# Pathways in the MMathStat degree

The example module plans below illustrate pathways in the MMathStat for a number of different specializations. Please note that these are suggestive only and you are free to choose any module combination that satifies the relevant course regulations as specified in the Course Handbook. The suggested module combinations may not satisfy the course regulations of other degree courses such as MMORSE. Please also note modules that are not core modules are subject to availabity.

Advanced Statistics Pathway This pathway provides students with a strong background in mathematical and statistical theory and methodology. It thus prepares students for a career as professional statisticians working in business or industry or for a research career in Statistics. To follow this pathway choose modules centred on statistical methodology and supplementary mathematical techniques, for an example module plan see here.

Computational Statistics Pathway Computational Statistics is concerned with the use of computer intensive approaches to modelling and analysis of complex systems and large data sets. It prepares students for careers in decision analysis and analytics or to work as consultants in close collaborations with engineers, scientists and social scientists. To follow this pathway supplement modules on statistical methodology with modules on algorithm design and computational methods. For an example, see here.

Biostatistics Pathway You may decide to focus on the use of Mathematics and Statistics in the Life Sciences including Biology and Medicine. This would prepare you for a career in fields such as bioinformatics, genomics, clinical trials and drug development. To follow this pathway we suggest you augment statistical methodology modules with modules on the interface to the Life Sciences, see here.

Mathematical Finance Pathway This pathway is for students looking for a career as quantitative analyst in the financial industry and students thinking about a PhD in Mathematical Finance. An example module plan is presented here.

Actuarial Science and Statistics Pathway This pathway emphasises the use of Mathematics and Statistics in the actuarial, banking and financial sector. It thus prepares for a career in the banking and insurance industry. See here for an example module plan.

Probability Theory Pathway You may decide to focus on Probability Theory and its applications. This would prepare you for a career with a focus on stochastic modelling not only in finance and insurance, but also in industries such as pharmaceutical and biotech, information technology, telecommunications or engineering. An example module plan can be found here.

#### Suggested module combinations:

Suggested optional modules:

Year 1: MA133 Differential Equations and MA134 Geometry and Motion.

Year 2: MA250 PDE and MA259 Multivariable Calculus.

Year 3

 Core CATS ST333 Applied Stochastic Processes 15 ST342 Mathematics of Random Events 15 ST404 Applied Statistical Modelling 15 List (A) ST323 Multivariate Statistics 15 ST340 Programming for Data Science 15 ST343 Topics in Data Science 15 List (B) MA3G1 Theory of PDEs 15 MA3H0 Numerical Analysis and PDEs 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST405 Bayesian Forecasting and Intervention with Advanced Topics 15 ST407 Monte Carlo Methods 15 ST409 Medical Statistics with Advanced Topics 15 ST410 Designed Experiments with Advanced Topics 15 ST413 Bayesian Statistics and Decision Theory with Adv Topics 15 ST906 Financial Time Series 15

Alternative suggested optional modules for years 3 and 4:

ST318 Probability Theory, ST329 Topics in Statistics, ST341/ST418 Statistical Genetics (with Advanced Topics), MA3B8 Complex Analysis, MA433 Fourier Analysis, EC306 Econometrics 2: Time Series, EC338 Econometrics 2: Microeconometrics.

Computational Statistics

Suggested optional modules:

Year 1: MA133 Differential Equations, MA134 Geometry and Motion, MA117 Programming for Scientists (may be taken as optional module in year 2).

Year 2: MA259 Multivariable Calculus.

Year 3

 Core CATS ST342 Mathematics of Random Events 15 ST404 Applied Statistical Modelling 15 ST406 Applied Stochastic Processes with Advanced Topics 15 List (A) ST340 Programming for Data Science 15 ST343 Topics in Data Science 15 ST412 Multivariate Analysis with Advanced Topics 15 List (B) MA3G1 Theory of PDEs 15 MA398 Matrix Analysis and Algorithms 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST405 Bayesian Forecasting and Intervention with Advanced Topics 15 ST407 Monte Carlo Methods 15 MA398 Matrix Analysis and Algorithms 15 MA433 Fourier Analysis 15 Optional Modules CS331 Neural Computing 15 IB352 Applied Optimisation Methods 15

Alternative suggested optional modules for years 3 and 4:

ST305/ST409 Medical Statistics (with Advanced Topics), ST318 Probability Theory, ST329 Topics in Statistics, ST341/ST418 Statistical Genetics (with Advanced Topics),

MA3B8 Complex Analysis, MA3J2 Combinatorics II, MA433 Fourier Analysis, MA4J3 Graph Theory,

CS301 Complexity of Algorithms, CS342 Machine Learning, CS356 Approximation and Randomised Algorithms, CS402 High Performance Computing, CS904 Computational Biology,

BioStatistics

Suggested optional modules:

Year 1: MA133 Differential Equations, MA134 Geometry and Motion, MA117 Programming for Scientists (may be taken as optional module in year 2).

Year 2: MA250 PDE, MA254 Theory of ODE, MA256 Introduction to Systems Biology, MA259 Multivariable Calculus.

