Undergraduate Course: Discrete Mathematics and Probability (INFR08031)
Course Outline
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  The first part of this course covers fundamental topics in discrete mathematics that underlie many areas of computer science and presents standard mathematical reasoning and proof techniques such as proof by induction. The second part of this course covers discrete and continuous probability theory, including standard definitions and commonly used distributions and their applications.
*This course replaces "Discrete Mathematics and Mathematical Reasoning" (INFR08023). from academic year 2020/21* 
Course description 
The course will cover roughly the following topics:
Block 1: Discrete Mathematics
 Logical equivalences, conditional statements, predicates and quantifiers
 Methods of proof using properties of integers, rational numbers and divisibility
 Set theory, properties of functions and relations, cardinality
 Sequences, sums and products, Induction and Recursion
 Modular arithmetic, primes, greatest common divisors and their applications
 Introductory graph topics
Block 2: Probability Theory
 Counting techniques: product rule, permutations, combinations
 Axioms of probability, sample space, events, De Morgan's Law
 Joint and conditional probability, independence, chain rule, law of total probability, Bayes' Theorem
 Random variables, expectation, variance, covariance
 Common discrete and continuous distributions (e.g., Bernoulli, binomial, Poisson, uniform, exponential, normal)
 Central limit Theorem

Information for Visiting Students
Prerequisites  Visiting students should have done a previous Universitylevel mathematics course, be comfortable with univariate calculus (differentiation and integration), and have some familiarity with basic concepts from discrete mathematics such as binary numbers, sets, functions, and relations. A previous computer science course is recommended. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2020/21, 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 15,
Revision Session Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
148 )

Assessment (Further Info) 
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %

Additional Information (Assessment) 
Assessment will consist of:
40% for weekly quizzes and engagement activities
60% for two class tests (30% each, one after each of the two blocks) 
Feedback 
Feedback is given weekly in tutorials, when students can discuss their solutions to homework questions. Sample answers are also given for students to compare their own homework answers. Peer assessment will also be carried out in tutorial sessions. Piazza will be used to answer student queries. This will give lecturers, TAs and fellow students the chances to help those who are struggling or have queries.
Formative and summative feedback is given on the assignments that are handed in and marked. The marks on these assignments make up the 15% coursework element of this course.

No Exam Information 
Learning Outcomes
On completion of this course, the student will be able to:
 Use mathematical and logical notation to define and formally reason about mathematical concepts such as sets, relations, functions, and integers, and discrete structures, including proof by induction.
 Use graph theoretic terminology and apply concepts from introductory graph theory 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
 Carry out practical computations with standard concepts from discrete and continuous probability, such as joint and conditional probabilities, expectations, variances, standardization.
 Recognize and work with standard discrete and continuous probability distributions and apply them to model and solve concrete problems.

Reading List
Discrete Mathematics and its Applications by Kenneth Rosen
http://discrete.openmathbooks.org/dmoi3.html 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Relations,Functions,Set Theory,Discrete and Continuous Probability,Conditional Probabilities,Proof 
Contacts
Course organiser  Dr Heather Yorston
Tel:
Email: Heather.Yorston@ed.ac.uk 
Course secretary  Ms Kendal Reid
Tel: (0131 6)51 3249
Email: kr@inf.ed.ac.uk 

