Data Science - BSc (Hons)

with a Foundation Year

Functions: Functions, inverse functions and composite functions. Domain and range.

Elementary functions including the exponential function, the logarithm and natural logarithm functions and ax for positive real numbers a. Basic introduction to limits and continuity of a function, without epsilon-delta proofs.The derivative: The derivative as the gradient of the tangent to the graph; interpretation of the derivative as a rate of change. The formal definition of the derivative and the calculation of simple examples from first principles. Elementary properties of the derivative, including the product rule, quotient rule and the chain rule; differentiation of inverse functions; calculating derivatives of familiar functions, including trigonometric, exponential and logarithmic functions. Applications of the derivative, including optimisation, gradients, tangents and normal. Parametric and implicit differentiation of simple functions. Taylor series.Graphs: Curve sketching including maxima, minima, stationary points, points of inflection, vertical and horizontal asymptotes and simple transformations on graphs of functions. Additional material may include parametric curves and use of Maple to plot functions.

This module introduces the ideas of integration and numerical methods.

a) Integration: Integration as a limit of a sum and graphical principles of integration, derivatives, anti-derivatives and the Fundamental Theorem of Calculus (without proof), definite and indefinite integrals, integration of simple functions.b) Methods of integration: integration by parts, integration by change of variables and by substitution, integration by partial fractions.c) Solving first order differential equations: separable and linear first order differential equations. Construction of differential equations in context, applications of differential equations and interpretation of solutions of differential equations.d) Maple: differentiation and integration, curve sketching, polygon plots, summations.

Additional material may include root finding using iterative methods, parametric integration, surfaces and volumes of revolution.

Students will be introduced to key mathematical skills, necessary in studying for a mathematics degree: use of the University Library and other sources to support their learning, present an argument in oral or written form, learn about staff in the School and beyond, etc. In particular, students will study various techniques of proof (by deduction, by exhaustion, by contradiction, etc.). These techniques will be illustrated through examples chosen from various areas of mathematics (and in particular co-requisite modules).

Statistical techniques are a fundamental tool in being able to measure, analyse and communicate information about sets of data. Using illustrative data sets we show how statistics can be indispensable in applied sciences and other quantitative areas. This module covers the basic methods used in probability and statistics using Excel for larger data sets.

Sampling from populations. Data handling and analysis using Excel. Graphical representation for the interpretation of univariate and bivariate data; outliers. Sample summary statistics: mean, variance, standard deviation, median, quartiles, inter-quartile range, correlation. Probability: combinatorics, conditional probability, Bayes' Theorem. Random variables: discrete, continuous; expectation, variance, standard deviation. Discrete and continuous distributions: Binomial, discrete uniform, Normal, uniform. Sampling distributions for the mean and proportion. Hypothesis testing: one sample, mean of Normal with known variance and proportion, 1- and 2-tail. Confidence intervals: one sample, mean of Normal with known variance and population proportion.

This module introduces fundamental methods needed for the study of mathematical subjects at degree level.

Trigonometry: introduction to the trigonometric functions, inverse trigonometric functions, radians, properties of sine and cosine functions, trigonometric identities, solving trigonometric equations

Geometry: circles and ellipses, triangles, SOHCAHTOA, sine and cosine rule, opposite and alternate angle theorems

Hyperbolic functions: introduction to hyperbolic functions and inverse hyperbolic functions including definitions, domains and ranges and graphs.

Complex numbers: introduction to the system of complex numbers and its geometrical interpretation..

Through this module, students will develop the transferable linguistic and academic skills necessary to successfully complete other modules on their programme and acquire the specific language skills that they will require when entering SMSAS and SPS Stage 1 programmes. The programme of study focuses on writing and speaking skills, enhancing academic language through classroom, homework and assessed activities. Writing skills will be used to write a technical report, interpret data and describe processes. Spoken skills will be used in presentations and seminars.

