Proposal for the basic course in discrete mathematics

[Engström Alexander]

Dear all,

The math department is developing a new set of bachelor courses in line with the Aalto-wide reform. Right now we discuss the very first basic courses. The idea is more or less that the different programs will choose from 5-6 basic math courses to get a suitable profile. Right now Camilla and I are working on the discrete math course, and your input would be great.

Here are the boundary conditions:

(*) The course gives 5 credits and is taught during 6 weeks. For each week there is 4 hours of lectures and 4 hours of other activities.

(*) The course should not be overloaded by content, because then all the time is spent on learning as much as possible by heart, instead of actually doing some reflection and problem solving.

(*) The course should be fun! There should be good material from the start to support lecturers/professors teaching it even if they don't have a solid background in discrete mathematics.

This is the current sketch:

Basic course in discrete mathematics

The book is “Discrete Mathematics and Its Applications”, 7th edition, by Rosen. This is a great book and it should be used in the course.

Content per week Sections

1. Foundations: Logic and proofs 1.1-1.8  

2. Basic structures: Sets, functions and sums 2.1-2.5

3. Modular arithmetic 4.1-4.3

4. Induction and recursion 5.1-5.3

5. Introducing graphs 10.1-10.4

6. Planar graphs and graph coloring 10.7-10.8

During parts 1-2 the teaching/exercises could be of traditional type. During parts 3-6 the content is restricted enough to allow time for problem solving and deeper understanding. This should preferably be done in groups and assistants should be present to help whenever questions arise. For parts 3-6 there should be no exercise sessions of traditional type with solutions done on the blackboard. 

At the end of chapter 10 there are 25 suggested writing projects. A mandatory part of the course is that each student should write a one page essay based on one of the writing projects. (Typical writing project: Discuss what can be learned by investigating the properties of the Web graph; Describe the Chinese postman problem and explain how to solve this problem; Describe some applications of edge colorings)

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The current sketch will be revised for a meeting on Thursday next week. I have attached a copy of the list of contents of Rosen. If you want an electronic copy of the book, please contact me.

Best,

Alex