BACHELOR OF SCIENCE HONOURS FINANCIAL MATHEMATICS (HFM)
| Module Code | Module Name | Description |
|---|---|---|
| HFM 102 | Calculus | This module aims to gently introduce the rigour of mathematical analysis to first year undergraduate students with some background in A-Level calculus. The concentration is on motivating results and concepts geometrically rather than on providing rigorous proofs. Concepts are defined carefully and results stated precisely, but illustrated by way of vivid, concrete examples. The module covers topics such as: Vectors; Lines and planes. Vector-valued functions. Functions of several variables; Integration. Infinite series and Taylor series. |
| HFM113 | Linear Mathematics and Ordinary Differential Equations | This module is mostly about algebraic ideas and complements the material in Calculus 1. It introduces and develops concepts (including complex numbers and the algebra of polynomials) necessary for a first module in linear algebra. Along the way some of the mathematical areas where linear structure emerges as the common feature are included to give motivation and to illustrate the theory. Revision of the basic techniques for the solution of first and second order ODE's. Modelling with first and second-order ODE's. Existence and uniqueness of solutions. Series solutions of linear ODE's, solutions near ordinary points, singular points, Euler equations. Laplace transform methods for solving initial value problem (IVP). Solution of IVP, Heaviside and Dirac functions. |
| HASTS101 | Probability Theory | Introduction to the theory of probability with emphasis on understanding of concepts. An applied approach with plenty of examples is preferred. Probability: Classical or a priori probability, frequency or a posterior probability, axiomatic probability, sets and events, sample space, conditional probability, independence, laws of probability. |
| MTHCS112 | Mathematical Discourse and Structures | The module aims to help students get an idea of what mathematics as a discipline really is, its language, structure and presentation. It also aims to help students to come to grips with abstract notions at an early stage in their university level training. Finally, it aims to provide the students with the foundations of advanced mathematics. By the end of this module a student should: Be able to understand sets and different types of relations on sets. Be able to construct proofs and to understand various types of proofs and how those proofs are applied. Demonstrate a strong grasp of the language of mathematics through effective writing and reading of mathematical arguments. To understand different types of structures and operations. Topics to be covered are: Sets and Relations. Logic. Operations and Structures. Numbers. |
| FM201 | Programming Fundamentals | This module introduces the student to the Python language. This module aims to equip students with practical skills and knowledge of application development using Python. This module is perched at an introductory level, assuming no previous knowledge of programming by students. This module forms the foundation of many higher-level modules. Upon completion of this module, students will be able to: (1) Execute Python code in a variety of environments; (2) Use correct Python syntax in Python programs; (3) Use the correct Python control flow construct; (4) Write Python programs using various collection data types ; (5) Write home grown Python functions; (6) Use many of the standard Python modules such as os, sys, math, and time; (6) Trap various errors via the Python Exception Handling model; (7) Use the IO model in Python to read and write disk files; (8) Create their own classes and use existing Python class; (9) Understand and use the Object Oriented paradigm in Python programs; (10) Use the Python Regular Expression capabilities for data verification |
| ECD101 | Principles of Micro-Economics | Microeconomics: covers types of economies (market, command and mixed economies) and scarcity. Partial equilibrium analysis of markets: demand analysis, supply analysis, elasticities, equilibrium in markets. Consumer behaviour: marginal utility theory, indifference curve and consumer surplus. Theory of Production and marginal products: production function, total, average and marginal product, law of diminishing returns, returns to scale; short run and long run. Production costs: short run and long run including marginal, average and total costs. Market structures: perfect competition, monopoly, monopolistic competition and introduction to oligopoly |