This module introduces the students to the basics of Maple and three topics in the mathematical sciences. The precise topics will vary in any particular year. Potential topics include (for example): history and/or people active in the mathematical sciences, algorithms, engaging the public in the mathematical sciences, mathematical games. Each topic is supported by a series of workshops introducing key aspects of the topic. Maple: the Maple environment, basic commands, basic calculus, curve sketching. There is no specific mathematical syllabus for the topics part of the module.

Algebra: simplifying expressions and rearranging formulae, indices, surds, algebraic fractions, solution of linear and quadratic equations and simultaneous equations, quadratic equations and the discriminant, inequalities and interval notation, binomial expansions, manipulating and factorising polynomials, exponentials and logarithms, equations involving exponentials. Functions and graphs: plotting and recognising the graphs of elementary functions (modulus, exponential, …), roots, intercepts, turning points, area (graphical methods), co-ordinate geometry of straight lines, parallel and perpendicular lines, applications to plots of experimental data, simple graph transformations.

This module equips students with an understanding of how modern cloud-based applications work. Topics covered may include:

A high-level view of cloud computing: the economies of scale, security issues, ethical concerns, the typical high-level architecture of a cloud-based application, types of available services (e.g., parallelization, data storage).

Cloud infrastructure: command line interface; containers and virtual machines; parallelization (e.g., MapReduce, distributed graph processing); data storage (e.g., distributed file systems, distributed databases, distributed shared in-memory data structures).

Cloud concepts: high-level races, transactions and sequential equivalence; classical distributed algorithms (e.g., election, global snapshot, consensus, distributed mutual exclusion); scheduling, fault-tolerance and reliability in the context of a particular parallelization technology (e.g., MapReduce).

Operating system support: network services (e.g., TCP/IP, routing, reliable communication), virtualization services (e.g., virtual memory, containers).

This module introduces widely-used mathematical methods for functions of a single variable. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage. Tutorials and Maple worksheets will be used to support taught material.

Complex numbers: Complex arithmetic, the complex conjugate, the Argand diagram, de Moivre's Theorem, modulus-argument form; elementary functions

Polynomials: Fundamental Theorem of Algebra (statement only), roots, factorization, rational functions, partial fractions

Single variable calculus: Differentiation, including product and chain rules; Fundamental Theorem of Calculus (statement only), elementary integrals, change of variables, integration by parts, differentiation of integrals with variable limits

Scalar ordinary differential equations (ODEs): definition; methods for first-order ODEs; principle of superposition for linear ODEs; particular integrals; second-order linear ODEs with constant coefficients; initial-value problems

Curve sketching: graphs of elementary functions, maxima, minima and points of inflection, asymptotes.

This module provides an introduction to object-oriented software development. Software pervades many aspects of most professional fields and sciences, and an understanding of the development of software applications is useful as a basis for many disciplines. This module covers the development of simple software systems.

Students will gain an understanding of the software development process, and learn to design and implement applications in a popular object-oriented programming language. Fundamentals of classes and objects are introduced and key features of class descriptions: constructors, methods and fields. Method implementation through assignment, selection control structures, iterative control structures and other statements is introduced. Collection objects are also covered and the availability of library classes as building blocks. Throughout the course, the quality of class design and the need for a professional approach to software development is emphasised and forms part of the assessment criteria.

Introduction to Probability. Concepts of events and sample space. Set theoretic description of probability, axioms of probability, interpretations of probability (objective and subjective probability).

Theory for unstructured sample spaces. Addition law for mutually exclusive events. Conditional probability. Independence. Law of total probability. Bayes' theorem. Permutations and combinations. Inclusion-Exclusion formula.

Discrete random variables. Concept of random variable (r.v.) and their distribution. Discrete r.v.: Probability function (p.f.). (Cumulative) distribution function (c.d.f.). Mean and variance of a discrete r.v. Examples: Binomial, Poisson, Geometric.

Continuous random variables. Probability density function; mean and variance; exponential, uniform and normal distributions; normal approximations: standardisation of the normal and use of tables. Transformation of a single r.v.

