SLIDE 1
How much should I work?
- According to UCD:
- So: 110/12 = 9.16 hours a week
- A bit much, but about 7 hours is possible
Graphs and Networks MATH20150 Vincent Astier Room: S1.72, Science - - PowerPoint PPT Presentation
Graphs and Networks MATH20150 Vincent Astier Room: S1.72, Science - - PowerPoint PPT Presentation
Graphs and Networks MATH20150 Vincent Astier Room: S1.72, Science South vincent.astier@ucd.ie How much should I work? According to UCD: So: 110/12 = 9.16 hours a week A bit much, but about 7 hours is possible How much should I
SLIDE 2
SLIDE 3
How much should I work?
- According to UCD:
- So: 110/12 = 9.16 hours a week
- A bit much, but about 7 hours is possible
SLIDE 4
How much should I work?
- According to UCD:
- So: 110/12 = 9.16 hours a week
- A bit much, but about 7 hours is possible
SLIDE 5
How much should I work?
- According to UCD:
- So: 110/12 = 9.16 hours a week
- A bit much, but about 7 hours is possible
SLIDE 6
How should I work?
- 1. Go to all lectures and tutorials
- 2. After each lecture:
- Learn it
- Work on it until you understand everything:
You need to be able to do all proofs (except a few), and to explain everything to someone else in the class It could take about 2 hours each week
- 3. Do all exercises before each tutorial
It could take up to 2 hours each week
Total: 7 hours a week (can vary)
SLIDE 7
How should I work?
- 1. Go to all lectures and tutorials
- 2. After each lecture:
- Learn it
- Work on it until you understand everything:
You need to be able to do all proofs (except a few), and to explain everything to someone else in the class It could take about 2 hours each week
- 3. Do all exercises before each tutorial
It could take up to 2 hours each week
Total: 7 hours a week (can vary)
SLIDE 8
How should I work?
- 1. Go to all lectures and tutorials
- 2. After each lecture:
- Learn it
- Work on it until you understand everything:
You need to be able to do all proofs (except a few), and to explain everything to someone else in the class It could take about 2 hours each week
- 3. Do all exercises before each tutorial
It could take up to 2 hours each week
Total: 7 hours a week (can vary)
SLIDE 9
How should I work?
- 1. Go to all lectures and tutorials
- 2. After each lecture:
- Learn it
- Work on it until you understand everything:
You need to be able to do all proofs (except a few), and to explain everything to someone else in the class It could take about 2 hours each week
- 3. Do all exercises before each tutorial
It could take up to 2 hours each week
Total: 7 hours a week (can vary)
SLIDE 10
How should I work?
- 1. Go to all lectures and tutorials
- 2. After each lecture:
- Learn it
- Work on it until you understand everything:
You need to be able to do all proofs (except a few), and to explain everything to someone else in the class It could take about 2 hours each week
- 3. Do all exercises before each tutorial
It could take up to 2 hours each week
Total: up to 7 hours a week (can vary)
SLIDE 11
Support
- 1. Myself
- Ask all your questions, at anytime
- Come to my office / email me / etc
- 2. Tutor
- Again: Ask all your questions
- 3. Maths Support Centre
SLIDE 12
Resources
- Course web page:
http://maths.ucd.ie/~astier/math20150/ (accessible from my web page)
- It contains:
➔ Course notes (my own handwritten ones)
not intended to replace attendance at every lecture
➔ Exercises for tutorials ➔ Recommended books for reading and extra
exercises
SLIDE 13
SLIDE 14
Graph Theory
SLIDE 15
Introduction
- 1. The Königsberg bridge problem
Königsberg, 1736 (now Kaliningrad, Russia)
SLIDE 16
Map of the bridges: Question: Is it possible to start at one point, cross every bridge exactly once, and end up at the same point?
SLIDE 17
Solution (and invention of graph theory): Leonhard Euler, 1736
- Represent it as a “graph”:
- Answer: Impossible
- Euler’s answer covers all such
questions, for instance:
SLIDE 18
Solution (and invention of graph theory): Leonhard Euler, 1736
- Represent it as a “graph”:
- Answer: Impossible
- Euler’s answer covers all such
questions, for instance:
SLIDE 19
- 2. The 4 colour problem (1852)
Can any map be coloured such that any two adjacent countries are of different colours?
Translation into graphs: Each country become a dot Join dots if they are adjacent: The problem becomes: Can we colour the points with 4 colours such that adjacent points have different colours?
SLIDE 20
- 2. The 4 colour problem (1852)
Can any map be coloured such that any two adjacent countries are of different colours?
Translation into graphs: Each country become a dot Join dots if they are adjacent: The problem becomes: Can we colour the points with 4 colours such that adjacent points have different colours?
SLIDE 21
- 2. The 4 colour problem (1852)
Can any map be coloured such that any two adjacent countries are of different colours?
Translation into graphs: Each country become a dot Join dots if they are adjacent: The problem becomes: Can we colour the dots with 4 colours such that connected dots have different colours?
SLIDE 22