Mathematical Techniques for Computer Science

COMP11120 Mathematical Techniques for Computer Science 20 Full year Undergraduate Level 1 Andrea Schalk Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors ' European Credit Transfer & Accumulation System Rating : 10.0 This course covers the fundamental maths required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. Topics covered include complex numbers, logic, probability, recursion and induction, relations, vectors, matrices and transformations. This course covers the fundamental maths required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. Topics covered include complex numbers, logic, probability, recursion and induction, relations, vectors, matrices and transformations.This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates. This is a full year course that focuses on areas of mathematics required to model and analyse the kind of problems that arise in computer science.Probabilities are used for example in artificial intelligence, and play a vital role in machine learning, while the combinatorics required here also plays a role in the field of computational complexity. Vectors and matrices are the mathematical model underlying computer graphics. Logic is a tool used to reason about computer programs as well as the real world. Recursion is an important programming principle that comes with an associated proof rule, and other mathematical notions such as functions and relations are used routinely in computer science, for example when talking about database systems. Theoretical computer science can be considered an area of mathematics, and the unit also provides an introduction to the fundamental notions of this area.Specifically the unit aims to- introduce  mathematical notions relevant to computer science and their applications;- illustrate how abstraction allows the formulation and proof of properties for real-world and computational phenomena, and enable students to apply this technique;- give an understanding and some practice in the fundamental notion of proof.Students are required to undertake background reading, which is supported by lectures to explain various notions and to show the application of various techniques using examples. The coursework requires the students to solve exercises each week. Feedback for and help with this work is provided in the examples classes. <wbr style="color: rgb(0, 0, 0); font-family: Times New Roman; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;" /><ul id="docs-internal-guid-43e3137c-7fff-f608-0d20-837a89600117"> <li dir="ltr"> perform the standard operations on complex numbers</li> <li dir="ltr"> apply formal definitions and construct formal arguments based on these in the context of mathematics relevant to computer science.</li> <li dir="ltr"> employ abstraction to move from concrete phenomena to ones which are amenable to the application of mathematical techniques.</li> <li dir="ltr"> interpret the meaning of logical formulae as part of a natural deduction system, via the model based on truth values, or via a given intended model.</li> <li dir="ltr"> construct logical formulae to describe aspects of a given system, and manipulate these formulae to derive properties of the system.</li> <li dir="ltr"> apply concepts from the mathematical theory of probability to describe and analyse a variety of situations.</li> <li dir="ltr"> use Bayesian reasoning to construct a simple algorithm for learning in a variety of situations.</li> <li dir="ltr"> recognize recursively defined structures and define recursive operations satisfying some given specification, as well as construct inductive arguments to prove some given property for such operations.</li> <li dir="ltr"> use vectors and matrices to describe suitable situations, such as systems of equations or operations in two- and three-dimensional space, and are able to carry out relevant calculations for these.</li> <li dir="ltr"> choose suitable mathematical techniques to analyse questions from computer science and devise approaches to solving them.</li></ul><br style="color: rgb(0, 0, 0); font-family: Times New Roman; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;" />  Analytical skills Problem solving This unit is delivered in blended manner. At the start of the week there is an examples class for students to engage with new concepts in groups with feedback given by unit staff. Students then move to self-study materials in the form of detailed notes, teaching videos and formative self-assessment quizzes. Towards the end of each week there is a session that allows students to ask questions about the materials and beyond, and discuss the ideas underlying the taught material.   1 Written exam 80% 2 Written assignment (inc essay) 20% Feedback is provided in the examples classes, via published solutions to exercises, via self-assessment quizzes and the discussion board. Students who are not from the School of Computer Science must have permission from both Computer Science and their home School to enrol. N <a href="http://studentnet.cs.manchester.ac.uk/syllabus/index.php?code=COMP11120&year=2020" target="_blank">COMP11120 reading list</a> can be found on the Department of Computer Science website for current students. Assessment written exam 4 Lectures 22 Practical classes & workshops 22 0 152 Exhaustive resources are available via the VLSE.