**Instructor: **Andr*é*s 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.

**Grading**

Your grade will be based on your in-class work, your written reports, and short oral presentations.

All of your time in-class will be devoted to our research projects. Come to class every day prepared to listen, think, and discuss mathematics with your group. Buy a notebook just for Math 287 and keep careful track of your thoughts and data. Assign yourself homework each class so you can bring new ideas to the next meeting. Since attendance and participation are crucial to your success, absences will lower your grade rapidly. [Documented absences are always excused, and you may have one or two free unexplained absences.]

At the end of each unit you will turn in a written article called a “lab report” that summarizes and explains the results of your activities. The majority of your grade will be based on these reports, each of which receives a letter grade.

You will also be asked to give several (typically very short) presentations on your work, individually or as a group. In total, these will be worth about the same as a lab report.

Further details will be provided once we get started.

Additional information will be posted in this blog, and students are encouraged to use the comments feature. Please use full names, which will simplify my life filtering spam out.

On occasion, I post links to supplementary material on Google+ and Twitter.

[…] met Ian Cavey, an undergraduate at Boise State, about a year ago. He took my Communication in the mathematical sciences course. It was a pleasure to have him as a student. (You can see the slides of one of his group […]