| ACCN101 | Business Accounting | This module provides students with a comprehensive understanding of accounting theories and financial procedures for limited liability companies and partnerships. It covers the theoretical framework of accounting, including definitions, objectives of financial statements, principles, assumptions, and the hierarchy of accounting qualities. Key topics include the structure and components of financial statements like income statements, balance sheets, and cash flow statements, alongside share and debenture issues. The module emphasizes financial statement analysis techniques such as trend and ratio analysis, the considerations for business takeovers (including performance assessment, due diligence, and accounting treatment for goodwill), and methods for valuing business interests and individual securities. Additionally, it introduces accounting for business interests, investment accounts, and relevant International Financial Reporting Standards (IFRS). The curriculum addresses share and debenture redemption processes, the legal framework for financial reporting, and the intricacies of consolidated financial statements for subsidiaries. Overall, this module equips students with essential knowledge for effectively navigating financial accounting in various business contexts. |
| HFM211 | Securities Markets | This module seeks to provide an understanding of (a) the role of securities markets in the economy (b) their basic mechanics and technical features (c) the valuation of financial assets (d) the operational and allocative efficiency of the market. By the end of the module students will be able to (i) appreciate the central role of securities markets in the economy. (ii) Understand and apply appropriate economic theory to market organisation (iii) display an understanding of the usefulness of portfolio theory and the approaches to the valuation of financial assets. (iv)Read the financial press and appreciate issues relating to the study of the securities markets. |
| HFMCS201 | Foundations of Financial Mathematics | The aim of this module is to provide a grounding in financial mathematics and its simple applications. Topics include: Generalised cash flow model; The time value of money; Interest rates; Real and money interest rates; Discounting and accumulating; Compound interest functions; Equations of value; Loan schedules; Project appraisal; Investments; Compound interest problems; The “No Arbitrage” assumption; Term structure of interest rates; Stochastic interest rate models. |
| HFM215 | Financial Risk Management and Regulations |
This module focuses on the various risks associated with banking, including liquidity, interest rate, credit, foreign exchange, and operational risks, along with integrated risk management strategies. It starts by defining risk and identifying its types and sources, emphasizing financial risks specific to banks. Key topics include risk diversification, management practices, and the regulatory framework guiding the banking industry, particularly the Basel Accords. Students will learn about the components of a bank's balance sheet and the significance of asset-liability management. The module covers liquidity risk management—its dimensions and measurement—along with techniques for managing interest rate risk, foreign exchange risk, and market risk, including the use of derivatives. Credit risk management frameworks will be explored in detail, highlighting policies for transactional management and active credit portfolio oversight. Additionally, operational risk management practices will address classification, quantification, and monitoring. Finally, the module underscores the importance of integrated risk management and the challenges involved, providing a comprehensive understanding of risk management in the banking sector. |
| HFM213 | Numerical Methods | This module is an introduction to the numerical analysis. The primary objective of the module is to develop the basic understanding of numerical algorithms and skills to implement algorithms to solve mathematical problems using computer software. Use numerical methods for solving a problem, locate and use good mathematical software, get the accuracy you need from the computer, assess the reliability of the numerical results, and determine the effect of round off error or loss of significance. |
| HFM214 | Regression analysis and ANOVA | This module is designed for researchers in the clinical and translational sciences who want to understand and use linear regression techniques. Topics covered include multiple linear regression, regression diagnostics, analysis of variance, analysis of covariance, confounding, mediation, moderation, interactions, and model selection. At the completion of the module, trainees should be able to demonstrate an understanding of the basic principles of ANOVA and linear regressions, to assess their adequacy and assumptions, to analyze simple data sets taken from the fields of medicine and public health, to summarize results from regression models via written communication, and to recognize situations that require more advanced methodologies. |
| HFM312 | Numerical Solutions of PDEs |
The module introduces numerical methods, especially the finite difference methods (FDM) technique for solving different types of partial differential equations (PDEs). The main numerical issues such as convergence and stability will bediscussed. The module will cover the following: 1.Introduction and Fundamentals:
(a) Grid points for Elliptic PDEs. (b) Application to steady state heat flow. (c) Iterative methods for Laplace methods. (d) Neumann problems. (e) Irregular regions. Curvilinear coordinates. Nonrectangular grids.
