Mathematical Techniques for Computer Science

COMP11120 Mathematical Techniques for Computer Science 20 Full year Undergraduate Level 1 Andrea Schalk Unit coordinator Department of Computer Science 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 mathematics required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. 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.  Underlying everything we do on this unit is the idea that we need to provide formal definitions of concepts, which then enable us to rigorously establish properties of these. At the start we introduce this new way of engaging with mathematics by studying notions already familiar to students, such as functions or operations such as addition of numbers in this style. Further topics covered include logic, probability, recursion and induction, relations, vectors, matrices and transformations. This course covers the fundamental mathematics required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. 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.  Underlying everything we do on this unit is the idea that we need to provide formal definitions of concepts, which then enable us to rigorously establish properties of these. At the start we introduce this new way of engaging with mathematics by studying notions already familiar to students, such as functions or operations such as addition of numbers in this style. Further topics covered include logic, probability, recursion and induction, relations, vectors, matrices and transformations. 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.  ILO 1: employ abstraction to move from concrete phenomena to ones amenable to the application of mathematical techniques;ILO 2: apply concepts from the mathematical theory of probability to describe and analyse a variety of situations;ILO 3: use Bayesian reasoning to construct a simple algorithm for learning in a variety of situations;ILO 4: choose suitable mathematical techniques to analyse questions from computer science and devise approaches to solving them;ILO 5: construct and manipulate logical formulae and derivations and compute their semantics in different frameworks;ILO 6: analyse vector spaces and linear transformations, making use of conceptual techniques or bases as appropriate;ILO 7: define recursive operations satisfying a given specification, as well as construct inductive arguments to prove a given property for such operations;ILO 8: apply formal definitions and construct formal arguments for these. Analytical skills Problem solving This course covers the fundamental mathematics required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. 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.  Underlying everything we do on this unit is the idea that we need to provide formal definitions of concepts, which then enable us to rigorously establish properties of these. At the start we introduce this new way of engaging with mathematics by studying notions already familiar to students, such as functions or operations such as addition of numbers in this style. Further topics covered include logic, probability, recursion and induction, relations, vectors, matrices and transformations. 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. Semester 1 exam: 40%Semester 2 exam: 40%Exercise Sheets: 20% Students who are not from the School of Computer Science must have permission from both Computer Science and their home School to enrol. N <ol><li>Epp, Susanna S. (2019). Discrete mathematics with applications. Cengage Learning. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,9781337694193&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 9781337694193</a>  </li><li>Angel, Edward, author. (2015). Interactive computer graphics: a top-down approach with WebGL. Pearson. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,9781292019345&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 9781292019345</a>  </li><li>Garnier, Rowan. (2002). Discrete mathematics for new technology. Institute of Physics. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,0750306521&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 0750306521</a>  </li><li>Houston, Kevin, 1968-. (2009). How to think like a mathematician a companion to undergraduate mathematics. Cambridge University Press. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,9781139129718&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 9781139129718</a>  </li><li>Jordan, D. W. (Dominic William). (2008). Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences. Oxford University Press. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,9780199282012&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 9780199282012</a>  </li><li>Poole, David, 1955- author. (2015). Linear algebra: a modern introduction. Cengage Learning. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,9781285463247&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 9781285463247</a>  </li><li>Truss, J. K. (1999). Discrete mathematics for computer scientists. Addison-Wesley. ISBN:<a href="https://www.librarysearch.manchester.ac.uk/discovery/search?query=isbn,contains,0201360616&search_scope=MyInst_and_CI&sortby=rank&vid=44MAN_INST:MU_NUI&lang=en&mode=advanced&offset=0" target="_blank"> 0201360616 </a></li></ol> Assessment written exam 4 Lectures 22 Practical classes & workshops 22 0 152