Year 3

 Core CATS ST318 Probability Theory 15 ST342 Mathematics of Random Events 15 ST404 Applied Statistical Modelling 15 List (A) ST301 Bayesian Statistics and Decision Theory 15 ST305 Designed Experiments 15 ST340 Prgramming for Data Science 15 List (B) MA390 Topics in Mathematical Biology 15 MA3G1 Theory of PDEs 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST405 Bayesian Forecasting and Intervention with Adv. Topics 15 ST406 Applied Stochastic Processes with Advanced Topics 15 ST409 Medical Statistics with Advanced Topics 15 ST412 Multivariate Statistics with Advanced Topics 15 ST418 Statistical Genetics with Advanced Topics 15 Optional Modules CS904 Computational Biology 15

Alternative suggested optional modules for years 3 and 4:

ST329 Topics in Statistics, ST301/ST413 Bayesian Statistics and Decision Theory (with Adv Topics), ST343/ST419 (Advanced) Topics in Data Science,

MA3B8 Complex Analysis, MA3H0 Numerical Analysis and PDE, MA3H2 Markov Processes and Percolation Theory, MA3J3 Bifurcations, Catastrophe and Symmetry, MA4E7 Population Dynamics: Ecology and Epidemiology.

Mathematical Finance

Suggested optional modules

Year 1: MA133 Differential Equations, MA134 Geometry and Motion.

Year 2: MA250 PDE, MA254 Theory of ODE, MA259 Multivariable Calculus.

Year 3

 Core CATS MA359 Measure Theory 15 ST318 Probability Theory 15 ST404 Applied Statistical Modelling 15 List (A) ST337 Bayesian Forecasting and Intervention 15 ST339 Introduction to Mathematical Finance 15 List (B) MA3B8 Complex Analysis 15 MA3G1 Theory of PDEs 15 MA3G7 Functional Analysis I 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST401 Stochastic Methods in Finance 15 ST403 Brownian Motion 15 ST407 Monte Carlo Methods 15 ST906 Financial Time Series 15 ST909 Continuous Time Finance for Interest Rate Models 15 MA482 Stochastic Analysis 15

Alternative suggested optional modules for years 3 and 4:

ST333/ST406 Applied Stochastic Process (with Adv. Topics), ST411 Stochastic Dynamic Control, ST958 Topics in Mathematical Finance,

MA3G8 Functional Analysis II, MA3H0 Numerical Analysis and PDEs, MA3H2 Markov Processes and Percolation, MA3H7 Control Theory, MA4A2 Advanced PDE.

Actuarial Science and Statistics

Suggested optional modules:

Year 1: MA133 Differential Equations, MA134 Geometry and Motion.

Year 2: MA250 PDE, MA254 Theory of ODE, MA259 Multivariable Calculus.

Year 3

 Core CATS ST318 Probability Theory 15 ST342 Mathematics of Random Events 15 ST404 Applied Statistical Modelling 15 List (A) ST339 Introduction to Mathematical Finance 15 ST412 Multivariate Statistics with Advanced Topics 15 List (B) MA3B8 Complex Analysis 15 MA3G7 Functional Analysis I 15 Optional Modules ST334 Actuarial Methods 15 ST335 Finance and Financial Reporting 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST401 Stochastic Methods in Finance 15 ST402 Risk Theory 15 ST406 Applied Stochastic Processes with Advanced Topics 15 ST906 Financial Time Series 15 Optional Modules ST338 Actuarial Models 15 ST345 Life Contingencies 15

Alternative suggested optional modules for years 3 and 4:

ST301/ST413 Bayesian Statistics and Decision Theory (with Adv Topics), ST337/ST405 Bayesian Forecasting and Intervention (with Adv Topics), ST340 Programming for Data Science, ST343/ST419 (Advanced) Topics in Data Science, ST407 Monte Carlo Methods;

MA3B8 Complex Analysis, MA3G1 Theory of PDEs, MA3G8 Functional Analysis II, MA3H0 Numerical Analysis and PDEs

Probability Theory

Suggested optional modules:

Year 1: MA133 Differential Equations, MA134 Geometry and Motion.

Year 2: MA250 PDE, MA254 Theory of ODE, MA259 Multivariable Calculus.

Year 3

 Core CATS ST318 Probability Theory 15 ST333 Applied Stochastic Processes ST342 Mathematics of Random Events 15 ST404 Applied Statistical Modelling 15 List (A) ST337 Bayesian Forecasting and Intervention 15 ST339 Introduction to Mathematical Finance 15 List (B) MA3B8 Complex Analysis 15 MA3H2 Markov Processes and Percolation Theory 15

Year 4

 Core CATS ST415 Statistics Masters Dissertation 30 List (A) ST401 Stochastic Methods in Finance 15 ST403 Brownian Motion 15 ST407 Monte Carlo Methods 15 ST411 Dynamic Stochastic Control 15 MA427 Ergodic Theory 15 MA482 Stochastic Analysis 15

Alternative suggested optional modules for years 3 and 4:

ST906 Financial Time Series,

MA3G1 Theory of PDEs, MA3G7 Functional Analysis I, MA3G8 Functional Analysis II, MA3H0 Numerical Analysis and PDEs, MA3H3 Set Theory, MA3H7 Control Theory, MA3J4 Mathematical Modelling with PDE, MA4A2 Advanced PDEs, MA4K3 Complex Function Theory, MA4L2 Statistical Mechanics