Data science takes a vital role in almost all jobs in the private and public sectors. The need to understand how data is used to inform decision-making has never been more important. This degree equips you with the skills to explore and analyze complex data sets. Solve practical problems using applied mathematics, statistics and computing. You will get a good grounding in mathematical and statistical methods, which provide the basis for data analysis. You will learn relevant computing skills, including programming and elements of machine learning and artificial intelligence, and gain experience using statistical software.

### The first stage 120 Credits

Today, more than ever, statistics is part of our lives. From this key introductory module you will learn how to use basic statistical tools and quantitative methods that are useful in business, government, industry, medicine, the economy, and most academic subjects. Topics covered include: summarising data; examining relationships; randomness and sampling distributions; probability; testing hypotheses; and estimation. Using data from a range of applications, you’ll learn practical statistical techniques and fundamental principles, as well as using software and a calculator to analyse data. The skills introduced will be ideal if you plan to study more mathematics modules or if you encounter data in another subject or your daily life.

What you will study

This key introductory statistics module is designed for people who have not studied statistics before. It focuses on the application of statistics, adopting the attitude that statistics is about solving problems. The module is data driven. We collect relevant data and we analyse them to answer the problems. The methods that are covered are not specific to one field of application alone, but apply to all areas in which statistics is used.

The text contains many exercises that you should work through to help you learn and to monitor your own progress. Most exercises involve calculations that you will do by hand (or by calculator), but some you will do by computer, using the software package Minitab, which you will be taught to use and which is supplied with the module. You will be encouraged to develop skills in interpreting and communicating your results and this will be assessed in assignment questions.

Providing you have the appropriate background knowledge (see Entry Requirements) you should expect to study for about nine hours a week. Many of the topics covered in the module depend on your understanding of topics in earlier units. So, if you have not adequately understood earlier material, you may find later material difficult and time consuming.

You will learn

Successful study of this module should begin to develop your statistical skills and enable you to analyse common forms of data so as to address practical problems.

**You will learn about:**

key ideas in statistics

statistical vocabulary and notation introduced in the module

selection and use of statistical techniques for exploring data

interpretation of results in the context of real life questions

communication of results

use of statistical software

use of relevant ICT tools for learning.

The module contains many data from real world situations based around three themes: economics, education and health.

This is the first of two ISC level one modules that introduce you to key concepts in computing and information technology (IT), such as digital technologies, programming and networking. This module will equip you with a comprehensive toolbox of relevant knowledge, understanding and skills and introduce you to issues encountered in computing and IT, including the profound social and ethical challenges posed by these technologies. You will also develop your key skills including communication, numeracy and digital and information literacy (DIL). This will give you a firm basis for further study, especially Introduction to computing and information technology 2.

What you will study

This module is presented in three courses:

‘The digital world’ – the digital technologies that pervade our home, work and social lives;

‘Creating solutions’ – programming skills for creating solutions to simple problems;

‘Connecting people, places and things’ – the computer networks that allow us to interact with others.

**Course 1 ‘The digital world’**

You’ll start with your own experience of using computing and IT systems, covering a range of topics. You’ll explore how computers and networks developed; how analogue images and sounds are converted into digital formats; and how data is stored and managed in databases. You’ll also gain practical experience of constructing webpages, and consider how interfaces help us to interact with computers successfully.

**Course 2 ‘Creating solutions’**

You’ll develop programming and problem-solving skills as you work within a graphical programming environment to create programs involving animation, sounds, numbers and text. Since programs don’t always work the first time they are run, or don’t work as expected, you’ll also develop skills in testing and debugging your programs.

**Course 3 ‘Connecting people, places and things’**

You’ll be introduced to communication networks, including the structure and operation of the Internet, and wired and wireless systems. You’ll also discover how these technologies are combined with connected devices in the Internet of Things. The course ends with a discussion of how people interact with each other online, and also how computing and IT systems relate to modern society.

Throughout the module, you will develop your study skills, digital and information literacy skills and employability skills.

This key introductory module provides a broad and enjoyable foundation for university-level mathematics, but you do require some prior knowledge. It teaches you the essential ideas and techniques that underpin university-level study in mathematics and mathematical subjects such as physics, engineering and economics. You’ll study a range of fundamental topics – including calculus, vectors, matrices and complex numbers – and use mathematical software to solve problems. You’ll also develop your skills in communicating results and defining problems.

What you will study

There are eleven study units in this module.

