LATIN SQUARES

MATHEMATICAL STRUCTURESMAT 300 PROJECT

LATIN SQUARES

NAME: ______________________________

Latin Squares – Equivalence Relation: Tasks, Guidelines, and Suggestions

In agreement with the criteria that qualify MAT 300 for General Studies (L) credit for “ Literacy and critical inquiry”, a substantial part of the grade for the course will come from an extended writing project. The up-coming slides provide a description of the task, the objectives, guidelines for the work, and suggestions for the inquiry.
deliverables , time-line, and due dates.
The final deliverable shall be a .pdf file, preferably typed (length 8 to 10 pages with e.g. 1.5 line-spacing).
The paper should have a professional appearance, but most important are its technical mathematical content, and excellent communication of your results and arguments.
The final paper in hard copy is due Wednesday August 5 during class-time.
You are encouraged to work together and welcome to use available literature, including the internet. But the final paper shall be written individually and must acknowledge all collaboration, outside help, and use of the literature. You shall earn credit for the problems you solved, not for the solutions you copied.
Objectives
This project shall

give you an introductory experience to open-ended mathematical problem solving that explores a longer and coherent line of inquiry,
give you an opportunity to apply strategies, tools, and methods to larger problems than in routine textbook exercises, and
ask you to develop and practice communication skills that are essential to sharing technical findings and arguments.
Assessment criteria

Did your inquiry result in a string of results that build on each other ?
Did you employ proofs applying core material from MAT 300?
Did you clearly communicate your findings in a professional format suitable for the intended audience?
Project
Define a Latin Square of order n on a set S of n distinct elements. Give two examples of Latin Squares.
Isotopy
Define the relation , isotopy, on the set of Latin Squares of order n. Give both a verbal and symbolic definition.

Isotopy Is An Equivalence Relation
Prove that isotopy is an equivalence relation.
Relation between The number of Latin squares of order n& The number Of Isotopy Classes
From known literature – Comment on the relation between the number of latin squares of order n and the corresponding number of isotopy classes. (About 8 – 10 lines)