Syllabus

Details

• Semester: Spring 2024
• Room: Evans 1015 (Enter from the third floor)
• Time: Friday 5-6 (Beginners); Friday 6-7 (Advanced)
• Starting Date: February 3rd
• Ending Date: April 27th
• Grading: 1 Unit P/NP only
• Office Hours: After class/By appointment/Instructor email
• Faculty Sponsor: Michael Hutchings

Objective

In this DeCal you will learn how to solve the Rubik’s Cube (Beginner section) or how to solve it much more quickly and efficiently (Advanced section), using concepts from group theory as they apply to the cube. Learning to solve the Rubik’s cube is a good way to build intuition for topics in abstract algebra without needing to worry too much about all the technical details, whether you plan to study mathematics or not. You will leave with better problem-solving abilities, improved understanding on the history and mathematics of the Rubik’s Cube, improved hand-eye coordination, increased finger dexterity, and a cool party trick!

Format

The format of this class will be a combination of lecture and group instruction, with a heavy emphasis on the latter. At the beginning of each class, we will give a brief overview of the lesson and then break into groups for the remainder of the hour. In these groups, you will practice the lessons taught during lecture with personal guidance from your group instructor (you will stay with the same instructor for the entire semester).

Content

In the Beginner section, we will be teaching the Layer-By-Layer method, which involves solving the cube “from the ground up”. In the last few weeks of class, we will be holding instruction on various topics such as solving the cube faster and solving other puzzles, or even solving the cube blindfolded! If you finish the basic curriculum early on, you will have the opportunity to learn more of these topics from your instructor.

In the Advanced section, we will be teaching the CFOP method, a more advanced version of the Layer-By-Layer method that many people learn. In addition, since more one-on-one instruction is available in the Advanced section, the class is much more flexible. If you have a particular cube-related topic that you would really like to learn, chances are there is an instructor who can teach it to you while or after you learn the regular curriculum. Just be aware that we expect you to fully learn the CFOP method that we teach, and utilize it in your solving (during the final and competition). Anything after that is up to you.

In both sections, students will learn how solving the Rubik’s cube is an application of group theory and the underlying mathematics taking place with each move. More specifically, we will discuss how the Rubik’s cube is an example of a group and explore what implications this has on the movement of pieces and potential permutations the cube can take. Algorithms we teach will be built up from the basics using easy to understand mathematical concepts, which makes them easier to remember as well as giving a deeper understanding of how the cube works. Of particular importance are the concepts of conjugation and commutators. Students will also gain familiarity with standard cube notation, which is taken from the notation of group theory. Particular emphasis is placed on notation in the advanced section.

Workload

Come to class

This is mandatory, as we will introduce a new topic each week and move fairly quickly through the steps. If you miss a class, you will be behind on material. Attendance will be taken weekly by your instructors — if you must miss a class, please let your instructor know ahead of time (unless it’s an emergency). We will allow 3 absences, either excused or unexcused. If you have 4 absences, we will fail you.

Work outside of class

Besides coming to class, you will need to practice on your Rubik’s Cube outside of class. This can be as little as 15 minutes per day, but obviously the more, the better. Practice hones your skills and helps you identify problem areas that you can then ask your instructor about during class. If you practice consistently, you will easily be able to learn the regular curriculum within the first few weeks. Additionally, you must read articles assigned every other week to further supplement your learning experience.

Do the readings

In both sections, there will be required biweekly readings consisting of articles and short documents on various aspects of the Rubik’s Cube. These articles will mainly highlight the mathematics and the history of the Rubik’s Cube and similar puzzles. Students will be required to do short exercises related to the readings.

Homework assignments will be released based on the readings (there will be around one every two weeks), and are graded on completion/effort rather than correctness

Pass the in-class examinations

Part 1: Solve the cube

For the Beginner section, this means solving the cube once in under 5 minutes or under 250 moves. You will have up to 5 attempts, if necessary. If you successfully solve the cube on your first try, you pass the test and do not have to complete your remaining attempts (unless you want to).

For the Advanced section, this means solving the cube in under 1 minute 15 seconds or under 85 moves at least once. You also must complete all five solves to pass.

Part 2: Take-home Exam

Additionally, for both sections, there will be a take-home final consisting of short answer and multiple-choice questions.

The take-home exam will test students on the semester’s readings and mathematical content, with emphasis on basic computations and permutation groups.

This portion is not required if you have full credit for homework, and you are able to solve the cube!

Grading

In addition to completing all the mandatory requirements for both the Beginner’s and Advanced section, a total cumulative grade of 70\% must be achieved in order to pass the class. Note that students will receive an NP if they have more than 3 absences. The breakdown is as follows:

Pre-requisites and Materials

For the Beginner section, the only prerequisite is that you have your own Rubik’s Cube to practice on. You will not be allowed to share with any other students. No other experience with the Rubik’s Cube or other puzzles is necessary, as we will teach you how to solve it from scratch.

For the Advanced section, you will also need your own Rubik’s Cube to practice with. You will not be allowed to share with any other students. In addition, you must already know how to solve the cube using any method before the first day of class. We would prefer that you know the layer-by-layer method; if you know another method, let us know so that we can tailor the course to meet your needs. This ensures that you have some experience with the cube and that you have some basic intuition with respect to how the cube works.

We will have cubes available for purchase for $10 at the beginning of the course. Cubes can be purchased from several online retailers, the largest of which is TheCubicle.

If you are confused on which section you belong in, talk to one of the facilitators during the first class, and we will determine which section you should take.

Special Accommodations

Please email one of the instructors (or talk to us during class) if you need special accommodations for anything!