MMath&Phys Mathematics and Physics

This course covers the techniques required to develop C++ programs that solve mathematical and scientific problems both as an individual and in groups.

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, debugging and code validation, version control and how to make code publicly accessible.

The material is examined primarily through programming projects, chosen from a list of mathematical topics, which will cover specific algorithms or techniques in more depth. The projects will be assessed by a written presentation and confirmation that the resulting code passes a set of tests.

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

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.

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

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 mathematical or scientific problem,
• Debug the code and validate its results in the context of the problem being solved
• 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.

- operator overloading

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

The main concepts will be delivered asynchronously through a set of bespoke videos and interactive online tests to give formative feedback on each student’s level of understanding. The concepts will be reviewed and implemented using appropriate software during the scheduled 2-hour lab sessions each week. These sessions will provide an opportunity for students' work to be discussed and also provide feedback on their understanding. Coursework will also provide an opportunity for students to receive feedback.  Students can get feedback on their understanding directly from the lecturers.

100% coursework/project, as follows:

1. selected example sheet questions, during lab sessions: 10%

2. smaller project, 2 weeks: 30%

3. main project, 4 weeks: 60%

Feedback given on individual and group projects.

•  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