Bhu Bsc Maths Hons Syllabus

[Laila Berri]

Weknow you care about your career. So we've got a maths course that will set you up for a well-paid one. We rapidly adapt what we teach to reflect the fast-moving graduate employment market, and our courses are built on the research expertise of our world-leading mathematicians.

When most people think of maths, they think of maths in theory alone, but we don't and neither do you. Maths at Kent is dual focused, so as much as theory is important, we care about application. Maths is astronomy, advertising, defense, logistics, media, sales and just about anything else you can think of.

If you bring us your talents in mathematics, we will give you the knowledge, skills and confidence to make it count. Maths is everywhere, and a degree in Mathematics from the University of Kent is your key to getting to wherever you want to go.

During Clearing our entry requirements change in real time to reflect the supply and demand of remaining course vacancies. If you think you've found the course for you, apply now to start your Kent journey this September.

The University receives applications from over 140 different nationalities and consequently will consider applications from prospective students offering a wide range of international qualifications. Our International Development Office will be happy to advise prospective students on entry requirements. See our International Student website for further information about our country-specific requirements.

This module serves as an introduction to algebraic methods. These methods are central in modern mathematics and have found applications in many other sciences, but also in our everyday life. In this module, students will also gain an appreciation of the concept of proof in mathematics.

This module is a sequel to Algebraic Methods. It considers the abstract theory of linear spaces together with applications to matrix algebra and other areas of Mathematics (and its applications). Since linear spaces are of fundamental importance in almost every area of mathematics, the ideas and techniques discussed in this module lie at the heart of mathematics. Topics covered will include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalisation, orthogonality and applications including conics.

This module introduces widely-used mathematical methods for vectors and functions of two or more variables. 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.

Vectors: Cartesian coordinates; vector algebra; scalar, vector and triple products (and geometric interpretation); straight lines and planes expressed as vector equations; parametrized curves; differentiation of vector-valued functions of a scalar variable; tangent vectors; vector fields (with everyday examples)

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.

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.

Limits of Sequences: Sequences, definition of convergence, epsilon terminology, uniqueness, algebra of limits, comparison principles, standard limits, subsequences and non-existence of limits, convergence to infinity.

This module builds on the Stage 1 Real Analysis 1 module. We will extend our knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives.

The outline syllabus includes: Continuity and uniform continuity of functions of one variable, series and power series, the Riemann integral, limits and continuity for functions of several variables, differentiation of functions of several variables, extrema, the Inverse and Implicit Function Theorems.

This module builds on MAST4014 Calculus and Differential Equations. The aim is to introduce the mathematical tools to perform calculations and apply these tools to interesting applications in physics. The syllabus is as follows:

Vectors: Introduction of vector algebra and products of vectors. Triple products of vectors. Vector geometry. Vector equations. Vector differentiation. Coordinate systems (Cartesian, plane polar, cylindrical polar and spherical polar coordinates).

This module builds on MAST4014 Calculus and Differential Equations. We will cover advanced methods for solving ordinary differential equations and introduce, and learn to solve, partial differential equations. We will explore the properties of these differential equations and discuss the physical interpretation of certain equations and their solutions.

The security of our phone calls, bank transfers, etc. all rely on one area of Mathematics: Number Theory. This module is an elementary introduction to this wide area and focuses on solving Diophantine equations. In particular, we discuss (without proof) Fermat's Last Theorem, arguably one of the most spectacular mathematical achievements of the twentieth century. Outline syllabus includes: Modular Arithmetic; Prime Numbers; Introduction to Cryptography; Quadratic Residues; Diophantine Equations.

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.

Probability: Joint distributions of two or more discrete or continuous random variables. Marginal and conditional distributions. Independence. Properties of expectation, variance, covariance and correlation. Poisson process and its application. Sums of random variables with a random number of terms.

This module is an introduction to the methods, tools and ideas of numerical computation. In mathematics, one often encounters standard problems for which there are no easily obtainable explicit solutions, given by a closed formula. Examples might be the task of determining the value of a particular integral, finding the roots of a certain non-linear equation or approximating the solution of a given differential equation. Different methods are presented for solving such problems on a modern computer, together with their applicability and error analysis. A significant part of the module is devoted to programming these methods and running them in MATLAB.

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.

Syllabus: What is "big data"? What is text mining? Exploratory data analysis for large datasets, and pre-processing and cleaning; Multivariate statistical analysis (both unsupervised, e.g. factor analysis or principle component analysis, and supervised, e.g. linear discriminant analysis); Data security; Data mining including techniques such as classification trees, neural networks, clustering, text analysis or network analysis.

In this module we study the fundamental concepts and results in game theory. We start by analysing combinatorial games, and discuss game trees, winning strategies, and the classification of positions in so called impartial combinatorial games. We then move on to discuss two-player zero-sum games and introduce security levels, pure and mixed strategies, and prove the famous von Neumann Minimax Theorem. We will see how to solve zero-sum two player games using domination and discuss a general method based on linear programming. Subsequently we analyse arbitrary sum two-player games and discuss utility, best responses, Nash equilibria, and the Nash Equilibrium Theorem. The final part of the module is devoted to multi-player games and cooperation; we analyse coalitions, the core of the game, and the Shapley value.

There is no specific mathematical syllabus for this module.Students will study a topic in mathematics or statistics, either individuallyor within a small group, and produce an individual or group project on thetopic as well as individual coursework assignments. Projects will be chosenfrom published lists of individual and of group projects. The coursework andproject-work are supported by a series of workshops covering various forms ofwritten and oral communication and by supervision from an academic member ofstaff.

This module looks into the training of modern deep neural networks: backpropagation, regularisation, automatic differentiation, computational graphs. Introduces different types of deep neural networks, such as, LSTM, convolutional networks, and autoencoders. Presents the theoretical underpinnings of deep learning and its mechanisms. Delves into selected recent advanced topics in deep learning. Examines applications of deep learning.

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