## 287 – Coloring of graphs

November 9, 2014

I am posting here the nice slides on this topic made by Ian Cavey, Christian Sprague, and Mac Stannard. The slides are meant for a presentation of about 20 minutes.

## 287 New working groups

October 22, 2014

(This post is specifically for Math 287 students.)

Starting Monday, you guys should be organized in new groups. No group can have three members that are together in the current groups. When I arrive on Monday, the groups should already be formed. You guys should start working on the laboratory on Polyhedra, Chapter 7. Make sure to bring whatever materials may be needed for this.

There have been complaints about not everybody contributing their share to their respective groups. This is not acceptable, but it is sadly the main reason for the reorganization. So: If I receive two complaints about a member not contributing as required, and there are no reasonable extenuating circumstances, that person will be dropped out of their group (receiving a zero in their current project as a result). If the issue is not expected to be resolved for the next report, a new reorganization of groups will be triggered as a result.

Also, I am unhappy with the level of some of the reports. It seems the peer reviewing of other groups’ drafts is not being taken as seriously as needed. So: Now, on the dates drafts are due, each group should bring three copies of their current draft. When you review another group’s draft, write the members of your group on the copy you are reviewing. I’ll collect the copies, with your comments, copy them for my records and return. If I identify something that a group should have noticed and mentioned, but did not, that group will be penalized (since this means the group did not take their refereeing role seriously). Conversely, if a group mentions something that should be addressed, but I do not see the issue resolved in the final report, the group that failed to address the given comments will be penalized.

Finally, this being a mathematics course, I expect your projects to include proofs. If a project lacks proofs it will receive a failing grade.

Feel free to contact me be email if any of the above needs clarifying.

## 287 Communication in the mathematical sciences – Syllabus

August 24, 2014

Instructor: Andrés E. Caicedo
Fall 2014

Time: MW 1:30-2:45 pm.
Place: Mathematics building, Room 139.

This class satisfies the CID requirement in mathematics.

Contact Information

• Office: 239-A Mathematics building.
• Phone number: (208)-426-1116. (Not very efficient.)
• Office Hours: W 12:00-1:15 pm. (Or by appointment.)
• Email: caicedo@math.boisestate.edu

Textbook

MR1443666
Mount Holyoke College
Laboratories in mathematical experimentation. A bridge to higher mathematics.
Textbooks in Mathematical Sciences. Springer-Verlag, New York, 1997. xx+278 pp.
ISBN: 0-387-94922-4.

Contents (Thanks to Samuel Coskey for suggestions)

The course decription at the Department’s site describes this course as follows:

Integrates mathematics content with the opportunity to develop proof writing and communication skills important in the mathematical sciences. Content is drawn from discrete and foundational math and elementary analysis. Introduction to and engagement with written and verbal communication practices characteristic to mathematical sciences. Introduction to and use of technologies that support communication in the mathematical sciences.

Following up on the theme introduced in Math 187, this course will help you transition from computational to proof-based mathematics. Skill at computations is of course still essential. However, in deeper mathematical study, we ask broader questions, and require that the answers be justified by proofs. In this course we will practice proving theorems, and along the way we will participate in the whole mathematical process.

A key realization is that, in actual mathematical research, we are not told what statement to prove, but must instead ask good questions and investigate them methodically. Even if there is a statement we are interested in, we typically do not know whether it is indeed true. In this class we will get practical experience in discovery, conjecture, and exposition of mathematical truth. We will learn to gather data to inform our conjectures, usually with the aid of a computer program. In the process we will learn to distinguish between evidence and proof, and to use both in support of our statements.

In most classes, you are expected to work individually and you are assessed in a timed environment. In a CID course such as this one, we focus instead on the activities that actually take place in the discipline: collaboration with our peers, writing research papers, attending and giving talks, and so on.  Accordingly, we will take a look at some of the key technologies that mathematicians use to carry out and share their work. There are many mathematical programming languages, but we will use Sage. We will typeset papers in LaTeX, and presentations in Beamer.

LaTeX

Please visit Sharelatex, where you can start practicing right away and work in groups. LaTeX has been the primary tool for the dissemination of mathematics (and many other sciences, take a look at the ArXiv to get an idea of how widely used the program is), and it has been so for almost 35 years, even though it has changed very little in that time. It is important to master the LaTeX system, since the language it provides for expressing mathematics will certainly be the standard for many years to come. MathJax and other technologies are expected to eventually replace LaTeX as the standard, but for the time being, knowing it is essential. for instance, Scott Aaronson lists as the first of his Ten Signs a Claimed Mathematical Breakthrough is Wrong that the authors do not use (La)TeX.

LaTeX is available as free software, and abundant documentation exists. A few useful references are The (not so) short introduction to LaTeX, the NASA guide to LaTeX commands, and The comprehensive LaTeX symbol list. I recommend that you also bookmark and visit frequently the Q&A site on Stack Exchange.

Beamer

Beamer is a LaTeX documentclass designed especially for creating powerpoint-style presentations. The output is a pdf file that you can click through page-by-page while you speak. In the code, you simply enclose each slide within \begin{frame}{My Title} and \end{frame}. Inside, simply use the LaTeX commands that you are used to. The ultimate Beamer reference is the full user guide, but this may contain too much information, and to get started the less intimidating short intro (and its source) may be more useful.

Sage and python

Sage is a computer algebra system and programming language. In the long term, knowing it may be just as important and useful if not more than knowing LaTeX. While you are welcome to use any language you prefer, I recommend Sage because it is free to use online, and has been developed as open source software from the beginning. The recently developed Sage Cloud makes its use even more convenient.

When getting started, check out the guided tour or the introductory video series. There is also a nice web site for the nuts and bolts of Python at learnpython. You can start using Sage very quickly by logging into sagenb.org using your google mail account.