Math 287, Spring 2014: Class Announcements


Welcome to the class! Class announcements and useful documents will appear here. New material will be added at the top. Make it a habit to look here.

Office Hours and Schedule

My office is MB240A. I have M287 (Communication in Mathematics) 12-2 pm T/Th and M406 (Number Theory) 10:30-11:45 am WF. I have logic seminar on Tuesdays at 2 pm. My official office hours will be 10:30-11:45 T/Th and 3:15-4:45 T/W/Th/F effective immediately. Students should be warned that afternoon department meetings or colloquium talks may cause 3:15 office hours to be cancelled; I will provide notification of this on my door, and will try to provide other notification online when I can. I will very likely not be on campus on Mondays; on the other four weekdays I will usually be on campus from 10:30 (or possibly earlier) to 5. If I am in my office I will usually be available to you.

Announcement: During the last two weeks of class Dr. Coskey will lead activities, as I need surgery soon after April 25th. I will be assigning final grades in the class, but I will be doing this from home later.

Unit 4 Status

Unit 4 will officially be due (a lab report in the style of Units 1 or 3, and you may tell me in email where I should find relevant Sage files recording your experiments) at the beginning of class Tuesday the 29th. I will evaluate these labs when I am computing your final grades after I am out of the hospital. Dr. Coskey should not be spending class time on Lab 4. I will be looking for evidence of activity and quality of writeup more than completeness; there is plenty of material in this lab, and a final version would contain even more, and I know we have not spent that long on it. Be sure to turn in your individual proofs for Question 1 along with your lab reports.

Also be sure to bring your clickers this Thursday. I shall try to do a brief intro to them so that Dr Coskey can start out quickly with the lab he will do with you starting next week.

Here is the text for Lab 4 (now complete). I am quite deliberately going to release it bit by bit rather than all at once (there are places where I want you to discover things which I will say openly later). The text may be a bit longer by Tuesday (when you will be able to start) or Thursday (when we will all start) but I won't show my whole hand all at once. You can also look at my Lab 4 file on Sage; please make your own copy rather than editing mine, of course. There is quite a lot more in the Sage file than in the lab text!

You may notice that I have cleaned up the files in the public Math 287 project. I have left files there that I identify as belonging to particular people, but please make a habit of keeping your working files in separate projects shared with your group members (and me).

Things to know before the first meeting

The book seems to be out of print. Please order a copy of Laboratories for Mathematical Experimentation, a bridge to higher mathematics, authors Cobb et. al. ISBN 0-387-94922-4 from Amazon or another used book outlet online. The statement on the shelf at the bookstore that the text is available as a free download is as far as I know incorrect.

Please do get a clicker. This was something the original instructor ordered for the class; he no doubt had some ideas of how to use it: I have a general idea about this and no doubt will develop specific ideas.

If you have a laptop computer please bring it with you. I want to know whether people can reliably connect to the university wireless in the room. It is not necessary for everyone in the class to have a computer, but it is advisable for the activities we have in mind to have a computer for at least one student in each working group. I need to know what our tech situation is right at the outset so that we can take any special measures that are needed promptly.

It is a good idea to set up your free Sage account (see links below) before the first session.

You should have a lab notebook dedicated to this class.

Lab I Iteration of Linear Functions

page 1 in the book. The computer code in the book is ancient, to be replaced by code supplied in my Sage project (which you can see that I have copied from Dr. Coskey; correct attribution of sources is important!) on Dr Coskey's site

My code project in Sage is at

You will need to make a free Sage account to access this, and you should copy the code I provide into your own Lab I Sage project.

We will start working on this in class as soon as we can (hopefully on day 1). I am not setting due dates until I see how the first day goes. More details of what is expected as a final product to appear!

What you should be doing is addressing the questions one by one in your lab group (somewhere between two and four students). You need to write something down in connection with each question. You should have a place to write things down: that is, you should have a lab notebook for this class. This should be some English (complete sentences) supported by evidence which you will describe (Sage computation of examples, a general algebraic computation that ought to work in all cases, an actual proof) for your answer to each question. This class is about communication: you are investigating a mathematical problem and communicating to me and/or your colleagues in your group and/or your colleagues in the whole class both what your solution is and what evidence you have for it. The process of investigation and reporting of results is just as important or more important than the specific content.

Resources is the home of the online SAGE computer algebra system, which we will be using as a resource. is the home of an online LaTeX editor. We will be learning LaTeX in this class, as this typesetting program is in effect the standard for mathematical communication. There is also a LaTeX environment integrated into SAGE.

The manual of logical style This is a document about proof style which I have been working on for many years and which exists in multiple versions. It will need revisions for use in this course, I am certain, which will be manifested here. Dr. Coskey's WordPress site for his past offering of Math 287. We will have our own WordPress site soon. I like his syllabus and his rubric for Lab Reports; take a look at these; I will have to make my own rubric for lab reports in due course.

