Undergraduate Course: Discrete Mathematics and Probability (INFR08031)
|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
|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*
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
|Pre-requisites||Visiting students should have done a previous University-level 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?
Course Delivery Information
|Academic year 2020/21, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 30,
Seminar/Tutorial Hours 15,
Revision Session Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|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 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
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.
|Discrete Mathematics and its Applications by Kenneth Rosen |
|Graduate Attributes and Skills
|Keywords||Relations,Functions,Set Theory,Discrete and Continuous Probability,Conditional Probabilities,Proof
|Course organiser||Dr Heather Yorston
|Course secretary||Ms Kendal Reid
Tel: (0131 6)51 3249