Computational Mathematics 1

The course is taken during the second semester of the Mathematics program, but can also be taken as a stand-alone course. The course can be included in the following programs: Mathematics program (N1MAT).

General entry requirements and the equivalent of the courses Single Variable Calculus 1 MMG230, Single Variable Calculus 2 MMG240, Linear Algebra MMG250, and Programming with Python MVG302.

The course introduces fundamental techniques in scientific computing and numerical linear algebra: Floating-point arithmetic and numerical errors. Systems of linear equations. LU and QR factorization methods. Iterative methods for linear systems. Vector and matrix norms, conditioning, and numerical stability. Linear least squares problems. Eigenvalue problems. Polynomial interpolation. Solution of nonlinear equations. Introduction to computational performance.

Programming assignments and computer labs are carried out using Python and/or C.

On successful completion of the course the student will be able to:

• formulate and implement numerical methods for solving systems of linear equations, non-linear equations, least squares problems, interpolation problems, and eigenvalue problems,
• analyze numerical algorithms with respect to accuracy, computational complexity, numerical stability, and convergence properties,
• implement scientific computing algorithms in Python and/or C, and evaluate their performance on practical computational problems,
• apply numerical methods to model and solve problems arising in science and engineering.

The course is assessed through mandatory computer labs and a written exam at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignments are small written tests, labs, and oral or written presentations. Information about this is found on the course home page.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.

The course MMG411 replaces the course Numerical Analysis MMG410. It is not permitted to register and/or be examined in more than one of these courses.