(a) Unsteady heat flow and diffusion. (b) Convergence, stability and consistency. (c) The explicit and implicit methods. (d) Crank-Nicolson. (e) Sweep and theta methods. (f) Derivative boundary boundary conditions. (g) Peaceman-Rachford methods
(a) CFL condition and Fourier analysis; (b) Upwind scheme and Lax-Wendroff scheme; |
| HFM315 | Stochastic Calculus | This module aims to provide a good and rigorous understanding of the mathematics used in derivative pricing and to enable students to understand where the assumptions in the models break down. Continuous time processes: basic ideas, filtration, conditional expectation, stopping times. Continuous parameter martingales, sub- and super-martingales, martingale inequalities, optional sampling. Wiener martingale, stochastic integral, the Itô calculus and some applications. Multi-dimensional Wiener process, multi-dimensional Itô formula. Stochastic differential equations Change of measure, Girsanov's theorem, equivalent martingale measures and arbitrage. Representation of martingales and the Ornstein-Uhlenbeck process. |
| HFM311 | Multivariate Methods | Descriptive statistics (sample means, sample covariance and correlation matrix), graphical techniques. Random vectors and matrices, their expectations and properties; expected values of the sample mean and sample covariance matrix. Properties; sampling distribution of sample mean and sample covariance matrix; Wishart-distribution. Transformations to near normality; testing for normality. Hotelling's T2 distributions and likelihood ratio test; comparison with one dimensional case; confidence regions and simultaneous comparisons of component means; Bonferroni method of multiple comparisons. Comparing mean vectors from two populations; comparisons of several multivariate population means(one way MANOVA); simultaneous confidence intervals for treatment effects; profile analysis; ideas of two way MANOVA. Multivariate linear regression Review of eigenvalues and eigenvectors; spectral decomposition of symmetric matrix. Principal component analysis. Factor Analysis. Canonical correlation analysis. Discrimination and classification. Discriminant analysis, cluster analysis. |
| HFM470 | Dissertation | Students are required to do a research product involving independent investigations of selected problems pertaining to the dissertation. The research project is a core module, that is, a student has to pass the project in order to graduate. |
| HFM302 | Partial Differential Equations | The module is an introduction to the theory of partial differential equations and also provides methods of solution of boundary and initial value problems of Mathematical Physics. Students are taught how to identify different types of partial differential equations and to obtain the equations that are satisfied by given functions. Analytical methods of solutions of first order equations having certain standard forms are given. Contents: Idea of partial differential equations PDE’s and boundary and initial conditions. Classification of PDE’s. Well posed problems and uniqueness of solutions; General methods for first order PDE’s. Linear and Quasi-linear equations and characteristics. Charpits and Jacobi’s method. Solution of pdes by the Fourier and Laplace transform methods; Laplace and Poison equations-maximum principle, uniqueness of Dirichlet problem on bounded domain, separation of variables in circular domains; Greens functions for the Heat, Wave and Laplace equations; Brief survey of nonlinear pdes. |
| HFM315 | Stochastic Processes | Classification of the general stochastic processes like the Poisson and Brownian motion or Wiener Processes and review probability. Discrete Markov chains: the Markov property, the Chapman- Kolmogorov equations, classification of states, stationary distributions, ergodic theorems, absorption, time reversibility. Continuous time Markov chains: Poisson process, birth and death processes, Kolmogorov differential equations, limiting distributions, applications to populations, stochastic models: Markov time independent and time/age dependent transition intensities. Kolmogorov equations for a model where transition intensities depend not only on age/time but also on duration of stay in one or more states. Sickness and marriage models in terms of Markov processes. Markov jump processes as a modelling tool and simulation of these models. Queueing Theory: M/M/1, M/M/s, M/G/1 etc in detail. |
| HMTHCS201 | Analysis 1 | Historical development of the real number system, with reference to the “four great problems of antiquity”, the classical algorithm for square roots and other famous problems involving convergence of sequences of rational numbers. Algebraic, geometrical and operational motives for the following sequence of proper inclusions: Boundedness theorem, intermediate value theorem,interval theorem, application to fixed point theory. Uniform continuity. Differentiability. Local extrema, Rolle’s Theorem, mean value theorem, L’Hopital’s rule, Leibniz’ theorem, Taylor’s theorem |
