Math 5300

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Table of contents

Math 5300: Computation in Mathematics for Teachers

Course description:

This course will explore the relationship between mathematics and the use of computers. The topic of digital images and computer graphics will be a main focus this term and the mathematics behind popular image manipulation software. Students will learn how computers represent images and then how subjects learned in high school such as calculus, linear algebra and discrete mathematics relate to computer graphics and digital image processing.

The book for the course is "Digital Image Processing," 3rd edition by Rafael C. Gonzalez and Richard E. Woods, Prentice Hall. I've been told you can order it from Amazon or you can get it at the bookstore. I will start to follow parts of it after the first week or so and Hongmei Zhu will cover entire chapters as soon as the second half of the course starts.

Facebook page (

Google Group (


There will be four components which I will evaluate you on for the first 6 weeks. You will also receive a grade for the second half of the course where the distribution of the grades will be different.

  • 25% class participation - this includes attendance, if you miss a class you are missing the equivalent of one full week of class time in a normal year long course. Your assignments MUST be on time and dedication (or lack thereof) to this class will be taken into consideration for this component.
  • 15% class summary - each of you will be asked to organize a page on the wiki which has class notes and material and a summary of what we did for one day of class. This includes supplementary material you wish to add (say, for instance, a link to a youtube video or website or your fellow student's blogs, etc.) You should be doing a good job on this piece because you are only responsible for one day.
  • 40% homework assignments - I don't want any paper homework assignments so these will be posted on your blog. I expect you to work together and help out your fellow students and read other assignments for ideas. We had our discussion about web tools and their relationship to 'cheating' on the first day of class.
  • 20% final project - ok, this project is only half the course so it will only use some of the basic components of image processing that we will learn.

List of topics

  • history and introduction to internet tools
  • logic and computer representation
  • introduction to GIMP
  • introduction to octave
  • color, light and the eye
  • representing colors and color spectrums
  • average color of a picture
  • cropping, copying, pasting
  • file compression and information theory
  • Bezier curves
  • randomness and computer generated images
  • Resizing an image
  • Rotating an image
  • Correcting intensity using simple functions
  • Equalizing intensity using histogram
  • Smoothing an image
  • Sharpening an image
  • Fourier Transforms in 1-D and 2-D
  • Filtering an image in frequency domain
  • Noise, noise remover


Mike Zabrocki

my personal web page:

To contact me, my email address is: mylastname at mathstat dot yorku dot ca

some notes about the topics of this course which will be ported over to this wiki:

A list of students in class with links to their blogs:

When you list your name below, please use your real name. The date next to each person on this list is the night that person is responsible for taking notes. The notes should be done one week from that date.

Some Announcements

(Tuesday June 10) I figured out last night after I got home that the last class that I will be teaching is on June 11. Hongmei will be teaching starting on June 16th. I will give you a 10th assignment, but it will be 'just for fun' and I will show you essentially how to do it in class.

(Thursday June 5) I will be out of town this weekend and so might not have the chance to answer back on Facebook as often as I have been recently.

(Thursday June 5) Just a clarification on Assignment 8, when you enlarge the images, enlarge the ones that you reduced in size in Assignment 7. Otherwise for the larger images and f=.1, when you enlarge by a factor of 1/f the picture might be a little too big.

(Wednesday May 28) There is a windows version of Octave with image already installed. This means that there is no need to download the compiler and no need to even download Image Magick. Go to Octave Forge. Download the version called octave-3.0.1-vs2008-setup.exe not the one above it that doesn't contain 'vs2008' in the name. Sorry to those that stayed after class and downloaded compilers for hours. :S Thanks to Thomas for noticing this.

(Monday May 26) I won't give a new assignment for Wednesday but we might talk more about bilinear and bicubic interpolation. Certainly we will talk about old assignments and anything you have questions on so please come with questions prepared.

(Thursday May 15) I have 20 people who are on my list of students above and 19 on Facebook. Who is missing? Can you please update your facebook name if it is not listed above? Add to the discussion going on there if you are having trouble completing some of the assignments. This will help me know what resources to add to the wiki. I will be posting some octave help on the Class4 page. Keep working on the assignments that I gave you. Monday of next week is Victoria Day so we have no class. Wednesday the 21th we will meet in the Chemistry building and talk a little more about Octave/Matlab before we go to the lab.

