Foundations in Pure Mathematics
This is the course webpage for the Foundations in Maths class at Maseno University, First Trimester. We will post all of the course readings, assignments, and other materials on this page, so check back often.
Instructors: Dr. Tom Denton and Dr. David Stern
Meeting Times: Tuesday, 6-8pm and Friday 7-9am.
Overview of the Course
A good foundation in mathematics provides the kinds of creative critical thinking and problem solving skills that allow one to excel in a wide range of other fields, ranging from law to astrophysics. Sometimes mathematical techniques are directly applicable (such as in harder science areas, like engineering), and sometimes the ways that we learn to think about mathematics are more useful than the particular techniques learned (such as in law). In any case, a good foundation in mathematics can provide the ability to think clearly about almost any problem.
As such, this course is an introduction to mathematical thought. We will cover a number of topics that will allow you to create rigorous mathematical arguments, also known as proofs. Along the way we'll encounter concepts from a range of mathematical areas.
Every Wednesday, we will have an in-class quiz to check understanding of the course material. The questions on the quizzes will be derived either from material presented in class or the assigned homework. Thus, if you have done the homework, you will do fine on the quizzes.
We've made a resource CD with the following content:
- Readings for most of the course. Some of these readings are in pdf, and others are in djvu format. To read the djvu files, install the program WinDjView, which is included in the top-level directory on the CD. The latest version of the CD (r3) includes David Mond's lecture notes on the foundations of mathematics, which are also available from this website if you don't want to track down a copy of r3.
- Mathematical programs. these won't be used in the course, but could be useful for learning a range of other mathematical concepts. Especially, CAST for statistics and Geogebra for Geometry.
- Five episodes of Radiolab, an American radio show about science topics. These are a lot of fun, but not required listening.
We've left a few copies of the resource CD at the Maths Lab. To get a copy of your own, bring a blank CD and the lab technician will help you get a copy.
Assignments and Readings
Week One: Functions, Sets, and Cardinality
Week Two: Functions and Infinity
Some Fun Math Links
Vi Hart - Hyperactive videos about beautiful math concepts.
Snowdecahedron - A mathematical art installation.
Tau - An alternative to pi.
BBC Brief History of Math - A Documentary.
John Baez - A maths superhero.