| HMTHCS231 | Analysis 2 |
Euclidean spaces: Sequences: Continuity: Differentiation: Sequences and series of functions: Integrals: Convergence concepts: Upper and lower limits of sequences, upper and lower semicontinuous functions. Algebras of sets: Algebra of sets, σ-algebras, Borel sets. Measure on the line: Outer measure, measurable sets, Lebesgue measure, properties of Lebesgue measure, the σ-algebra of measurable sets, examples of non-measurable sets Measurable functions: Properties and characterisation of measurable functions. Convergence almost everywhere, convergence in measure. Lebesgue Integral: Classes of integrable functions, comparison with Riemann integral, Bounded convergence theorem, Lebesgue theorem, Fatou's lemma, Monotone convergence theorem. |
| HFM402 | Martingale Theory for Finance |
The module aims to provide a firm grasp of a range of basic concepts and fundamental results in the theory of martingales and to give some simple applications in the rapid developing area of financial mathematics. Martingales are a special class of random processes which are key ingredients of the modern probability and stochastic calculus. They can be used as mathematical models for fair games. In recent years, the martingale theory also plays a vital role in the area of mathematical finance. This module will introduce a circle of ideas and fundamental results of the theory of martingales and provide some applications in the discrete time financial models. On successful completion of the module students will be able to compute integrals of simple random variables with respect to a probability measure and apply the dominated, monotone convergence theorems; use the computational rules of conditional expectation and prove that a given stochastic process is a martingale; apply Doob Optional Sampling Theorem to calculate interesting probabilities concerning some practical problems, e.g. the gambler ruin problem; answer simple questions regarding Brownian motion and Poisson processes; compute brackets of simple semi martingales; answer simple questions about self-financing portfolios and complete markets; determine when a financial market is arbitrage-free; find out a replicating strategy for a financial claim; calculate the fair price of a financial claim in a financial market. |
| HFM412 | Stochastic Optimal Control with Applications |
The module presents an introduction to control theory, to a very active area of research, both in pure and applied mathematics. The aim is to learn the basics of the mathematical theory, and to understand some real-world applications, primarily in finance and economics. It offers an opportunity to see the connections between different fields, (controlled dynamical systems, optimization, Non-linear PDEs), and the underlying ideas unifying them. Students will learn: - Discrete time case: Controlled Markov chains, backward induction,optimal stopping in discrete time. - Continuous time case: Controlled ODEs, Controlled diffusion processes, Bellman principle, Hamilton-Jacobi-Bellman equations, optimal stopping in continuous time, variational inequalities, Calculating American options in the Black Scholes model, Optimal investment-consumption problems. |
| HFM401 | Mathematical Risk Theory | Upon completing this module, students will develop a thorough understanding of risk management in actuarial contexts. They will be able to define the loss/risk function, apply game theory strategies, and utilize decision criteria like Minimax and Bayes rules. The course covers the sums of independent random variables, deriving their distribution and moment-generating functions, as well as various compound risk models such as Poisson, binomial, and geometric. Students will learn to use convolutions to compute distribution functions for aggregate claims and understand stop-loss reinsurance, calculating its premiums for different severities. The curriculum emphasizes the application of Panjer’s equation and the individual risk model to assess expected losses for group insurance policies. Additionally, students will explore the classical surplus process ruin model and derive the moment-generating function while applying Lundberg's inequality for probability assessments. Students will address delayed claims through reserving techniques, using the chain ladder method, and estimate ultimate claims using the average cost per claim method. Finally, they will employ loss ratios and the Bornhuetter-Ferguson method to estimate eventual losses and revise claims with credibility factors. Overall, this module equips students with essential skills for managing risks in financial and actuarial fields. |
| HFM405 | Stress Testing and Risk Integration |
