# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# Undergraduate Course: Discrete Mathematics and Mathematical Reasoning (INFR08023)

 School School of Informatics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 2 Undergraduate) Availability Available to all students SCQF Credits 20 ECTS Credits 10 Summary Discrete mathematics and formal mathematical reasoning. Course description 1) Foundations (Chapters 1 & 2 of [Rosen]) 2) Basic number systems, and rudimentary algorithms on numbers and matrices (Chapter 3, [Rosen]) 3) Induction and Recursion (Chapter 4 [Rosen]) 4) Basic Counting (Chapter 5 [Rosen]) 5) Graphs (and binary relations): [Chapter 9, and parts of Chapter 8]] 6) Trees: (Chapter 10 [Rosen]) 7) Discrete probability [Chapter 6, plus some supplementary material]
 Pre-requisites Students MUST have passed: Introduction to Linear Algebra (MATH08057) It is RECOMMENDED that students have passed Informatics 1 - Functional Programming (INFR08013) AND Informatics 1 - Computation and Logic (INFR08012) AND Informatics 1 - Object-Oriented Programming (INFR08014) AND Informatics 1 - Data and Analysis (INFR08015) AND Calculus and its Applications (MATH08058) Co-requisites Prohibited Combinations Other requirements Higher Mathematics or A-level at Grade A, or equivalent
 Pre-requisites None High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 30, Seminar/Tutorial Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 154 ) Assessment (Further Info) Written Exam 85 %, Coursework 15 %, Practical Exam 0 % Additional Information (Assessment) You should expect to spend approximately 40 hours on the coursework for this course. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) 2:00 Resit Exam Diet (August) 2:00
 - Reason mathematically about basic (discrete) structures (such as numbers, sets, graphs, and trees)used in computer science. - Use of mathematical and logical notation to define and formally reason about mathematical concepts such as sets, relations, functions, and integers, and discrete structures like trees, graphs, and partial orders; - Evaluate elementary mathematical arguments and identify fallacious reasoning - Construct inductive hypothesis and carry out simple induction proofs; - Use graph theoretic models and data structures to model and solve some basic problems in Informatics (e.g., network connectivity, etc.) - Prove elementary arithmetic and algebraic properties of the integers, and modular arithmetic, explain some of their basic applications in Informatics, e.g., to cryptography. - Compare the asymptotic growth growth rates of basic functions; derive asymptotic bounds, and limits, for simple series and recurrence relations. Use these to derive bounds on the resource consumption (e.g., running time) of simple iterative and recursive algorithms. - Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations. - Be able to construct discrete probability distributions based on simple combinatorial processes, and to calculate the probabilities and expectations of simple events under such discrete distributions.
 REQUIRED TEXTBOOK: * Kenneth Rosen, Discrete Mathematics and its Applications, 7th Edition, McGraw-Hill, (due to be published in July), 2012. Alternatively, 6th Edition, 2007. Additional Reference Material: * MIT Mathematics for Computer Science Lecture notes (online)
 Course URL http://course.inf.ed.ac.uk/dmmr Graduate Attributes and Skills Not entered Keywords Not entered
 Course organiser Prof Colin Stirling Tel: (0131 6)50 5186 Email: cps@inf.ed.ac.uk Course secretary Ms Kendal Reid Tel: (0131 6)50 5194 Email: kr@inf.ed.ac.uk
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