In the first two, you’ll revise and extend the basic mathematical knowledge and skills in basic algebra and graphs that should mainly be familiar to you. This revision material should help you identify and fill any gaps in your previous knowledge, and develop your basic mathematical skills to the level that you’ll need in the rest of the module. Much of the material in these two units will be available online, so you can make a start on your revision even before the module begins, if you wish. The first two units also teach you about communicating mathematics, and introduce you to the mathematical software that you’ll use in the module.

**In the remaining study units you’ll cover these topics:**

**Functions**: these provide a means of representing situations where one quantity depends on another. For example, the distance travelled by a car depends on the time that it has been travelling. You need to know about functions before you can study calculus.

**Trigonometry:** you’ll revise the relationships between the angles and side lengths of triangles, and the definitions of the trigonometric functions sine, cosine and tangent for angles of any size. You’ll learn many useful properties of these functions, which are used to model a wide range of cyclical phenomena, such as rotating objects, and waves.

**Vectors:** these are quantities that have both a size and a direction. You’ll learn about the mathematics of vectors, and how to use them to model a variety of physical quantities, such as speed in a particular direction.

**Calculus:** this is one of the most important and widely applicable topics in mathematics. It is concerned with quantities that change continuously, such as the distance travelled by, and the speed of, a moving object. You’ll be introduced to differentiation and integration, and learn how to use calculus to model a range of different situations and to solve problems from areas such as physics and economics.

**Matrices:** these are arrays of numbers, which can be manipulated mathematically in various ways. They’re used extensively in both pure mathematics and mathematical applications.

**Sequences:** you’ll learn how to work with some commonly occurring types of number sequences, such as those in which each number is obtained by multiplying the previous number by a constant.

**Complex numbers:** these form an intriguing set of numbers that includes all the usual numbers, and also many `imaginary’ numbers, such as the square root of minus one. They have many uses in applied mathematics, as well as being the basis of some fascinating pure mathematics.

You’ll work mainly from the module books, which are available in various electronic formats as well as in print. You can view many of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You’ll also use specially designed software applications to help you understand the concepts taught, and you’ll learn to use a mathematics computer package to solve problems. There are many online interactive practice questions to help you consolidate your learning.

You will learn

Successful study of this module should begin to develop your skills in:

expressing problems in mathematical language

using mathematical techniques to find solutions to problems

communicating mathematical ideas clearly and succinctly.

Essential mathematics 1 is designed to be taken either as your first university-level mathematics module or following on from Discovering mathematics.

Essential mathematics 2 is designed to follow on from Essential mathematics 1. Normally, you should have completed this module first. However, if you have plenty of study time and a high level of confidence and fluency with algebraic manipulation you could study both modules in one year.

Alternatively, if you are considering progressing to Mathematical methods , normally you should have also completed this module.

This module builds on Introduction to computing and information technology 1 and prepares you for further study of computing and IT modules. You will:

learn about a variety of information technologies – including basic computer architecture, the cloud and mobile computing – while training your numerical skills;

develop problem-solving skills as you get familiar with the Python programming language, analyse real-world data and carry out a programming project;

practise your communication and analytical skills as you explore the profound legal, social, ethical and security challenges posed by information technologies.

What you will study

This module consists of three subjects:

Essential information technologies

Problem solving with Python

Information technologies in the wild

**Subject 1: Essential information technologies**

You’ll learn, among other things, about:

how computers store and process data – and why they use binary

the hardware components of your computer

different types of cloud

the parts of a mobile device, from sensors to batteries

how to use latitude and longitude to look up locations on online maps

what happens under the bonnet when you delete a file on your computer.

You’ll also develop your numeracy skills – from using scientific notation and percentages to calculating with binary representations.

**Subject 2: Problem solving with Python**

You will:

learn to use the Python programming language

analyse, with Python, health and well-being data from the Office for National Statistics

complete a small programming project.

You’ll also be introduced to a range of problem solving strategies, which you’ll practise as part of your project.

**Subject 3: Information technologies in the wild**

You’ll study

how hackers pose a threat beyond the digital world

how you can secure your data

how the Internet is enabling crime, surveillance, and digital freedom.

You’ll also develop your analytical and communication skills – including collecting and using evidence to argue a point.