Introduction to Stress Testing: Understand the fundamentals of stress testing in finance. Definition and purpose of stress testing. Historical context and regulatory requirements. Types of stress tests (e.g., scenario analysis, sensitivity analysis). Risk Identification and Assessment. Identify and assess various types of financial risks. Credit risk, market risk, liquidity risk, operational risk. Techniques for risk identification (e.g., risk registers, workshops). Risk assessment methodologies (qualitative vs quantitative). Designing Stress Scenarios: Learn how to design realistic stress scenarios. Scenario selection criteria. Historical versus hypothetical scenarios. Incorporating macroeconomic factors and business-specific conditions, Quantitative Techniques for Stress Testing: Apply quantitative methods to stress testing. Statistical models and simulations (e.g.,Monte Carlo simulations) Value-at-risk (VaR) and expected shortfall (ES) Calibration of models for stress scenarios. Risk Integration Frameworks: Explore frameworks for integrating risk across organizational silos. Enterprise risk management (ERM) principles Integration of stress testing results into risk management frameworks Regulatory expectations for risk integration. Reporting and Communication of Results: Effectively communicate stress test results to stakeholders. Key performance indicators (KPIs) for reporting. Best practices for reporting to executives and regulators. Case studies on successful communication of stress testing outcomes. Case Studies and Practical Applications: Analyze real-world examples of stress testing. Case studies from banks and financial institutions. Lessons learned from major financial crises. Future Trends in Stress Testing: Discuss emerging trends and technologies in stress testing. Technological advancements (AI, machine learning in risk assessment) Changing regulatory landscapes and expectations The role of big data in enhancing stress testing accuracy |
| HFM403 | Trading and Risk Systems Development | The "Trading and Risk Systems Development" module provides a thorough exploration of trading systems, covering key concepts such as trading strategies, market microstructure, and the roles of traders and algorithms. Students will learn essential risk management principles, including types of risks and assessment methodologies like Value-at-Risk, and develop a risk management framework tailored to trading systems.The curriculum includes designing and implementing trading algorithms through back-testing and optimization, analyzing data acquisition practices, and establishing effective risk controls. Performance measurement, focusing on key metrics such as the Sharpe ratio, will be addressed alongside the impact of emerging technologies like AI and blockchain in trading. |
| HASTS401 | General Linear Models | Form a unified underlying theory that covers simple and multiple linear regressions with special emphasis on full rank models. The module also covers aspects on the general linear hypothesis, models of not full rank and introduction to variance components. |
| HFM415 | Stochastic For Derivatives Modelling |
The "Stochastic for Derivatives Modelling" module offers a comprehensive examination of stochastic processes and their significance in financial derivatives. It begins with an introduction to stochastic processes, focusing on randomness and probability theory as foundational concepts. Students learn about Brownian motion in detail, including its properties and relevance in modelling asset prices. The module then delves into Ito's calculus, emphasizing stochastic integration and differentiation, which are essential for derivatives pricing. The Black-Scholes model is analysed thoroughly, covering its derivation, assumptions, and the principles of risk-neutral valuation. Moving beyond the basics, participants will explore advanced derivative pricing models such as the Heston model and jump-diffusion models, discussing their applications and implications. Numerical methods are also a key component, where students learn techniques such as Monte Carlo simulations and finite difference methods for solving stochastic models. The module addresses risk management within a stochastic framework, equipping students with tools to assess and mitigate risks associated with derivatives. |
| HFM414 | Commodity and Energy Markets | The "Commodity and Energy Markets" module provides a comprehensive overview of the dynamics that govern these critical sectors. It begins with an introduction to the fundamental concepts of commodity and energy markets, exploring their roles in the global economy and the factors influencing supply and demand. Students will examine various types of commodities, including agricultural products, metals, and energy resources, learning about their characteristics, pricing mechanisms, and market structures. The module delves into price formation and trading strategies, discussing how spot and futures markets operate, as well as the significance of derivatives in managing price risk. Participants will explore the role of market participants, such as producers, consumers, and speculators, and how