This assignment is the final deliverable for your project (worth 10 points). It is an individual, not a group, assignment and should be submitted by email, not on the OpenLab.

The Semester Project consisted of a number of related activities and assignments – before you begin writing, please take a look at the list and click each of the links to remind yourself of all the parts of the project.

Group Presentations Schedule : 12/1: Group 4 (Chris, Ihn, Luis), Group 3 (Amy, Irina, Jared) 12/3: Group 2 (Allison, Matt), Group 1 (Jack, Jodel, Denyese)

The last significant group assignment for your semester project is a group presentation (there will be one more individual assignment, a reflection on the process, which will be assigned near the end of the semester). I’ll put the details here, followed by an outline of the grading criteria. The presentation is worth 20 points total.

The group process paper will be worth 35 points towards your Project grade. I will be filling out the sheet below for each paper submitted. Please let me know if you have any questions.

In his essay A Mathematician’s Lament, Paul Lockhart says “A good problem is something you don’t know how to solve.” This is quite different from most of the “problems” that appear in our mathematics education. In the past weeks, you’ve all spent some time individually and in groups working on such problems, in the context of graph theory (“Bridges and Walking Tours”).

As a group, write an account of your experiences working on your puzzle/problem. You should include the following elements:

Description of the Bridges and Walking Tours problem, in your own words.

An account of working on your problem as a group, from playing with the problem to formulating and perhaps proving a conjecture. What did your group do/think/feel? You can include examples of puzzles and solutions if you wish, as well as work by individual group members completed outside the group (both optional). Your goal is not to go over every detail, but to tell a story that your readers will enjoy – “what was it like”?.

A statement of your group’s chosen conjecture, and a proof (or disproof) of the conjecture.

At least three images (more if you wish). They can include images of puzzles you’ve created or solutions, but you can also be creative with images or photos related to your puzzle, your group or your story in some way. Each image should have a caption describing. NOTE: You may freely use your own drawings, images or photos. If you wish to use photos from another source, they must be from a legal source (for example, Creative Commons licensed, with proper attribution – the library or your professor can help with this).

Basic details: the names of all group members, the date, course and section numbers, and your professor’s name.

I will be meeting with each group next Tuesday, November 10th, in class. Please be in touch with your other group members before then! Be prepared to discuss your progress so far – at the very least, you should be able to describe how you are dividing up the work of the paper among your group.

The first draft of this assignment is due in class on Tuesday, November 17. Each group should submit one paper, of no less than 1500 words. You may decide as a group how to divide up the work. Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.

The final draft of this assignment is due in class on Tuesday, December 1.

REGARDING SEMESTER PROJECT: As you may recall from the Course Description, the semester project is worth 10% of your overall grade. The project consists of a number of interrelated activities (many of which have already been completed) – complete details can be found on the Project Overview & Deliverables page. The group paper assigned here forms a significant portion of the project.

Your assignment for the coming week+ is to try to prove the conjecture that your group created in class on Tuesday, 10/20 (10/20 working space (Google Doc) with group conjectures is here). You may need to refine/expand your conjecture first (let’s discuss this in class). You must spend at least 90 minutes working on this. Trying to prove something can consist of many different activities, such as the following (you do NOT have to do all of these things – you can choose how to spend your time – they are provided for inspiration only).

In 2002, a mathematician named Paul Lockhart wrote an essay called “A Mathematician’s Lament,” a passionate criticism of mathematics education in America. It has become widely known among mathematicians and mathematics educators – not everyone agrees with everything he says (though many do), but everyone seems to have something to say about “Lockhart’s Lament,” as it is called. For this week’s assignment, you will read a short excerpt (three pages) from his essay and respond to the prompts below.

The assignment below is due BEFORE CLASS on Thursday, October 8th (it is essential that you complete it before class, as we will be doing a class activity building on the assignment).

We are going to play a game creating walking tours of cities with bridges. We begin in the city of King’s Mountain, which is built on four land masses – both shores of a river and two islands in midstream – connected by a total of seven bridges (shown in green).

EXAMPLE 1: Can you create a walking tour of the city that crosses every bridge exactly once? You can begin anywhere you like, and end anywhere you like, as long as you cross each bridge just once.

Background – Graph Theory

We can simplify the picture of King’s Mountain to make it easier to deal with:

The key elements of the map are the four land masses (let’s label them A, B, C, and D) and the seven bridges (p,q,r,s,t,u and v) (thanks to mathisfun.com for the images):

For the purposes of our problem, we can simply think about each land mass as a point (A, B, C, and D), and the bridges as lines connecting the points (p,q,r,s,t,u and v) – like this:

We call this kind of picture a graph – the points are called vertices and the the lines are called edges. Our goal of finding “a walking tour that crosses each bridge once” is now matter of tracing out all the edges without lifting our pencil (and without repeating any edge).

Assignment, Due Thursday 10/8 (beginning of class)

Warm up (This Warm Up is just for practice – you do NOT need to submit your answers – see below for the four-part Assignment to be submitted). The following examples build on the example above.

EXAMPLE 2: If you are given the freedom to build one new bridge in King’s Mountain (“make one new edge in the graph”), can you do it in such a way the walking tour becomes possible? Do it!

EXAMPLE 3: If you are given the freedom to destroy one bridge (“erase one edge”), can you do it in such a way that the walking tour becomes possible? Do it!

EXAMPLE 4: Construct walking tours for each of the following graphs (or decide if it is impossible).

Assignment. Your assignment has 4 parts.

PART 1. For each of the four graphs below (G1 – G4), decide whether it is possible to create a walking tour crossing each bridge exactly once. Post your solutions here (TO POST A SOLUTION, JUST LIST THE POINTS OF YOUR WALKING TOUR IN ORDER). If it is not possible to create a create a solution, say so!

PART 2. Challenge your friends: Now it’s up to you to build your own graph, and challenge your classmates to construct a walking tour (or to determine if it is impossible). It can consist of as many points as you wish, and as many bridges (edges) connecting them. You MUST label your points “A, B, C…” etc. When you’re finished, decide for yourself if a walking tour crossing each bridge exactly once is possible. Remember, the most challenging puzzles are the ones where the answer is difficult to determine. Post two puzzles in the comments. See the note “POSTING YOUR PUZZLE ONLINE” below for instructions on how to draw and share graphs online.

PART 3. Solve a friend’s puzzle. Leave a response to a friend’s posted puzzle, giving a solution. TO POST A SOLUTION, JUST LIST THE POINTS OF YOUR WALKING TOUR IN ORDER.

PART 4. The last part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt. Be sure to respond to each part:

Writing Prompt: Did you enjoy this assignment? Why or why not? Describe a connection between this assignment and our work in the class. (If you don’t believe there is a connection, try to imagine why we are doing this). Leave your response in the comments.

POSTING YOUR PUZZLE ONLINE. I recommend the site sketchtoy.com – it allows you to draw something, then click “SAVE” and get a link to your drawing. If you have another (free) solution that you’d like to use, that’s fine! You can post the link in a comment, and we’ll be able to click on it and view your drawing. Don’t worry if it’s not pretty! For example, here is a graph that I drew (can you find a walking tour that crosses all edges?): http://sketchtoy.com/67467556

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