Overview

Description

CALENDAR DESCRIPTION:

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics. Students may repeat this course for further credit under a different topic.

COURSE DETAILS:

Permutation Puzzles: A Mathematical Perspective

In this course we will play around with Rubik’s cube, TopSpin, and other fun, but challenging puzzles to develop an understanding of, and intuition for group theory. You’ll even learn some computing. The course begins with a handheld electronic game called Lights Out. We'll see how to use concepts from linear algebra to completely understand the puzzle and develop an optimal solution strategy. The course will then move on to the 15 Puzzle, TopSpin and other planar puzzles. We'll develop the theory of permutation groups as we proceed in investigating these puzzles. You'll learn enough group theory to make you a dangerous puzzle solver. We then move on to Rubik's cube and other 3D twisty puzzles, and we will apply what we learned in group theory to uncover the secrets of Rubik's cube.

Don't know how to solve Rubik's cube? Don't let that stop you. By the end of the course you'll not only know how to solve the cube, but you'll learn how to build you're own moves to solve hundreds of other similar puzzles.

You will learn how to use the mathematical software package SageMath to model these puzzles. Computing experience is not required, but can be helpful.

Assignments - Each assignment consists of 10-15 questions. Selected questions will be hand graded for correctness/clarity/presentation, and the whole assignment will receive a grade for completeness.  

Poster Session - This is an end of term poster presentation. Students work in groups of size 3, and create and 8 page physical poster (4 pages if creating a website or app). Each students will also give a 3-minute verbal presentation on the content in their poster. This presentation will be done multiple times in a one hour session, each time to a small group of students around their poster.  In the other 2 hours of the poster session students will be listening and grading posters/presentations of their peers.   

Students posters/presentations will be graded by the instructor, teaching assistant, peers, and special guests from the department of mathematics. Students will also be graded on the quality of their grading of their peers.

Grading

Materials

REQUIRED READING: