DanM
Math Student
- Joined
- 8/1/09
- Messages
- 179
- Points
- 28
I was wondering how beneficial an Applied Mathematics MSc would be for pursuing a career in QF.
It's a 2 year, thesis-based/research-oriented program, where you have to complete 5 courses and participate regularly in graduate seminars.
The courses I would be taking:
Analysis and Probability
Vectors and complex calculus. ODEs, PDEs, eigenfunction expansions and integral equations. Measure spaces, random variables and modes of convergence, algorithms for simulation of distributions, martingales, Brownian motion and stochastic integration, stochastic differential equations.
Principles and Techniques in Applied Mathematics, Part I
Integral transform and applications to ODEs and PDEs; discrete Fourier transforms, FFT and applications; asymptotic expansions; perturbation methods; calculus of variations, optimizing functionals and applications.
Principles and Techniques in Applied Mathematics, Part II
Numerical methods; numerical linear algebra; numerical methods for ODEs; numerical methods for PDEs; numerical simulations.
Financial Mathematics
This course covers the fundamentals of mathematical methods in finance. Bonds, annuities, amortization, futures, profit/cost optimization. Decisions under certainty/uncertainty, capital budgeting and risk and return. Risk management, value at risk, credit risk. Modern portfolio theory. Arbitrage, utility theory, complete and incomplete markets. Modern theory of derivative pricing, Black-Scholes formulation. European, American options and credit derivatives. Numerical methods, Cox-Ross binomial models and finite difference schemes, lattice models for interest-rate derivatives.
And the final course would be one of the following:
Applied Statistical Methods
This course covers a wide variety of statistical methods with application in medicine, engineering, and economics. Exploratory data analysis. Parametric probability distributions. Sampling and experimental designs. Estimation, confidence intervals and tests of hypothesis. Analysis of variance. Multiple regression analysis, tests for normality. Nonparametric statistics. Statistical analysis of time series; ARMA and GARCH processes. Practical techniques for the analysis of multivariate data; principal components, factor analysis.
OR...
Partial Differential Equations
Hyperbolic equations, weak solutions, shock formation, non-linear
waves, reaction-diffusion equations, traveling wave solutions,
elliptic equations, numerical methods, applications.
Additionally, each student is assigned to an advisor who will assist them in the preparation of a thesis.
Some of the available opportunities for research topics based on the research interests of participating faculty members includes:
-Multivariate Stochastic Processes. Time Series Modelling. Mathematical Finance. Biostatistics. Dependence Structures.
-Applied mathematics: Financial mathematics, times series, signal processing, pattern recognition, mathematical software development. Pure mathematics: Ergodic theory, approximation of stochastic processes, real analysis.
-Applied stochastic modeling: asymptotical statistical inference, actuarial and financial models, branching processes.
It's a 2 year, thesis-based/research-oriented program, where you have to complete 5 courses and participate regularly in graduate seminars.
The courses I would be taking:
Analysis and Probability
Vectors and complex calculus. ODEs, PDEs, eigenfunction expansions and integral equations. Measure spaces, random variables and modes of convergence, algorithms for simulation of distributions, martingales, Brownian motion and stochastic integration, stochastic differential equations.
Principles and Techniques in Applied Mathematics, Part I
Integral transform and applications to ODEs and PDEs; discrete Fourier transforms, FFT and applications; asymptotic expansions; perturbation methods; calculus of variations, optimizing functionals and applications.
Principles and Techniques in Applied Mathematics, Part II
Numerical methods; numerical linear algebra; numerical methods for ODEs; numerical methods for PDEs; numerical simulations.
Financial Mathematics
This course covers the fundamentals of mathematical methods in finance. Bonds, annuities, amortization, futures, profit/cost optimization. Decisions under certainty/uncertainty, capital budgeting and risk and return. Risk management, value at risk, credit risk. Modern portfolio theory. Arbitrage, utility theory, complete and incomplete markets. Modern theory of derivative pricing, Black-Scholes formulation. European, American options and credit derivatives. Numerical methods, Cox-Ross binomial models and finite difference schemes, lattice models for interest-rate derivatives.
And the final course would be one of the following:
Applied Statistical Methods
This course covers a wide variety of statistical methods with application in medicine, engineering, and economics. Exploratory data analysis. Parametric probability distributions. Sampling and experimental designs. Estimation, confidence intervals and tests of hypothesis. Analysis of variance. Multiple regression analysis, tests for normality. Nonparametric statistics. Statistical analysis of time series; ARMA and GARCH processes. Practical techniques for the analysis of multivariate data; principal components, factor analysis.
OR...
Partial Differential Equations
Hyperbolic equations, weak solutions, shock formation, non-linear
waves, reaction-diffusion equations, traveling wave solutions,
elliptic equations, numerical methods, applications.
Additionally, each student is assigned to an advisor who will assist them in the preparation of a thesis.
Some of the available opportunities for research topics based on the research interests of participating faculty members includes:
-Multivariate Stochastic Processes. Time Series Modelling. Mathematical Finance. Biostatistics. Dependence Structures.
-Applied mathematics: Financial mathematics, times series, signal processing, pattern recognition, mathematical software development. Pure mathematics: Ergodic theory, approximation of stochastic processes, real analysis.
-Applied stochastic modeling: asymptotical statistical inference, actuarial and financial models, branching processes.