Each subject consists of parts – you’ll study one part per week. The subjects are interleaved throughout the module. So, you may study a part on ‘Essential information technologies’ in one week and another part on, say, ‘Problem solving with Python’ in the next week and then another part on ‘Essential information technologies’ the following week. This allows you to revisit and strengthen your understanding of the concepts and skills of each subject over the course of the module. Problem solving and programming skills especially can’t be learned in a few weeks; they require continued practice throughout the module.

### The second stage 120 Credits

This module explores the fundamental statistical techniques and ideas used for analysing and interpreting data, covering models for data, estimation, confidence intervals, hypothesis testing and regression. The emphasis is on the practical side, although some of the underlying theory is also included. The statistical software package Minitab is supplied with the module and use of a computer is essential: you’ll receive detailed guidance for all the computer activities. This module is ideal if you would like to develop the skills to make sense of data. It also provides the necessary foundations required for studying further modules in statistics.

What you will study

This module builds on the statistics introduced at level 1 through the ISC module Introducing statistics. The module will investigate a greater range of statistical techniques than those introduced at level 1, and will also provide a deeper understanding of the techniques that were introduced.

In this module you will explore the fundamental statistical techniques which can be used to analyse data to answer real, practical, questions such as ‘Does drug A work better than drug B?’ and ‘How often do major earthquakes occur?’

The starting point for answering such questions is to model the variation in data: some of the most commonly used models for variation are considered in the first part of the module and some of their properties are investigated. The module then goes on to develop statistical techniques for using data and models of the variation to draw conclusions and answer questions of interest: the specific statistical techniques studied in the module include estimation, confidence intervals, hypothesis tests and regression.

An important skill for any statistician is the ability to communicate their statistical analysis clearly to others, both statisticians and non-statisticians. Statistical report writing is considered in one of the final units of the module.

In addition to the module texts, student learning is supported throughout by short video presentations, computer animations and online interactive practice quizzes.

You will learn

Successful study of this module should improve your skills in analysing and interpreting data.

The aim of this module is to help you become a computational problem solver. You’ll learn techniques to efficiently solve computational problems and apply them using the Python programming language. You’ll also learn about the limitations of computing: which problems can’t be solved algorithmically or for which no efficient solutions are known. This is the module for you if – whatever your field – you need to implement an efficient algorithm or to understand both the power and the limitations of computing. Though the focus is on the underlying ideas, you’ll also work with some mathematical concepts and notation.

What you will study

You’ll learn to take a problem and state it precisely in order that it can be solved with a computer. In other words, you’ll learn to express the problem in a way which allows you to write an algorithm for solving it. However, not all algorithms are equally good solutions. For that reason, you’ll also learn how to analyse the speed and efficiency of algorithms and establish whether an algorithm really does what it is supposed to do. Finally, you’ll delve into the very foundations of computing. You’ll learn which problems cannot be solved with an algorithm. You’ll also learn what the limits are on the speed with which algorithms can solve many important practical problems.

The module comprises three parts, each ending with an assignment:

Course 1

In the first part, you’ll learn about the basic data structures for organising data, like lists, stacks, queues, dictionaries, and sets. You’ll also learn how to analyse the complexity of an algorithm and how to measure its runtime.

Course 2

The second part covers two non-linear data structures: trees and graphs. The former can represent hierarchical data and the latter can model social, transport and other kinds of networks. The main focus of the second part are algorithmic techniques like search (brute-force, breadth-first and depth-first), divide and conquer, recursion and greedy algorithms. These are general-purpose techniques for solving a wide range of problems.

Course 3

In the third part, you’ll further develop your understanding of graphs and algorithmic techniques (backtracking, dynamic programming). You’ll also learn about the limitations of computational problem solving (non-computability and the P ≠ NP conjecture).

This module is designed to teach you about a variety of mathematical methods which are used in modelling through their application to solving real world problems. These methods include differential equations, linear algebra and vector calculus. You will become familiar with new mathematical skills mainly by using pencil and paper and by thinking. This module will give you a good foundation for higher-level study and is essential preparation for most ISC level 3 mathematics, statistics or physics modules. To study this module you should have a sound knowledge of algebra, calculus, and geometry as provided by the appropriate ISC level 1 study.

What you will study

The mathematical methods covered by this module are the core analytic methods that are useful for modelling the real world. The analytical (as opposed to numerical) solution of first and second-order ordinary differential equations is discussed, followed by linear algebra (vectors, matrices and determinants). We develop the elements of the calculus of functions of several variables, including vector calculus, which is followed by an introduction to methods for solving partial differential equations.

