MATH 432 (2024) - Home Page

Welcome to the website for MATH 432: Discrete Mathematics. All course-related material will be available here.

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Announcements

• Assignment 4 is available below, due Friday 17 May.
• The test will be at 10am on 27 May (in the lecture time in week 12). See below for last year's test.

Course information

• Course information.
• Lectures are in Von Zedlitz 108 at 10am-11:50am on Mondays and Wednesdays. Typically these will be around 1.5 hours (but might run a bit longer on occasion).
• The course coordinator and lecturer is Nick Brettell. I have an office hour 4:10-5:00pm on Tuesday (in Cotton 427).

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Course notes and lecture notes

Course notes	Lecture notes	Extra material
1. Introduction	Lecture 1	Solutions to exercises (updated 6 March)
	Lecture 2
	Lecture 3	Assignment 1 solutions
2. Graphic, linear, and transversal matroids	Lecture 4	Assignment 2 solutions
	Lecture 5
3. Duality	Lecture 6
	Lecture 7
	Lecture 8
	Lecture 9
4. Minors	Lecture 10
	Lecture 11
	Lecture 12
5. Closure and Flats	Lecture 13
6. Cryptomorphisms	Lecture 14
7. Representability	Lecture 15
	Lecture 16
	Lecture 17
8. Connectivity	Lecture 18

Assessments

Assessment will consist of four assignments, and one final test. Each will be worth 20% of the final grade.

• Assignment 1, due 5pm Friday 15 March. (Note: earlier typos in Q7 and Q8d are fixed in this version)
• Assignment 2, due 5pm Monday 15 April,
• Assignment 3, due 5pm Thursday 2 May,
• Assignment 4, due 5pm Friday 17 May

Please submit your assignment via nuku.

You have two options:

1. you can either complete your assignment by hand, and scan/photograph each page and convert to a PDF. Please check that each page is present and legible before submitting.
2. you can use the mathematical mark-up language LaTeX, see below.

The final test will be 90 minutes, at 10am on 27 May (in the lecture time in week 12). See the 2023 test here.

Textbook

All material for this course will be in the course notes and in lectures, but you may also like to consult the text book "Matroid Theory" by James Oxley. I have a few spare copies I can lend out on request.

Student	textbook copy number
Fallon Hendrie	2

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Related material

Here I occasionally have links to related material that was touched on in lectures, but didn't have time to go in to detail.

• Projective space, projective geometries, and in particular the Fano plane (lecture 3)
• We touched on finite fields in lecture 4, in particular their existence and uniqueness.
• Near the end of lecture 8, we briefly mentioned that matroid duality has links with orthogonal complements in vector spaces, and parity-check matrices in coding theory.
• In lecture 16, we saw Pappus's hexagon theorem.

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LaTeX

By the time you reach 400-level courses in mathematics, learning how to use the mathematical word-processing system LaTeX is well worth your effort, especially if you are considering taking further mathematics. LaTeX is tailor-made for creating mathematical documents; for example, all the materials for this course (online notes, assignments, etc.) are made using LaTeX.

You can either install LaTeX on your own computer, or you can use a web interface such as Overleaf. Overleaf is a popular way to get started on LaTeX: you can create LaTeX documents in the cloud, using only a browser, and then download your output files. Creating an account is free. They also have a good guide to get started.

Alternatively, you can install LaTeX on your own computer. If you have a machine running Windows, you can install MikTeX. The equivalent LaTeX installation for Apple computers is MacTeX. You can then either use a text-editor of your own choosing, or an editor included in the LaTeX installation.

Inserting diagrams into your LaTeX document is very easy with the graphicx package. All you need to do is make sure you have saved your image file in the same folder as your tex file. Then call the package with the command \usepackage{graphicx} in the preamble. At the place you want to insert the image, use the commands \begin{center}\includegraphics{yourfilename}\end{center}.

If you want to create diagrams for your LaTeX documents using a graphics editor, one option is Ipe. Another option is to draw directly using LaTeX commands, using the Tikz library. For drawing graphs, there is also the library tkz-graph (though, admittedly, the documentation leaves something to be desired). See examples of graphs drawn in this way here.

I am happy to help if you have any questions about using LaTeX.