Trent University, Winter 2009

Mathematics 2084H - *Recreational mathematics*

(Formerly Mathematics 284H.)

**Prerequisite:** A Grade 12 Mathematics credit or equivalent and two full credits in any subject(s) at the 100 level, or permission of the instructor. Not for credit towards a major in Mathematics.

**Exam Period Office Hours**

(Potentially subject to change...)

10:00-12:00 on Monday, 6 April, 2009.

~~10:00-12:00 on Thursday, 9 April, 2009.~~

10:00-12:00 on Monday, 13 April, 2009.

10:00-12:00 on Thursday, 16 April, 2009.

10:00-12:00 on Wednesday, 22 April, 2009.

(All in GCS 337.)

Stefan Bilaniuk

*office:* GCS 337

*hours:* Monday & Tuesday 12:00-12:50, ~~and~~ Thursday ~~& Friday~~ 11:00-11:50, and Friday 13:00-13:50, or by appointment, or just drop by...

*phone:* 705 748-1011 x7474

*home phone:* 705 742-7862 (Do *not* call between 10 p.m. and 8 a.m. unless it's an emergency.)

*e-mail:* `sbilaniuk{at}trentu{dot}ca`

*web:* `http://www.trentu.ca/mathematics/sb/`

Mathematical Recreations and Essays (Thirteenth Edition), by W.W. Rouse Ball \& H.S.M. Coxeter

Dover Publications, New York, ISBN 0-486-25357-0

*Lectures:* Monday 15:00-15:50 in GCS 103, Tuesday 11:00-11:50 15:00-15:50 in OCA 206, and Thursday 16:00-16:50 in GCS 103.

*Seminar:* Thursday 12:00-12:50 in EPC 101.

There will be six fortnightly assignments, a project, and a take-home Ūnal examination. The assignments will be handed out and collected every other week, the project will be due at the end of the term, and the Ūnal examination will be written during the examination period and will be due at its end, on Friday, 24 April. The final mark will be calculated as follows:

Best 5 assignments (5 @ 10% ea.) | 50% |

Project | 25% |

Final Examination | 25% |

Work submitted after the due date will not normally be accepted unless it was late due to circumstances beyond your control. Note that there is no requirement to attend classes, but the consequences of not doing so are your responsibility to manage. Note that MATH 2084H will not make use of "personal response systems" such as clickers.

This scheme may be modified for students in *exceptional* circumstances. Any such modification will require the agreement of both the student and the instructor.

We will cover various recreations which have mathematical content and the mathematics behind them. The topics covered will probably include magic squares, puzzles of various sorts, some toys and tricks with mathematical content, and polygonal dissections and tiling problems. Additional topics may be covered in class, depending on time and interest, and on the projects.

The obligatory statement concerning **academic dishonesty** reads as follows:

Academic dishonesty, which includes plagiarism and cheating, is an extremely serious academic offense and carries penalties varying from failure in an assignment to suspension from the University. Definitions, penalties, and procedures for dealing with plagiarism and cheating are set out in Trent University's Academic Dishonesty Policy which is printed in the University Calendar and on the university web site at:http://www.trentu.ca/deansoffice/policies\_dishonesty.php.

For clarity, the following guidelines will apply in MATH 2084H:

Students are permitted and encouraged to ask anyone willing (especially the instructor!) for explanations, hints, and suggestions on the assignments and projects, and to consult whatever sources they wish, with the exceptions that

students may not consult the work returned to other students until they have submitted their own and may not consult anyone who has taken a similar course recently or their work. However,all work submitted for credit must be written up entirely by you(with the exception of group projects), giving due credit to all relevant sources of help and information. The take-home final exam will have more restrictive conditions that will be spelled out on the exam.

In some circumstances you may also be eligible for special help or accommodation. The obligatory statement concerning **access to instruction** reads as follows:

It is Trent University's intent to create an inclusive learning environment. If a student has a disability and/or health consideration and feels that he/she may need accommodations to succeed in this course, the student should contact the Disability Services Office (Bata Library Suite 109, 705 748-1281,disabilityservices@trentu.ca) as soon as possible.

Some or all of these may prove useful. Others may be suggested by the instructor, depending on the topics covered.

- New Recreations With Magic Squares, W.H. Benson & O. Jacoby

Dover Publications, New York, 1976. (ISBN 0-486-23236-0) - Various articles and books by Martin Gardner.
- Polyominoes, Solomon W. Golomb

Charles Scribner's Sons, New York, 1965. - Old and New Unsolved Problems in Plane Geometry and Number Theory, V. Klee & S. Wagon

Mathematics Association of America, 1991. (ISBN 0-88385-315-9) - Polyominoes, George E. Martin

Mathematical Association of America, 1991. (ISBN 0-88385-501-1) - Various articles and books by Raymond Smullyan.

Here are some links to (mainly lists of links to) web sites on recreational mathematics:

- Recreational Mathematics page at the Canadian Mathematical Society
- David Eppstein's links on recreational mathematics
- Recreational Mathematics Links compiled by Michael Gilleland
- Math Recreations directory at Google
- Journal of Recreational Mathematics (Sadly available only in print except for some sample material online.)
- The Unreasonable Utility of Recreational Mathematics, Chronology of Recreational Mathematics, and List of material on Recreational Math, by David Singmaster
- Recreational Mathematics links compiled by Mario Velucchi
- Recreational mathematics, main article at Wikipedia
- Recreational Mathematics Links compiled by David Wilkinson
- Recreational Mathematics index on Wolfram MathWorld

- MATH 2084H Course Outline
- Assignment # 1, 2, 3, 4, 5, 6
- MATH 2084H Projects
- Take-home Final Exam

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 2009.04.09.