Discrete Maths
242-213, Semester 2, 2015-2016
0. Preliminaries
Please ask
questions
Who I am:
Andrew Davison
WiG Lab
ad@fivedots.coe.psu.ac.th
• Objective
 to give some background on the course
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Overview
1.
2.
3.
4.
5.
What is Discrete Maths?
Meeting Times / Locations
Workload
Exercises
Course Materials
6. Books
7. Video
8. Math Web Sites
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1. What is Discrete Maths?
 The study of discrete mathematical objects
 Examples: integers, steps taken by a computer program,
distinct paths to travel from point A to point B on a map
along a road network, ways to pick a winning set of
numbers in a lottery
 Provides mathematical background needed for many
branches of computing.
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Goals of a Course in Discrete Maths
 Mathematical Reasoning: Ability to read,
understand, and construct mathematical arguments
and proofs.
 Combinatorial Analysis: Techniques for counting
objects of different kinds.
 Discrete Structures: Abstract mathematical
structures that represent objects and the relationships
between them.
 e.g. sets, relations, graphs
continued
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 Algorithmic Thinking: Involves specifying
algorithms, analyzing the memory and time required
by their execution, and verifying that an algorithm
produces the correct answer.
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Some Problems Solved Using Discrete Maths
 How many ways can a password be chosen following
specific rules?
 How many valid Internet addresses are there?
 Is there a link between two computers in a network?
 How can I encrypt a message so that bad guys cannot read
it?
 How can we build a circuit that adds two integers?
continued
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 What is the shortest path between two cities?
 Find the shortest tour that visits each of a group of
cities only once and ends back in the starting city.
 How can we represent sentences so that a
computer can reason with them?
 How many steps are required to do sorting?
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Discrete Mathematics as a Gateway
 Importance in many computing courses:
 Computer Architecture, Data Structures, Algorithms,
Programming Languages, Compilers, Computer
Security, Databases, Artificial Intelligence, Networking,
Graphics, Game Design, Theory of Computation, ...
 Uses beyond computing:
 Concepts from discrete maths have been applied to
many areas, such as chemistry, biology, linguistics,
geography, business, etc.
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Prerequisites
• You must have passed “Computer Programming
Techniques” (or similar)
 knowledge of C is assumed
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2. Meeting Times / Locations
• Monday
Friday
13:00 – 13:50
9:00 – 9:50
S201
A400
• I can change these times, but only if (almost) all
the students in the class agree to the change.
• I will be away for the last 2 weeks of the semester,
and so I will need to move 4 classes to earlier in
the semester
• I will do that after the mid-term exam
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3. Workload
• Mid-term exam:
35%
 27th Feb. to 6th March (week 9)
(2 hours)
• Final exam:
45%
 25th April to 7th May (weeks 7-8)
(3 hours)
• Two exercises:
20% (2*10)
• weeks 7-8 and weeks 15-16
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Non-Attendence Penalty
• I may take registration at the start of a class.
• If someone is not there, they lose 1%
(unless they have a good excuse).
• A maximum of 10% can be lost
 deducted from your final mark
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4. Exercises
• The two exercises are worth a total of 20%
(each worth 10%).
• They will be maths problems, perhaps with
some simple algorithms to design/write.
• no / tiny amounts of coding
• They are intended to help you review for the
exams.
continued
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• Planned exercise times (which may change):
 ex. 1 in weeks 7-8 (Feb. 15 – 26)
 ex. 2 in weeks 15-16 (April 11 – 22)
• Cheating will result in 0 marks.
 YOU HAVE BEEN WARNED!!
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5. Course Materials
Print out and
BRING TO CLASS
• I will hand out only the exercises.
• All the handouts (and other materials) will be
placed on-line at
http://fivedots.coe.psu.ac.th/
Software.coe/DiscreteMaths/
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6. Books
• Discrete Mathematics and its Applications
Kenneth H. Rosen
McGraw Hill, 2007, 7th edition
main source;
very clear
http://www.mhhe.com/math/advmath/
rosenindex.mhtml
 I have a copy that you can borrow.
 There is an old version in the CoE library
continued
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• Schaum's Outlines: Discrete Mathematics
Seymour Lipschutz and Marc Lipson
McGraw Hill, 2007, 3rd ed.
 less mathematical, more examples
 I have a copy that you can borrow.
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7. Video
 Discrete Mathematics (Arsdigita University)
Instructor: Shai Simonson
 http://www.youtube.com/
watch?v=Nt7JeGCZL5M&list=PL45589688F3702281
 Based on the Rosen textbook
 More information at:


http://archive.org/details/arsdigita_02_discrete_math
http://www.aduni.org/courses/discrete/
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8. Math Web Sites
 There are many – search for "Discrete Math"
 One beautiful, fun site:
 Mathigon: World of Mathematics
 http://world.mathigon.org/
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