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Discrete Maths Objective to give some background on the course 242-213, Semester 2, 2013-2014 Who I am: Andrew Davison WiG Lab ad@fivedots.coe.psu.ac.th 0. Preliminaries Please ask questions 1

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Overview 1. What is Discrete Maths? 2. Meeting Times / Locations 3. Workload 4. Exercises 5. Course Materials 6. Books 7. Video 2

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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. 3

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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? 4 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? 5

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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, trees, automata 6 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. 7

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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. 8

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Prerequisites You must have passed “Computer Programming Techniques” (or similar) knowledge of C is assumed 9

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2. Meeting Times / Locations Wednesday13:00 – 13:50A403 Thursday14:00 – 14:50S203 I can change these times, but only if (almost) all the students in the class agree to the change. 10

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3. Workload Mid-term exam:35%(2 hours) 27th July to 4th August (week 9) Final exam:45%(3 hours) 30th Sept. to 12th October (weeks 18-19) Two exercises:20% (2*10) weeks 6-7 and weeks 15-16 11

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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 12

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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. continued 13

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Planned exercise times (which may change): ex. 1 in weeks 6-7 (July 8-19) ex. 2 in weeks 15-16 (Sept. 9-20) Cheating will result in 0 marks. YOU HAVE BEEN WARNED!! 14

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5. Course Materials 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/ Print out and BRING TO CLASS 15

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6. Books Discrete Mathematics and its Applications Kenneth H. Rosen McGraw Hill, 2007, 7th edition http://www.mhhe.com/math/advmath/ rosenindex.mhtml I have a copy; old version in the CoE library Discrete Mathematics for Computer Scientists John K. Truss Addison-Wesley, 1999, 2nd edition main source; very clear main source; very clear continued 16

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Discrete Mathematics Richard Johnsonbaugh Macmillian Pub. Co., 1997, 4th ed. less mathematical, more examples there is a copy in the main PSU library I have a copy 17

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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/ 18

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