(Tuesday May 13) We will be going to the computer lab on Wednesday (we will meet in the Chemistry building first to talk about linear algebra). Make sure that either (a) you activate your AML accounts on Passport York or (b) you bring your laptop with octave installed or (c) you bring your laptop and you can 'ssh -X'

(Sunday May 11) If you need some help on the homework it is a good idea to check the discussion board on Facebook. Some ideas have been exchanged there about how to do problem number 6. I will try to monitor this and add comments as is necessary.

(Thursday May 8) Answer to question 1: you don't need to include the full question, but you do need some indication of what it is you are answering. To make this clearer, please don't put "#2. 4" if the answer to question 2 is 4. Put something like "#2. the number of ways of doing something is 4." As a general rule, answer with complete sentences and you should be fine. Answer to question 2: this is not a good place to ask questions. Do it on facebook.

Jen Woodcock: (Thursday May 8) Question: Is the new Mike going to insist that we include copies of the questions in our assignment solutions? (also, is this where we should ask questions?)

(Wednesday May 7) I found a way to do the problem about pictures using GIMP using layers and one of the options about merging layers. You might want to look in the Layers/Channels/Paths window if you are looking to do this problem.

(Wednesday May 7) I know the mod 8, mod 3 and mod 7 part of the assignment that I handed out is a bit unclear, but to try to make it a little better you are expected to do ALL of problems 1, 4, 5, 7, the section on 'orders of magnitude' but only one part of problem 2, 3 and 6. I posted an updated pdf that has a few of the typos corrected on the class2 page.

(Wednesday May 7) The facebook part of the assignment was a bit of a disaster. If you tried to join the group before, try again now. The group was originally on the "York University" network so if you weren't part of that network then it was impossible to join and it was impossible to join the network without giving facebook a Yorku email address. This should all be fixed now and I will be deleting the old group shortly. Use the link below to access the facebook group.

(Tuesday May 6) Just to be clear we are back in CB 122 for the class on Wednesday May 7. We probably won't be going to the computer lab at all because I think that the assignment we do on Wednesday will not require computers. I have taught classes in third world countries and they had computer labs better than this!.

(Tuesday May 6) I've had a lot of questions about signing up for the wiki and facebook steps. It is easy for me (possibly because I am listed as the admin for both of these things) and hard for everyone else to (a) sign up for the wiki and (b) sign up for the facebook group.

Try to log into the facebook group with this link here:

I have to register you for a wiki account so if you would like one you should email me and I will send you a password in return. Those of you that have asked me about a wiki account will receive an email shortly.

Summaries of classes:

  • May 5, 2008 - getting accounts and getting started - class1
  • May 7, 2008 - computers and logic - class2
  • May 12, 2008 - color representations - class3
  • May 14, 2008 - matrices and Octave/Matlab - class4
  • May 21, 2008 - review + Octave commands for/if - class5
  • May 26, 2008 - review, bilinear interpolation, average color - class6
  • May 28, 2008 - Helpful hints for Ass't 5 and 6, average color of an image - class7
  • June 2, 2008 - Shrinking an image - class8
  • June 4, 2008 - Shrinking and enlarging an image - class9
  • June 9, 2008 - reducing the color spectrum - class10
  • June 11, 2008 - more about the photomosaic, swirling - class11
  • June 23, 2008 - histograms and histogram processing - class14
  • June 25, 2008 - Histogram Equalization and Filters - class15a
  • June 30, 2008 - Sharpening Spatial Images - class15
  • July 2nd, 2008 - Sharpening and Refocusing in Spatial domains - class 16a
  • July 7,2008 - Colour Models - class16
  • July 9, 2008 - Colour Image Processing - class17
  • July 14, 2008 - Fourier Transforms Part 1 - class18
  • July 16, 2008 - Fourier Transforms Part 2 - class19
  • July 23, 2008 - Presentation - class22