Simon Fraser University
Engaging the World

Course Outlines

Spring 2021 - MATH 304 D100

Mathematical Journeys IV (3)

Permutation Puzzles

Class Number: 3590

Delivery Method: Remote

Overview

  • Course Times + Location:

    Jan 11 – Apr 16, 2021: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Prerequisites:

    MATH 152 or 155 or 158, and MATH 232 or 240. There may be additional prerequisites depending on the specific course topic.

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. Quantitative.

COURSE DETAILS:


This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable
Course Outline

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


COURSE DELIVERY

  •  Lecture: synchronous- lectures will be held at fixed times, on-line
  •  Midterm(s): synchronous; date: TBA
  •  Final exam: synchronous; date: TBA

Grading

  • Assignments 30%
  • Midterm 1 25%
  • Midterm 2 25%
  • Final/Poster 20%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION. 
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. 
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

MATERIALS + SUPPLIES:

Required: 

  • Access to strong and reliable internet.
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)

REQUIRED READING:

The textbook for the course is available here

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SPRING 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).