These mathematical methods are illustrated by putting them in the context of real world applications (such as simple mechanical systems). You will be assessed only on your mathematical skills, not on your knowledge of the context used. The module teaches ‘pencil and paper’ mathematical skills: although it explains where numerical methods are important, there is no programming or special software required.

You will learn all the core mathematical methods that are needed for further studies in applied sciences. In further study you will begin to appreciate the power of the methods introduced here – they are applicable in a very wide variety of situations.

The module is delivered as printed material in four books. There are some optional supporting materials on the website.

The module introduces four major topics of modern applied statistics: medical statistics, time series, multivariate analysis, and Bayesian statistics. It’s ideal if you’ve already studied a general introductory statistics module and wish to broaden your knowledge of the field. The module emphasises underlying principles and practical applications rather than technical details. Use of a computer is an essential component – the module includes SPSS and WinBUGS software, which you’ll use to analyse data and develop your understanding of statistics. To study this module you should have a sound knowledge of basic mathematics as provided by the appropriate ISC level 1 module, and statistical competence at the level developed by the appropriate ISC level 2 study.

What you will study

The module begins with an Introduction to statistical modelling in which the statistical prerequisites are reviewed and the statistical software package SPSS is introduced. Then the four topics of the module are introduced in successive books, each with associated computer material.

Book 1 Medical statistics

The first book describes how to identify factors associated with disease, and includes topics such as cohort and case-control studies; investigating sources of bias; randomised trials; and meta-analysis.

Book 2 Time series

The next book covers methods for analysing data collected over time, and forecasting future values using exponential smoothing and ARIMA models.

Book 3 Multivariate analysis

The third book discusses statistical methods for presenting and analysing data on several variables, with sections on principal component analysis and discrimination.

Book 4 Bayesian statistics

Book 4 introduces the Bayesian approach to statistics, in which expert knowledge can be incorporated into statistical models. This approach has become very popular in recent years, in part owing to the availability of special statistical software such as WinBUGS, which is used in this module.

Review unit

The final unit takes a look back at the module as a whole.

The module is illustrated with practical examples and real data sets from a range of subject areas, including epidemiology, economics, education, genetics, and environmental science. Numerous activities and exercises, also based on real data, are used to illustrate the methods and develop statistical modelling and critical assessment skills.

You will learn

Successful study of this module should improve your skills in analysing and interpreting data, communicating statistical ideas clearly and succinctly, and in using professional software.

### The thrid stage 120 Credits

Computers are getting smarter. Intelligent assistants like Alexa and Siri, image searches that find the topic of a photo, self-driving cars. These intelligent systems use machine learning to develop their expertise. In this module, you’ll learn about a range of machine learning techniques, but concentrate on deep neural learning. You’ll learn about the underlying theory and get hands-on experience of creating, training, evaluating, and using machine learning systems. You’ll also look at how these technologies are used and misused, and what that means for our societies and communities.

What you will study

The module is divided into several blocks. Each covering a different aspect of machine learning.

You’ll start with an introduction that outlines some of the issues surrounding machine learning, including questions about how machine learning systems are used and their social effects.

Deep neural learning is introduced, with a look at neural networks. You’ll create, train, and evaluate some neural networks, to perform tasks such as handwriting recognition. You’ll also see how these networks don’t scale up to larger problems.

Convolutional neural networks solve many of these problems. You’ll learn how these networks start by identifying small features in their inputs (normally images). Successive layers in the inputs combine these features into larger ones, eventually leading to a classification in the image.

Recurrent neural networks operate on time-dependent data, such as language. You’ll learn how they retain information seen earlier in order to interpret what’s happening now. You’ll use them to understand and generate some text.

Autoencoders teach themselves to compress and reconstruct their inputs. You’ll see how to use this for both compression and to clean data and replace missing data. You’ll see how this can be used to generate “deepfakes” to fool people, and what that means for trust.

You’ll also look at alternatives to deep learning; you’ll compare their strengths and weaknesses to the deep learning systems you’ve seen. Part of the differences lies in how the data should be prepared for different systems. As well as the time needed, preparation is another way for bias to creep into the system.

The conclusion asks you to review the technical aspects of machine learning; to consider how these systems are used; and the effects this could have on individuals and society.

