragraphs to delineate the parts of a proof.
- Define all symbols before using them.
- Start each sentence with a word, not a mathematical symbol.
- Two mathematical expressions or formulas in a sentence should be separated by more than just a space or by punctuation; use at least one word.
- When proving a statement of the form P implies Q don't mistakenly prove Q implies P by starting with Q and deducing something from it.
- Words have meanings: be aware of them. For example, an equation has an equal sign in it.
- Never say "it is easily verified that ..." or "it is easy to see that ...". The temptation to write such a phrase indicates you know some further justification is required, so provide something with content.
- Don't use abbreviations.

## Typesetting Mathematics

For those wishing to type their solutions, LaTeX is an obvious choice; NSML's questions and solutions are all typed using LaTeX. Information about installing and running LaTex can be found here. A good starting point to learn LaTeX basics is Getting Started With LaTeX.

Most versions of Microsoft Word also have a mathematics editor, although it is clunkier and not as pretty as mathematics typeset using LaTeX.