# MMath Mathematics with Financial Mathematics

Year of entry: 2023

## Course unit details:Scientific Computing

Unit code MATH49111 15 Level 4 Semester 1 Department of Mathematics No

### Overview

This course covers the techniques required to develop C++ programs that solve mathematical and scientific problems.

As well as covering the rudiments of C++ (which will be taught with no assumed prior knowledge) the course will also outline the basic techniques used in scientific programming, such as discretisation of equations, numerical error and code validation.

The material is examined primarily through two programming projects, chosen from a list of mathematical topics, which investigate particular algorithms or techniques in more depth. The projects will be assessed by a written report and a demonstration/oral description of the code.

Much of this course is taught in practical computer labs, which limits the number of places available.

### Pre/co-requisites

Students are not permitted to take, for credit, MATH49111 in an undergraduate programme and then MATH69111 in a postgraduate programme at the University of Manchester, as the courses are identical.

### Aims

To develop the knowledge required to solve mathematical and scientific problems by writing computer programs in C++.

### Learning outcomes

On successful completion of this module, students will be able to:

• Implement numerical algorithms by writing simple object-oriented C++ programs,
• Create and evaluate different algorithms and C++ code architectures that could be used to solve a given numerical problem,
• Debug the code and validate its results in the context of the mathematical program,
• Explain and justify your numerical results by creating and combining written arguments, figures and numerical data.

### Syllabus

Introduction to C++ programming language:
- statements, expressions, control flow, functions, types
- standard C++ library: streams and file i/o, strings, containers, algorithms
- use of external libraries

Code structure and object-oriented programming:
- methods, member data, constructors, destructors, access specifiers
- inheritance, virtual methods and run-time polymorphism.

Fundamental concepts and techniques:
- numerical error
- discretisation
- writing efficient code (algorithm complexity, optimisation, parallelism)
- communication and visualisation of numerical results
- common algorithms (covered in coursework, and in lectures as time permits) such as numerical linear algebra, root finding, quadrature, sorting, BVPs, PDEs

Debugging and validation:
- error handling
- testing and test-driven development
- debugging
- validation of numerical results

### Assessment methods

•     Weekly courseworks: 10%
•     Project 1: 40%
•     Project 2: 50%

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

•  S.B. Lippman, J. Lajoie, B. Moo. C++ Primer (Fourth edition). Addison Wesley, 2005. (Available as an e-book from the university library)
•  W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. Numerical Recipes: The Art of Scientific Computing (Third edition). Cambridge University Press, 2007.
•  B. Stroustrup. The C++ Programming Language (Third edition). Addison-Wesley, 1997
•  S. Meyers. Effective C++: 55 specific ways to improve your programs and designs (Third edition). Addison-Wesley, 2005.
•  D. Yang. C++ and object-oriented numeric computing for scientists and engineers. Springer, 2000.

### Study hours

Scheduled activity hours
Lectures 10
Practical classes & workshops 22
Independent study hours
Independent study 118

### Teaching staff

Staff member Role
Christopher Johnson Unit coordinator