Discrete Maths Objective to give some background on the course , Semester 2, Who I am: Andrew Davison WiG Lab 0. Preliminaries Please ask questions 1

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

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

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

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

Algorithmic Thinking: Involves specifying algorithms, analyzing the memory and time required by their execution, and verifying that an algorithm produces the correct answer. 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 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

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

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. continued 13

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

5. Course Materials I will hand out only the exercises. All the handouts (and other materials) will be placed on-line at Software.coe/DiscreteMaths/ Print out and BRING TO CLASS 15

6. Books Discrete Mathematics and its Applications Kenneth H. Rosen McGraw Hill, 2007, 7th edition 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

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

7. Video Discrete Mathematics (Arsdigita University) Instructor: Shai Simonson watch?v=Nt7JeGCZL5M&list=PL F Based on the Rosen textbook More information at: