Syllabus

Course information

Course title: Communication in mathematics
Meeting times: M,W from 1:30 to 2:45pm
Meeting place: ILC 313
Textbook: Laboratories in Mathematical Experimentation (Mount Holyoke)
Instructor office: MG 237-A
Office hours: T 12pm and W 3pm

This class satisfies the CID requirement in mathematics.

What this class hopes to accomplish

A bridge to higher mathematics: Continuing on the path of Math 187, this course will help you transition from computational mathematics to proof-based mathematics. Computational mathematics means solving well-defined questions using established techniques, such as in trigonometry or calculus. However in deeper mathematical study we ask much broader questions, and demand that the answers be accompanied by a proof. In this course we will practice proving theorems, and along the way we will participate in the whole mathematical process.

Research experience: In mathematical research, we are not told what statement to prove, but must instead ask good questions and investigate them methodically. 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 a statement or theorem.

Genres of communication: 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.

Technologies: We will visit just a few of the key technologies that mathematicians use to carry out and share their work. There are many mathematical programming languages, but we will use only Sage. We will typeset papers in LaTeX, and presentations in Beamer. Later on you will practice mathematical blogging by posting your work to this site!

What is expected of you

In-class work: All of our 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.]

Written work: At the end of each unit you will turn in a written article called a “lab report” which 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 turn in several smaller assignments such as drafts and extra exercises.

Presentations: You will be asked to give several very short presentations on your work, both indivdually and as a group. In total, these will be worth about the same as a lab report.