Undergraduate Course: Modelling and Computing (MATH08084)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This course is a first course in mathematical computing, teaching the fundamentals of programming, particularly as they relate to computational mathematics problems. Alongside this, students will develop aptitude in modelling by casting problems into mathematical form to describe them, and potentially solve them.
Students will develop their professional skills in applying mathematics, developing code, and explaining mathematical analyses of problems. |
| Course description |
This course presents an introduction to mathematical computing. It will focus on effective production of computer code in a professional style, using a relevant professional toolset. The language used will be Python. Various fundamental algorithms will be introduced alongside a general discussion about how computational mathematics is done, and the sorts of convergence and accuracy trade-offs that usually arise.
The course also introduces the way an applied mathematician might go about modelling problems or systems that they are interested in. This includes being explicit about what sorts of assumptions or approaches might be used, how these can be described mathematically, and ultimately applying appropriate techniques to solve some of the problems.
The mathematical component of the course structure will involve some core content and examples of mathematical modelling, followed by a choice of topics for groups of students to work on as part of their final assessment on the course. Examples of the sorts of mathematics you may encounter in the course include: linear programming, applications of linear algebra, modelling of real-life problems through differential equations, and machine learning.
Summary of student experience: You will develop, without any assumed prior knowledge, competency in Python programming, including the use of a professional toolset, providing vital skills both for your future mathematical study and also for many careers. The programming and scientific computing aspects will motivated by, and applied to, a range of mathematical problems, including modelling with differential equations and optimization. Alongside these practical skills and applications, you will develop your mathematical knowledge, for example, developing the techniques necessary to compute exact solutions to simple differential equations, which can be used to validate your numerical implementations. Following on from the prerequisite Year 1 courses, you will further enhance your communication and groupwork skills.
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Write short programs in a professional way using Python, employing suitable tools and writing well-formatted code.
- Explain the purpose and logic of some fundamental computational algorithms.
- Use mathematics as a tool to model some simple systems, state assumptions made, and critically analyse the results.
- Communicate knowledge about mathematical and computational topics in a range of contexts, including written and oral presentation.
- Contribute as part of a group to the study of a mathematical topic.
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Reading List
S. Linge and H.P. Langtangen, Programming for Computations, Python, Springer, 2016
P.R. Turner, T. Arildsen, and K. Kavanagh, Applied Scientific Computing with Python, Springer, 2018. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Computing,Mathematical Modelling,Applications of Mathematics |
Contacts
| Course organiser | |
Course secretary | |
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