# Distance Learning - Applied Numerical Methods

Foundations for Computational Finance, Engineering and Data Sciences

## DESCRIPTION

Originator and trainer: Dr. Daniel J. Duffy

The goal of this practical and self-contained distance course is to introduce the most important and relevant numerical methods for applications in engineering, science and computational finance. This comprehensive and detailed course discusses numerical methods in each module:

• Basic Level: understanding the main concepts and how they fit together. Understand a numerical method in terms of its input and output. Basic exercises will help you through this process.
• Intermediate Level: the focus at this level is to apply more numerical methods in a module and to understand the nuances and applicability of the methods in a given context. Advanced exercises.
• Advanced Level: customising, extending and fine-tuning algorithms to suit new requirements. This involves a combination of analysis, numerical experimentation and coding in C++, C# and Python.

In short, the ideal approach is to mix theory and practice. In this way you will get a good grounding in the mathematical foundations in combination with hands-on numerical and coding activities to get optimal benefit from the course.

Subjects Covered

• Vector spaces and linear transformations.
• Background theory of matrices.
• Numerical linear algebra and the solution of matrix systems.
• Interpolation; orthogonal polynomials.
• Numerical differentiation and numerical quadrature.
• The solution of nonlinear equations.
• The finite difference method in a nutshell.
• Probability, distributions and random number generation.
• Optimisation.
• Generic algorithms (GA) and Differential Evolution (DE).
• Numerical foundations and preparation for Machine Learning (ML).

Course Benefits

• Become acquainted ASAP with high-priority and universal numerical methods.
• Practical, to-the-point and timely approach to numerical analysis.
• Full ‘lifecycle’: analysis, methods, programming, exercises and applications.
• Support in C++, C# and Python libraries.
• Competitively priced.

For whom is the Course and what are the Prerequisites?

This course is suitable for both professionals in industry and finance as well as for advanced undergraduate and MSc/MFE students. The prerequisite knowledge is calculus to the level as seen in the book by D.V. Widder 1989 Advanced Calculus Dover.

If you any queries please do not hesitate to contact me to discuss the course (dduffy@datasim.nl).

Structure of Course and Student-Trainer Interaction

This course takes an incremental/inductive approach by first examining model problems in detail and then extending them to more advanced applications. Student progress is measured by working on graded exercises. Regular communication takes places by e-mail and Skype.

Students receive a certificate on successful completion of the course.

Course Resources
The course consists of  videos (that you get lifelong access to),  exercises as well as the hard-copies (in pdf format) of the videos.

Books provided with this course:
Matrix Operations by R. Bronson Schaum Series.
Numerical Methods by A. Bjoerck and G. Dahlquist Prentice-Hall.
Demming, Robert & Duffy, Daniel J. (2010). Introduction to the Boost C++ Libraries. Volume 1 - Foundations. Datasim.

ISBN 978-94-91028-01-4. (e-book)
Demming, Robert & Duffy, Daniel J. (2012). Introduction to the Boost C++ Libraries. Volume 2 - Advanced Libraries. Datasim. ISBN 978-94-91028-02-1. (e-book)

Daniel J. Duffy, Financial Instrument Pricing Using C++ (second edition), John Wiley and Sons

The optimal way to learn in our opinion is by executing the following steps. This discussion pertains to studying and learning the contents of a single module:
1. Listen to the audio show and use the printed PowerPoint slides as  backup.
2. Read the relevant material in the provided book(s).
3. Do the exercises; compile and run the programs.
4. If you are having problems, go back to one of more of steps 1, 2, 3.
5. If step 4 has been unsuccessful then post your problem on the Datasim forum.
6. Go to next module.