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 1 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 2 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 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 4 Algorithmic Thinking: Involves specifying algorithms, analyzing the memory and time required by their execution, and verifying that an algorithm produces the correct answer. 5 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 6 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? 7 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 Prerequisites • You must have passed “Computer Programming Techniques” (or similar) knowledge of C is assumed 9 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 10 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 11 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 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 13 • 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!! 14 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/ 15 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 16 • 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. 17 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 8. Math Web Sites There are many – search for "Discrete Math" One beautiful, fun site: Mathigon: World of Mathematics http://world.mathigon.org/ 19