This module will interest you if you need to create mathematical models or if you use numerical software in industry, science, commerce or research. It’s concerned with the skills needed to represent real optimization problems as mathematical models, and with techniques used in numerical analysis and operational research for solving these models by computer. Explaining how and when modelling and numerical techniques can be applied, the module covers solutions of non-linear equations; systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimization problems. Knowledge from ISC level 2 study of calculus and matrices is assumed.

What you will study

The module is divided into three courses of work: solutions of non-linear equations, systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimization problems. You will be expected to run given computer programs as part of your study, but you will not be required to write any computer programs.

In the broad area of operational research, the module will enable you to formulate a real problem in mathematical terms; to recognise whether the problem can be solved numerically; to choose a suitable method; to understand the conditions required for the method to work; to evaluate the results and to estimate their accuracy and their sensitivity to changes in the data.

Optimization is a practical subject, although it is supported by a growing body of mathematical theory. Problems that require the creation of mathematical models and their numerical solutions arise in science, technology, business and economics as well as in many other fields. Creating and solving a mathematical model usually involves the following main stages:

formulation of the problem in mathematical terms: this is the creation of a mathematical model

devising a method of obtaining a numerical solution from the mathematical model

making observations of the numerical quantities relevant to the solution of the problem

calculating the solution, usually with a computer or at least with a scientific calculator

interpreting the solution in relation to the real problem

evaluating the success or failure of the mathematical model.

Many of the problems discussed in the module arise in operational research and optimization: for example, how to get the most revenue from mining china clay when there is a choice of several mines. In this example the mathematical model consists of a set of linear inequalities defining the output from each mine, the number of mines that can be worked, the correct blend of clay and the total amount of clay mined each year. The method of solving the problem uses mixed linear and integer programming; the numerical data that need to be observed include the financial implications of opening a mine, the number of mines that can be worked with the labour force, and the quality of clay from potential mines. These data will be fed into a computer, which will combine them with the chosen method of solving the equations to produce solutions consisting of outputs from each mine in each year of operation.

This module examines all the stages but concentrates on: the first stage, creating the mathematical model; the second stage, devising a method; the fourth stage, calculating numerical solutions; and the fifth stage, interpreting the solution. Each of the three courses of work takes about ten weeks of study:

Course I

– Direct and iterative methods of solving single non-linear equations, systems of linear equations and systems of non-linear equations; mathematical modelling; errors in numerical processes, convergence, ill-conditioning and induced instability.

Course II

– Formulation and numerical solution of linear programming problems using the two-phase simplex method; formulation of integer programming problems and the branch and bound method of solution; sensitivity analysis.

Course III

– Formulation and numerical solution of unconstrained and constrained non-linear optimization problems using, among others, the DFP and BFGS methods with line searches; illustrative applications.

You will learn

Successful study of this module should enhance your skills in:

mathematical modelling

operational research

linear programming and non-linear optimization methods

the use of iterative methods in problem solving

the use of Computer Algebra Packages for problem solving.

This module provides you with the mathematical underpinning for statistical methods in general and – in particular – for other ISC statistics modules. You will gain a thorough grounding in mathematical statistics, together with generic skills. You will study distribution theory, leading on to the theory of statistical inference developed under both classical and Bayesian approaches. In the classical case, you will focus on maximum likelihood estimation. You’ll also explore the development of these ideas in the context of linear modelling (regression and extensions). To study this module, you should have a sound knowledge of basic statistical ideas and competence in calculus, algebra and matrices, as provided by the appropriate ISC level 1 and 2 study.

What you will study

Other ISC statistics modules focus on hands-on practical applications of statistical techniques and interpretation of data and statistical analyses. This module complements these modules by providing the mathematical theory underlying the methods and concepts, including a treatment of both classical and Bayesian statistics. A considerable amount of mathematics is sometimes required for this development.

This module is delivered online, with integrated use of exercises, animations, audio and video segments. You will also be provided with printed versions of the main units, extra exercises and a handbook.

The module is divided into four courses of study.

Course 1: Review and distribution theory

The first course comprises a review unit and units introducing distribution theory. The review is mostly of fundamental statistical ideas of the type taught in Analysing data (M248), (see Entry requirements for details); there is also a speedy reminder of important relevant methods in mathematics, including calculus and matrices. Two units in this course introduce the theory of continuous distributions. You will learn, for example, how to evaluate moments of distributions and about other properties of some important univariate distributions. The mathematical structure of multivariate distributions will be explored, with some emphasis on the multivariate normal distribution.