Joint distributions. Discrete r.v.'s; independent random variables; expectation and its application.

Generating functions. Idea of generating functions. Probability generating functions (pgfs) and moment generating functions (mgfs). Finding moments from pgfs and mgfs. Sums of independent random variables.

Laws of Large Numbers. Weak law of large numbers. Central Limit Theorem.

An introduction to databases and SQL, focussing on their use as a source for content for websites. Creating static content for websites using HTML(5) and controlling their appearance using CSS. Using PHP to integrate static and dynamic content for web sites. Securing dynamic websites. Using Javascript to improve interactivity and maintainability in web content.

Introduction to R and investigating data sets. Basic use of R (Input and manipulation of data). Graphical representations of data. Numerical summaries of data.

Sampling and sampling distributions. ?² distribution. t-distribution. F-distribution. Definition of sampling distribution. Standard error. Sampling distribution of sample mean (for arbitrary distributions) and sample variance (for normal distribution) .

Point estimation. Principles. Unbiased estimators. Bias, Likelihood estimation for samples of discrete r.v.s

Interval estimation. Concept. One-sided/two-sided confidence intervals. Examples for population mean, population variance (with normal data) and proportion.

Hypothesis testing. Concept. Type I and II errors, size, p-values and power function. One-sample test, two sample test and paired sample test. Examples for population mean and population variance for normal data. Testing hypotheses for a proportion with large n. Link between hypothesis test and confidence interval. Goodness-of-fit testing.

Association between variables. Product moment and rank correlation coefficients. Two-way contingency tables. ?² test of independence.

To be confirmed.

Built on the foundation of object-oriented software development, this module provides an introduction software development for Artificial Intelligence (AI). In this module, students will gain an understanding of data analysis and statistics techniques, including summarising data, using measures of central tendency and dispersion, and effective graphical representations. Various probability models, including normal and binomial distributions, sampling and inference and predictive techniques are introduced.

Throughout the module, students will learn to embed data analysis and statistics concepts into a programming language which offers good support for AI (e.g., Python). Students will learn to use important AI-purposed libraries and tools, and apply these techniques to data loading, processing, manipulation and visualisation.

Building scaleable web sites using client-side and and server-side frameworks (e.g. JQuery, CodeIgniter). Data transfer technologies, e.g. XML and JSON. Building highly interactive web sites using e.g. AJAX. Web services. Deploying applications and services to the web: servers, infrastructure services, and traffic and performance analysis. Web and application development for mobile devices.

This module aims to strengthen the foundational programming-in-the-small abilities of students via a strong, practical, problem solving focus. Specific topics will include introductory algorithms, algorithm correctness, algorithm runtime, as well as big-O notation. Essential data structures and algorithmic programming skills will be covered, such as arrays, lists and trees, searching and sorting, recursion, and divide and conquer.

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This module covers the basic principles of machine learning and the kinds of problems that can be solved by such techniques. You learn about the philosophy of AI, how knowledge is represented and algorithms to search state spaces. The module also provides an introduction to both machine learning and biologically inspired computation.

This module provides an introduction to the theory and practice of database systems. It extends the study of information systems in Stage 1 by focusing on the design, implementation and use of database systems. Topics include database management systems architecture, data modelling and database design, query languages, recent developments and future prospects.

This module is designed to provide students with an introduction to the use of data analytics tools on large data sets including the analysis of text data. The module will begin by discussing the principles of text-mining and big data. The module will then discuss the techniques that can be used to explore large data sets (including pre-processing and cleaning) and the use of multivariate statistical techniques for supervised and unsupervised learning. The module will conclude by considering several data mining techniques.

Constructing suitable models for data is a key part of statistics. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. Even if the temperature and pressure are fixed, there will be variation in the yield which motivates the use of a statistical model which includes a random component. In this module, students study linear regression models (including estimation from data and drawing of conclusions), the use of likelihood to estimate models and its application in simple stochastic models. Both theoretical and practical aspects are covered, including the use of R.