Lab Report Criteria

You may notice that I have taken this straight from Dr. Coskey's class resources. I may make revisions to this as I see how the class goes.

Most of the actual investigation and experimentation will be done during class time. For homework, you will be asked to document the results of your experiments in the form of a lab report. Make sure that you keep a notebook for your classroom experiments so you can still reference them when you go home to write up your report!

Guidelines for writing

Lab reports consist of at least three sections, outlined below. In the Introduction, the textbook describes one possible layout for your write-ups. You may follow their advice, or alternatively, mine here:

Section 1: Begin by writing an introduction explaining the topic of the module. Assume that your audience is somebody who is familiar with mathematical language, but not necessarily with this particular topic. Be sure to include motivation for studying this topic, either from the text or from your own thoughts. Write careful definitions for any of the fundamental concepts used in the module (again, remember your audience). Finally, preview some of the questions you will be addressing in the upcoming sections.

Section 2: In this section, describe the technical results of your investigations. Results come in three types: examples and counterexamples, conjectures supported by experimental evidence, and theorems supported by formal proof. Provide context for each of your results, giving thought to the order in which you give them and the transitions between them. Try to state each result as a mathematical statement using language which is as precise as possible. Sometimes, you have more results than you have space to write up, and in that case choose the most important ones. Be sure to include at least one formal proof in this section.

Section 3: In the last section, summarize the state of your progress on this line of research from a very high level. Always include material for further research—it is impossible to answer everything in one go! What were the questions you were unable to answer, and why are they important to you? Did you make any further conjectures that you are currently unable to support with solid evidence or proof?

Grading rubric

Your labs will be assessed on the following four criteria:

Exposition: The quality and effectiveness of your writing, not including proofs. Includes introduction and motivation, presentation of results, style, structure, and clarity throughout.

Proofs: The quality and clarity of your technical mathematical writing, that is, the statements of results and definitions and the proofs of results.

Depth: The strength and completeness of your experimental and theoretical results, scientifically speaking.

Synthesis: How well you conveyed understanding of the results and goals of the lab as a whole. This can be done in many ways, including: summarizing results, motivating and asking questions, making conjectures, and drawing connections between the results, evidence, and conjectures.

Current Activities and Resources: working in Unit II [old]

We are currently working on Unit 2 on logic and proof. I would like any proof write-ups from the first couple of days turned in by Tuesday the 25th. I will have the ones that I have in hand from the 18th reviewed and back to you on the 25th (I was distracted with getting the computer lab ready).

Here is the promised summary of what is required. I expect in-class work on this unit to be finished by Thursday March 6, though I may accept computer submissions longer than that. This isnt a guarantee, of course: it depends on how things go.

Here is the Python source code for the theorem prover. I may make improvements: I will advise you if you should download a new version. (As of 2/25/2014, you should download the new version – it has much better display, spaces added for readability and no dots! 2/27/2014 there is a minor improvement to the display)

I have reorganized the actual Lab 2 file in the shared Sage project so that it looks like a tutorial more or less following what we did in class, and added some helpful notes. The actual assigned work is preserved in comments at the front. Notice that there are also some writing exercises. I will do at least one more extensive demonstration proof.

We are not in a hurry; we may spend a couple of days working with the software giving you time to get friendly with it, and there will be more discussion of format for proofs in English:

The manual of logical style This is a document about proof style which I have been working on for many years and which exists in multiple versions. It will need revisions for use in this course, I am certain, which will be manifested here.

here is the document with the axioms for the inclass proof writing exercises.

Current Activities in Unit 3 (old)

Currently, we are in the middle of Lab 3. By request from the class, I have moved the due date for Lab 3 to end of class on Tuesday April 8th. The report on Lab 3 should be of the same general kind as the report on Lab 1: I am especially interested in statistics and graphs giving summaries of your numerical experiments, in this lab.

I have not made a formal requirement that you turn in a draft, but if you do turn in a draft of your project materials before the end of the day Thursday the 3rd, I will review it and get comments back to you before the weekend.

There is an additional proof question which you may work on (easier than question 5 I would say): show that if you take two steps of the Euclidean algorithm the remainder you get will be reduced by a factor of more than 2 (will be cut in half and then some). This fact tells you something about why the algorithm is fast (and perhaps about what kind of function of N the number of steps to compute the gcd of two numbers less than N will be). Here are the notes on this.

I believe that everyone understands how to retune Euclid1 to return the gcd value instead of the number of steps: I do point out that you could actually make separate copies of the functions Euclid1 to Euclid3 for each kind of output, as one student at least has done.

I'll have more general guidance about the lab to offer at the beginning of the period on Thursday the third. Here are some notes of guidance for working on your Lab 3 report.