Course 2: Classical inference

The second course is about the classical approach to statistical inference. You will learn how to use calculus to obtain maximum likelihood estimators of parameters. You will also learn about the properties of maximum likelihood estimation and of point estimation more generally. The mathematics underlying hypothesis tests and confidence intervals will be explored. There is also a unit on asymptotic (large sample) analysis, giving an insight into how statisticians study properties of statistical procedures by approximate methods.

Course 3: Bayesian statistics

In the third course you’ll consider the Bayesian approach to statistical inference. The emphasis is first on so-called conjugate analysis which constitutes the type of Bayesian analysis most amenable to straightforward mathematical development. You’ll consider prior to posterior analysis first, followed by Bayesian estimation based on decision theory. Markov chain Monte Carlo (MCMC) is a technique often used for tackling Bayesian problems which are not conjugate; you’ll investigate the mathematical ideas leading to the basic methods of MCMC.

Course 4: Linear modelling

The fourth and final course gives some of the mathematical development underlying linear modelling. The material covers linear regression on a single explanatory variable; multiple linear regression where there is more than one explanatory variable; and generalised linear modelling for regression situations where the normal distribution is not a suitable model for variation in the response. Both classical and Bayesian approaches to the analysis of these models are considered.

You will learn

Successful study of this module should enhance your skills in understanding some useful mathematical theory, interpreting mathematical results in a statistical context, constructing logical arguments, and finding solutions to problems.

From small apps to large business systems, from smart phones to smart environments, from wearables to ambient installations, from virtual reality to augmented reality – interactive computing technologies have become part of the fabric of everyday life. This module will help you on your way to becoming an effective interaction designer. You’ll learn what interaction design is about and how to design interactive products that offer good user experiences. You’ll learn about the multitude of factors that influence user experience; the theories that underlie good interaction design; and the methods and techniques designers use to create effective interactive products.

What you will study

Why are some interactive products so popular? How do you create products that everybody wants? One of the fundamental things you will learn in this module is the importance of user-centred design.

You will learn the value of moving away from your desk and ‘stepping out into the world’ to involve potential users in your early design ideas for interactive products. It is all too easy to assume that others think, feel and behave in the same way as we, the designer or developer, do. It is essential to take into account the diversity among users and their different perspectives and getting their feedback will help you to avoid any errors and misunderstandings that you may not have thought of. Involving users in the process is vital to creating great products and makes good business sense: after all, who wants to buy a bad product?

With our guidance, through hands-on activities you’ll work through the design process on a project of your choice. This will include hands-on activities and form part of the tutor-marked assignments (TMAs). Each TMA addresses one stage in the design life-cycle. By the end of the module you will have practical experience of the full life-cycle through your own project. You will acquire practical skills that will equip you with the tools you need to analyse, design and evaluate interactive products. You will develop skills that will be important to you in a variety of employment settings – whether working as a developer as part of a large software development team, as a partner in a small start-up, or in some other role involved in the managing of, or decision making around interactive products that will be used by others.

The module uses the international best-selling book Interaction Design: Beyond Human-Computer Interaction as a reference text and is organised in four courses:

Course 1 – Introduction and overview

What is interaction design? This course gets across the fundamental idea of what we mean by interaction design and the importance of it being user centred. You will begin to reflect on what makes some designs usable and satisfying – and others not – and get hands-on experience of the process of designing. An important principle of our approach to interaction design is that there is diversity among users – not only in terms of their physical characteristics and capabilities, but also of their cognitive and sensory characteristics.

Course 2 – Requirements

Who are the users and what do they want? As part of the process of defining the requirements for an interactive product we need to know the user’s characteristics but we also need to be aware of the user’s context – both in terms of their physical environment and in terms of the activities they are engaged in. This course studies a range of requirement gathering approaches including talking to users, observational methods including the use of technology probes, and more. You will also learn to use tools and techniques such as developing personas and scenarios, which will help you share information with the stakeholders (the team, the users, the customer) and communicate effectively about the requirements for an interactive product.

Course 3 – Design

Designing is about balancing the requirements. It involves thinking through the underlying idea for the interactive product and the more concrete, physical aspects. This course tackles all these things. You will learn to use reflective tools to help you work out and communicate the main idea for a design, including what users will be able to do with it, and how they will experience it. We discuss a range of interface types, from more traditional screen-based forms of interaction to mobile, wearable, haptic and other interface types and you will learn and use a range of prototyping methods and tools.