their interactions shape market behaviour. Risk management techniques specific to commodity and energy trading will also be covered, equipping students with tools to analyse and mitigate risks in volatile markets. In addition to theoretical foundations, case studies will provide practical insights into real-world commodity and energy trading scenarios, enhancing students' understanding of market trends and events. The module will also address emerging trends affecting these markets, such as technological advancements and regulatory developments. Assessment methods will include quizzes, group projects, and analyses of current market situations. By the module's end, students will gain a robust understanding of commodity and energy markets, enabling them to navigate and analyze these sectors effectively. |
| HFM413 | Data Science for Finance | The "Data Science for Finance" module provides a thorough exploration of the intersection between data science and financial applications. It begins with an introduction to the fundamental principles of data science, including data collection, cleaning, and preprocessing techniques, tailored specifically to financial datasets. Students will learn about exploratory data analysis and visualization methods, essential for uncovering insights within financial data. The module progresses to statistical methods and machine learning algorithms commonly used in finance, such as regression analysis, classification techniques, and clustering methods. Participants will explore how to implement predictive modelling for various financial applications, including credit scoring, algorithmic trading, and risk assessment. Additionally, the curriculum covers big data technologies and tools that are integral to financial analysis, such as Python, R, and SQL, providing hands-on experience in working with large datasets. Discussion of ethical considerations and compliance in data science applications within the finance sector will also be emphasized. |
| HFM416 | Quantitative Risk Management and credit products | The "Quantitative Risk Management and Credit Products" module offers an in-depth examination of risk management techniques and their applications within credit markets. It begins with an overview of quantitative risk management principles, emphasizing the importance of modelling risks associated with credit products, including loans, bonds, and derivatives. Students will explore various types of risks, such as credit risk, market risk, and operational risk, and learn to employ statistical methods to quantify these risks. The module will cover key concepts such as Value-at-Risk (VaR), credit exposure modelling, and stress testing, providing students with tools to assess and manage risk in financial portfolios. Participants will delve into the intricacies of credit products, studying their structures, pricing mechanisms, and the factors that influence their value. Advanced topics such as portfolio credit risk modelling, credit derivatives (including credit default swaps), and the impact of macroeconomic factors on credit risk will also be discussed. The module incorporates practical applications through case studies and real-world data analysis, allowing students to apply quantitative methods to assess credit risk and develop risk mitigation strategies. Assessment will include quizzes, projects, and presentations focused on risk management solutions in the context of credit products. By the end of the module, students will achieve a comprehensive understanding of quantitative risk management methodologies and gain skills applicable to credit risk analysis and management in the financial industry. |
| HACS419 | Financial Risk Management and Capital Markets | Derive future prices by no arbitrage stock indices, dividend paying stock, investment commodities, futures in hedging, futures contracts, hedging strategies, interest rates derivatives (treasury rates, LIBOR, REPO rates, forward rates, swaps, treasury bonds futures, European Swap options(swaptions), caps and caplets, floor and floorlets and Bermudan swaptions). Exotic equity and foreign exchange derivatives: Quanto, chooser, barrier, binary, Lookback, Asian, Exchange and Basket options. Theories used in calculating derivatives and their hedging strategies using the Black-Scholes model including Brownian Motion, Ito Calculus, Ito’s formula, the Cameron- Martin- Girsanov theorem, the Radom-Nikodyn derivative, change of measure, the Martingale Representation theorem, the Black-Scholes-Merton partial derivative, the pricing formula, Hull and White models, Swap Market model etc. |
| ECD104 |
Principles of Macro-Economics |
Tools of macroeconomics: fiscal and monetary policy, circular flow of income. Measuring economic performance, national income accounting concepts, gross domestic product. Two ways of measuring GDP: expenditure and income approaches. Price indices (CPI and GDP Deflator) and inflation. Shortcomings of GDP. |
