Bertrand Russell and Ludwig Wittgenstein debate the foundations of mathematics.

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.

Continuous Assessment

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.

Resource CD

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.


15 Responses to SMA109-Foundations

  1. matta milton says:

    In today's lesson,quite sad on my side though i was very interested.I couldn't understand anything.could you help this during tomorrow's lesson please.I also suggest that you adjust on your audibility and analysis.Thank you and have a nice eve.

  2. tom denton says:

    Thanks for the feedback. We'll try to be more clear. Please interrupt us when you don't understand!

  3. Felix Getao says:

    Hei, i missed the first two classes which the second one a CAT was done. Are there any handouts available to help me catch up with the rest of the students. I enjoyed my first lecture.

    • tom denton says:

      Hi, Felix;
      If you scroll up a bit, there's a link to the readings and homework for the first week. Also, bring a blank CD to the maths lab and you can talk to the technician and have a copy of the resource CD made.

  4. stephen odeny says:

    try to give more examples for our understanding.

  5. my comment is about the venue of tuesdays 6:15-8:15pm lecture,i am suggesting that we change the venue of that lecture from tuition block 5 to millinium complex lecture halls,since millinium is central position for all.this is because the lecture time is night hours.

    • tom denton says:

      Hi! For now, let's stick with the current location and time for next week, as we discussed at the end of class. Good board space is hard to come by, and the room we were in last night had pretty great boards; additionally, it can be hard to change rooms. We'll discuss again at the end of next week.

  6. hello sir, i wanted to know job oppurtunity to a graduate who has done mathematics science as a course. And also if in third year of our academic one can branch to specialize in acturial , statistic and pure math.

    • tom denton says:

      David will have to reply on the specialization; I'm less knowledgeable of the specifics of the different programs.

      As for job opportunities, Kenya is sorely lacking in people with the kind of strong reasoning skills that are necessary to make all kinds of different institutions run. What we're aiming to do through this course is get you into the habit of thinking clearly and problem solving; if you build up these skills, you'll be imminently employable and adaptable to numerous kinds of work. It's worth noting that Kenya produces many many many students with actuarial sciences degrees each year, and yet there's only one certified actuary working in Kenya right now; the paper won't help you pass the actuarial exam, but good mathematical skills will. In fact, most actuaries in the US were math students who later took the actuarial exams. Put in the work and build your skills and you'll go far.

  7. Thanks Tom for your encouraging word am working harder to become a good mathematician i nowadays understand a good percentage of wat u teach thanks

  8. We are greatful 4 the progress we are making but cant we come up with more examples to aid understandng.n asist the absenties.

  9. Hae,my concern is about exams setting.because question one takes 3o marks then it should be conversant with large % of the stundents, since,the quiz so far handled prove that they are les than 30marks n for Godsake to show our fruits of being loyal n atentive wt regular quiz throughout the da best.

    • tom denton says:

      Hi, Robert;
      The point-structure of the exam is (I believe) based on University standards for the structure of exams. The core question will have a bunch of parts to it, hitting on basic knowledge of the course that everyone should be able to answer.

  10. We will be greatful to get out of exam room with smiling faces, if that is so.

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Some Maths 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.
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