This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams. The word ‘graphs’ refers to diagrams consisting of points joined by lines. These points may correspond to chemical atoms, towns, electrical terminals or anything that can be connected in pairs. The lines may be chemical bonds, roads, wires or other connections. The main topics of mathematical interest are graphs and digraphs; network flows; course designs; geometry; codes; and mathematical modelling. Application areas covered include communications; structures and mechanisms; electrical networks; transport systems; and computer science. To study this module you should have a sound knowledge of relevant mathematics provided by the appropriate ISC level 2 study.

What you will study

What codes are used by spacecraft in communicating with Earth? Where do you brace a framework to make it rigid? How many colours are needed for a map to ensure that neighbouring countries have different colours? How can you assign people to jobs for which they are qualified? These are some of the questions to be answered in the module. The problems range from those arising in technology, operational research and the sciences to puzzles of a recreational nature. We show the connections between problems in widely differing areas and describe methods for their solution that use the properties they have in common.

The material is presented in a down-to-earth manner, with the emphasis on solving problems and applying algorithms, rather than on abstract ideas and proofs.

The module is divided into three related areas: graphs, networks and design. The Introduction introduces two themes of the module, combinatorics and mathematical modelling, and illustrates them with examples from the three areas.

Graphs 1:

Graphs and digraphs discusses graphs and digraphs in general, and describes the use of graph theory in genetics, ecology and music, and of digraphs in the social sciences. We discuss Eulerian and Hamiltonian graphs and related problems; one of these is the well-known Königsberg bridges problem.

Networks 1:

Network flows is concerned with the problem of finding the maximum amount of a commodity (gas, water, passengers) that can pass between two points of a network in a given time. We give an algorithm for solving this problem, and discuss important variations that frequently arise in practice.

Design 1

: Geometric design, concerned with geometric configurations, discusses two-dimensional patterns such as tiling patterns, and the construction and properties of regular and semi-regular tilings, and of polyominoes and polyhedra.

Graphs 2:

Trees Trees are graphs occurring in areas such as branching processes, decision procedures and the representation of molecules. After discussing their mathematical properties we look at their applications, such as the minimum connector problem and the travelling salesman problem.

Networks 2:

Optimal paths How does an engineering manager plan a complex project encompassing many activities? This application of graph theory is called ‘critical path planning’. It is one of the class of problems in which the shortest or longest paths in a graph or digraph must be found.

Design 2:

Kinematic design The mechanical design of table lamps, robot manipulators, car suspension systems, space-frame structures and other artefacts depends on the interconnection of systems of rigid bodies. This unit discusses the contribution of combinatorial ideas to this area of engineering design.

Graphs 3:

Planarity and colouring When can a graph be drawn in the plane without crossings? Is it possible to colour the countries of any map with just four colours so that neighbouring countries have different colours? These are two of several apparently unrelated problems considered in this unit.

Networks 3:

Assignment and transportation If there are ten applicants for ten jobs and each is suitable for only a few jobs, is it possible to fill all the jobs? If a manufacturer supplies several warehouses with a product made in several factories, how can the warehouses be supplied at the least cost? These problems of the system-management type are answered in this unit.

Design 3:

Design of codes Redundant information in a communication system can be used to overcome problems of imperfect reception. This section discusses the properties of certain codes that arise in practice, in particular cyclic codes and Hamming codes, and some codes used in space probes.

Graphs 4:

Graphs and computing describes some important uses of graphs in computer science, such as depth-first and breadth-first search, quad trees, and the knapsack and travelling salesman problems.

Networks 4:

Physical networks Graph theory provides a unifying method for studying the current through an electrical network or water flow through pipes. This unit describes the graphical representation of such networks.

Design 4:

Course designs If an agricultural research station wants to test different varieties of a crop, how can a field be designed to minimise bias due to variations in the soil? The answer lies in block designs. This unit explains the concepts of balanced and resolvable designs and gives methods for constructing block designs.

Conclusion In this unit, many of the ideas and problems encountered in the module are reviewed, showing how they can be generalised and extended, and the progress made in finding solutions is discussed.

You will learn

Successful study of this module should enhance your skills in finding solutions to problems, interpreting mathematical results in real-world terms and communicating mathematical ideas clearly to both experts and non-experts.

This module addresses some of the key concepts required for the traditionally important area of data management, and the increasingly important area of data analytics. You’ll gain a practical, legal and ethical understanding of how to access, query and manage data collections, using traditional relational databases and contemporary NoSQL approaches. Using real-world datasets, standard software packages and data visualisation techniques, you’ll learn how to organise and analyse data collections to answer questions about the world, as well as developing an appreciation of user needs surrounding data systems.