| HASTS202 | Statistical Computing | This module aims to introduce the student to a variety of modern computing techniques, including use of everyday packages for data storage, management, analysis and reporting. Students learn about hard statistical and actuarial packages including programming. Using Statistical Packages- SPSS, STATA, SAS, MINITAB, EPI-INFO, and CSPro for analysing different types of data. Programming - Using R or SPLUS for data analysis and simulation, Latex for typesetting in preparation for writing up Mathematical papers. Using EXCEL programming to solve various problems by designing algorithms and other new specialised programmes. |
| FINMGT203 | Financial Management |
The "Financial Management" module equips students with essential principles and practices for managing financial resources within organizations. It covers core concepts such as financial analysis, planning, and control, emphasizing the role of finance in strategic decision-making. Students learn to interpret key financial statements and explore topics like time value of money, capital budgeting, and investment analysis for informed decision-making. The module addresses risk assessment and management, focusing on identifying and mitigating financial risks, as well as examining financing options such as debt and equity. It also emphasizes working capital management to maintain liquidity and optimize efficiency. Through real-world case studies, students apply theoretical concepts to practical situations. Assessment methods include quizzes, assignments, and group projects. By the end, participants will have a strong understanding of financial management, preparing them for careers in finance and business management. |
| HMTHCS301 | Real Analysis | Convergence concepts: Upper and lower limits of sequences, upper and lower semicontinuous functions. Algebras of sets: Algebra of sets, σ-algebras, Borel sets.Measure on the line: Outer measure, measurable sets, Lebesgue measure, properties of Lebesgue measure, the σ-algebra of measurable sets, examples of non-measurable sets Measurable functions: Properties and characterisation of measurable functions. Convergence almost everywhere, convergence in measure. Lebesgue Integral: Classes of integrable functions, comparison with Riemann integral, Bounded convergence theorem, Lebesgue theorem, Fatou's lemma, Monotone convergence theorem. Absolutely continuous functions. Product measures. The Fubini theorem. Completion of product measures. Distribution functions. Integration on product spaces. Introduction to linear vector spaces. Normed spaces. Lp-spaces. Space L1. The Holder and Minkowski inequalities. Convergence in Lp. Comparison with other kinds of convergence. Measure space. |
| HMTHCS305 |
Nonlinear Ordinary Differential Equations |
Topics include linear and non-linear equations, linear and non-linear systems of equations, stability theory, and bifurcations. After completing this module, students should demonstrate competency in the following skills: To understand the dynamics, and the structure of the phase-plane of linear systems. To apply local techniques, for the analysis of the local phase portrait of non-linear systems. To apply Lyapunov and invariant manifold methodologies, in order to analyze the stability properties of nonlinear systems. To understand and recognize fundamental nonlinear phenomena such as the emergence of limit cycles, and bifurcations. To understand and apply global non-linear techniques, based on Poincaré-Bendixson theorem. To understand and analyze the global phase portrait of 2nd order conservative systems, the notions of homoclinic and heteroclinic connections, and their importance as underlying structures, emerging complex behaviour in nonlinear systems. |
| HFM318 | Investments and Asset Liability Management | This module aims at the application of actuarial planning and control to the appraisal of investments and be able to select the best options appropriate for the investors. Topics covered are risk free returns, taxation of investments, fundamental share analysis trust law corporate government, financial services, theory of finance, financial planning, specialized financial instruments, investment strategy (corporate finance), investment strategy, asset pricing models, portfolio risk and return analysis, investment olio indices, portfolio management, currency hedging risk budgets |
| HMTHCS324 | Mathematical Modelling | The objective of the module is to introduce mathematical modelling, that is, the construction and analysis of mathematical models inspired by real life problems. The module will present several modelling techniques and the means to analyze the resulting systems. By using fundamental calculus concepts in a modelling framework, the student investigates practical problems chosen from common experiences encompassing many academic disciplines, including the mathematical sciences, operations research, engineering and the management and life sciences. |
