Week 11
Combinatorics
Business
⦿ Monday. Distributions of possible outcomes
Exercises
If you're comfortable with the topics above you're ready to work on:
Supplementary resources:
The Math is Fun folks who provide the simulator have a good discussion of the Quincunx.
In College
Mathematics for Everyday life by Inigo, Jameson, Kozak, Lanzetta, and Sonier
§4.3
covers the binomial distribution.
⦿ Wednesday. Case study: Mark-recapture
- Mark and recapture Pencast 21:36| PDF
- We can rarely go and count all the individuals in an animal population. Instead we have to take a sample and infer the population from the sample. Mark-recapture is a common way of doing this.
Exercises
If you're comfortable with the topics above you're ready to work on:
- Exercise Set 11 Part 3: Mark-recapture likelihood via Excel Problems.
Supplementary resources:
I used the simplest possible mark-recapture model and formula here. Given its centrality to wildlife population management extensive work has been done on mark-recapture strategies and modelling. If you want to know more about Mark-Recapture techniques Chapter 2 Estimating Abundance and Density: Mark-Recapture Techniques in Ecological Methodology 3ed by C.J. Krebs is one well-written resource that is available online.
⦿ Friday: Graph Theory
What graph theory is: Introduction and background
- Introduction to Graph Theory Video 4:56
- The graphs of Graph Theory aren't like the ones you are used to, though I have drawn some from time to time. This video also goes over the jargon and nomenclature we use to describe and refer to graphs.
- The Birth of Graph Theory Video 6:58
- Graph Theory has an interesting origin story. Watch this if you're curious.
- General Applications of Graph Theory Video 11:25
- This narrated slide show describes some of the many applications of graph theory.
- Applications of Graph Theory in the Life Sciences Video 11:31
- This narrated slide show describes two applications of graph theory in the life sciences: Trophic webs, and Landscape connectivity.
Spanning Trees
- Spanning trees PDF 1 page
- Hand drawn notes explaining what spanning trees are. Because before we try to find minimal spanning trees, we need to know what they are.
Minimal Spanning Tree On-the-graph
- MST example done on-the-graph Pencast video 4:35 | PDF
- The MST algorithm is simple enough you might be able to learn it just by watching me do these two examples. But if not there are the detailed notes below to refer to.
- Minimal Spanning Tree Algorithm: On-the-graph PDF 4 pages
- Detailed notes on how to find the minimal spanning tree of a weighted graph.
Shortest Route Algorithm On-the-graph
- Shortest Route example done on-the-graph Pencast video 9:44 | PDF
- The shortest route algorithm involves some fussy bookeeping. You might want to skim the notes below before watching the example in this video.
- Shortest Route Algorithm: On-the-graph PDF 3 pages
- Detailed notes on how to find the shortest route from one node to another in a weighted graph.
Exercises
If you're comfortable with the topics above you're ready to work on:
Supplementary resources:
§6.1-6.3 in Chapter 6 of College Mathematics for Everyday life by Inigo, Jameson, Kozak, Lanzetta, and Sonier.
Chapter 6: Graph Theory in Math in Society by David Lippman.
5: Graph Theory in Combinatorics and Graph Theory by David Guichard.
Assignment
Assignment 11 is posted. Due by 1 pm Wednesday April 8. Note that the problems are worth different numbers of marks. Use your time wisely.
- You can hand in work done by hand to me in class or in dropbox A19.
- Excel or other binary files should be sent as file attachments to an email message.
- Google sheets can be submitted by sharing a link to them.
- Work done in Desmos can be submitted by sharing a link to your saved graph.
Name the file you submit A11_firstname.pdf, e.g.
A11_Tim.pdf
If you have to submit multiple files, add a suffix number to each, e.g.
A11_Tim_1.pdf
A11_Tim_2.pdf