What you will study

This module will provide you with a broad overview of the concepts, techniques and tools of modern data management and analysis. It will compare traditional relational databases with an alternative model (a NoSQL database), and will help you learn how to choose the most appropriate means of storing and managing data, depending on the size and structure of a particular dataset and its intended use. You will be introduced to preliminary techniques in data analysis, starting from the position that data is used to answer a question, and introduced to a range of data visualisation and analysis techniques that will instil an understanding of how to start exploring a new data set.

To ensure that you are comfortable with handling datasets, you will explore a range of real-world datasets to illustrate the key concepts in the module. Sources such as data.gov.uk, the World Bank, and a range of other national and international agencies may be used to provide appropriate data. You will spend approximately equal time between issues in data management (technical and socio-legal issues in storing and maintaining datasets), and issues in data analytics (understanding how data can be used to answer questions).

The module is framed around a narrative that looks at how to manage and extract value and insight from a range of increasingly large data collections. At each stage, a comparison will be drawn between different ways of representing the data (for example, using different sorts of charts or geographical mapping techniques), and limitations of the mechanisms presented. To enable you to get a feel for the use of data, each stage will also include an overview of some data analysis techniques, including summary reporting and exploratory data visualisation. This module is driven by Richard Hamming’s famous quote: ‘The purpose of computing is insight, not numbers’.

Some of the key ideas are:

Introducing data analysis

Starting with a data file such as a spreadsheet, this unit will provide you with a brief introduction to some basic operations on simple data files. This will give you an opportunity to study an outline of the key ideas in the module and help you become familiar with the module software.

Concepts in data management

You will look at three key areas in data management: data architectures and data access (CRUD), data integrity, and transaction management (ACID). Each of these topics will be illustrated using a relational database, and one non-relational alternative. The advantages and limitations of each model are discussed.

Legal and ethical issues

Here you will consider the legal and ethical issues involved in managing data collections. You will be required to obtain and read (parts of) the Data Protection Act and the Freedom of Information Act, and demonstrate how these apply to issues in data management. You will also consider privacy, ownership, intellectual property and licensing issues in data collection, management, retrieval and reuse.

Concepts in data analytics

These sections will focus on using data to answer a real question; the focus will be on exploratory techniques (such as visualisation) and formulating a question into a form that can be answered realistically using the data that is available. Issues in processing techniques for large and real-time streamed data collections will also be addressed along with techniques and technologies (such as MapReduce) for handling them. In this part of the module you will use a statistical package such as the python scientific libraries and/or ggplot2 to visualise the data and carry out appropriate analyses.

If you are considering progressing to The computing and IT project, this is one of the ISC level 3 modules on which you could base your project topic. Normally, you should have completed one of these ISC level 3 modules (or be currently studying one) before registering for the project module.

This module introduces models to describe patterns of events that occur in time (such as earthquakes), and in space (for instance, the occurrence of a species of plant). Situations that occur only at discrete time points, including the ruin of a gambler, are studied. Probability models are developed for those situations, such as the spread of an epidemic, in which events may occur at any time. The module ends with other situations involving probability including genetics and changes in stock market prices. You are expected to be reasonably competent in calculus and algebra.

What you will study

This module in probability and its applications emphasises probability modelling and developing the properties of the models. A considerable amount of mathematics is sometimes required for this development, but we do not always give formal proofs, particularly if the proof does not illuminate the probabilistic ideas.

The module consists of five books.

The first one, which is introductory, revises and develops ideas about probability and introduces some techniques that will be used frequently in the module.

The second book develops models for events occurring in time, including the Poisson process and several extensions of it, and patterns in space, including models for random scatter and clustering of objects.

The third book develops models for processes in which events can occur only at discrete time points, such as a Bernoulli process. This includes practical situations such as the ruin of a gambler and the extinction of a family surname.

In the fourth book, probability models are developed for situations in which events can occur at any time. Examples include queues, the spread of epidemics, and the change in the size of a population due to births and deaths.

In the fifth book, models are developed for various situations, including genetics, the renewal of components, and the change in stock market prices.

You will learn

Successful study of this module should enhance your skills in understanding mathematical arguments, expressing problems in mathematical language, finding solutions to problems and interpreting mathematical results in real-world terms.