Mathematics of computer science
Many aspects of computer science are underpinned by mathematical principles – most of which will not encountered by students of other subjects. This topic covers the basic building blocks of computer data represented using binary, denary and hexadecimal number systems. It covers the logical operations that are applied to these representations of data and their algebraic laws. Set theory, formal languages and floating point binary are also covered in depth.
Links and Resources
A fun introduction to algebra within computer science via the medium of a card trick. This resource is part of the CS4FN series from Queen Mary, University of London. The resource consists of an introductory presentation and accompanying activity sheet for students.
This is a great resource for providing underpinning mathematical knowledge for A level computer science. It is broken down into topics so could be used in small sessions to reinforce understanding. Set theory, numbers, cardinality, cartesian product, regular expressions, vectors and dot product, functions and Big O notation are all covered in this very comprehensive which is also very useful for teachers whose background does not include mathematics.
Students always need practice in number system conversion. This resource gives them instant feedback and allows them to progress from conversion to binary addition. This would make an ideal homework activity. the file is a macro enabled worksheet and can be downloaded from the zip file.
A student worksheet with answers covering the topic of floating point binary representation. It contains answers so can be used for independent study.
Normalisation of floating point binary numbers is usually a topic where students require practice. This pair of documents explain the technique and then provide a set of questions with answers for independent working.
One of the series of Royal Institution Christmas lectures focusing on Bayes’ theorem. The topic of the resource is an investigation into stolen chocolate biscuits so would make an interesting end of term diversion.
A resource from the CS4FN bank produced by Queen Mary and King’s College, University of London. Students will be able to link the algorithms that they have learned and the relative complexity expressed in Big O notation. The resource consists of a series of slides, program files with solution, an activity sheet and a separate homework sheet.
This set of resources provides comprehensive coverage of the topic of logic, Boolean algebra and simplifying expressions using Karnaugh maps. There are a series of student activities involving deriving expressions from logic gate combinations, rules of Boolean algebra and building logic expressions.
Students need to be aware of the trade-off when the number of bits allocated to the mantissa and exponent are increased or decreased. This worksheet allows them to answer practice questions. Answers are provided.
This document is a Computing at School community resource that covers the laws of Boolean algebra. It consists of a student worksheet and answer sheet. It is very suitable as a revision resource.
Another great resource from the Computing at School community which is suitable as a consolidation activity for small groups, the set of triominoes allows students to convert numbers to build the completed solution. Great for revision.