MAMO2200 Advanced Modeling and Computing Course description

The course covers approximations and numerical methods that are central to analyzing, computing, and simulating mathematical models. Through implementation on a computer, students will learn to perform systematic numerical experiments. Examples and tasks are drawn from natural sciences, engineering, and economics. The topics addressed are intended to prepare and motivate students for further studies in applied and computational mathematics.

The course will utilise 'blended learning', with a combination of in-person teaching or guidance, and use of online material. The students will be working on interdisciplinary cases focused on critical reflection.

None.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Knowledge

The student can:

• explain methods for the numerical solution of nonlinear algebraic equations and differential equations.
• explain how and in which cases functions can be approximated with polynomials and trigonometric functions.
• explain standard methods and the use of stochastic simulations for estimating definite integrals.
• explain the fundamental properties of stochastic processes and Markov chain models.
• explain how the numerical methods can be implemented in Python.

Skills

The student can:

• use and implement methods for the numerical solution of equations, as well as analyze deviations.
• use and implement methods for numerical integration.
• approximate functions using Taylor polynomials to analyze deviations in numerical integrators.
• use and implement methods for the numerical solution of initial value problems.
• use and implement Markov chain models.
• implement numerical methods using Python programming.

General competence

The student can:

• read and understand texts and participate in discussions regarding modeling, computation, and implementation.
• assess the accuracy of numerical estimates and choose appropriate parameters to ensure the estimates are accurate enough.
• interpret and evaluate the results of numerical calculations.
• assess which algorithms should be used in different cases.

Lectures and exercise sessions with extensive use of software and computer coding. The exercises combine the use of pencil and paper with computational tools under the guidance of the instructor and/or student assistant.

The following coursework requirements must be approved to be eligible for assessment/exam:

Two out of three group assignments where

• each group shall consist of 1 to 4 students.
• each group assignment is submitted as a report of 8-15 pages.
• each assignment can be resubmitted once if it is not approved.

The purpose of the coursework is for students to gain practical experience with project work and to combine several of the learning outcomes in the process.

Individual oral exam of about 30 minutes consisting of a student-led presentation followed by questions.

The exam result cannot be appealed.

In the case of a new or postponed exam, a different examination format may be used.

The student may use his/her own computer for the presentation.

Digital competence is a key factor in ensuring the employability of candidates in all professions vital to our society. This course will provide a fundamental understanding of our digital world. It gives an overview of how technology affects our lives and the way we work, as well as our social structures, work patterns and individual preferences contributing to shaping technology. Social media, digital governance, and eHealth are all examples of how technology has profoundly changed our everyday lives in the last few decades. An understanding of the benefits and limitations of technology is vital in any profession, regardless of field or speciality. In this course, students will acquire the basic knowledge required to harness the potential of technology and recognise its limitations and potentially harmful consequences on work and society. They will learn to identify the opportunities to use technology to foster inclusion and participation in an increasingly diverse and multicultural society. They will practice communicating orally the concepts they acquire in a structured manner.

This course is given in English.

After completing this course the student should have the following learning outcome:

Knowledge

On successful completion of this course the student understands:

• basic terms and concepts related to digital technology and society
• the role of technological innovation with regards to consumption, economic growth and sustainable development
• the democratic principles behind inclusion and a universally designed society
• the basic ideas behind of algorithms, and how their use may constrain or enable work processes and other aspects of everyday life

Skills

On successful completion of this course the student can:

• use basic terms and concepts from the curriculum to discuss problems arising at the intersect of technology and society.
• collaborate on problem-solving and complete self-directed student activities in groups
• evaluate and discuss technological and societal aspects of a case in a specific domain
• describe and discuss ethical challenges at the intersection of technology and society, including issues of integration and participation
• identify, respond to and limit the negative impact of unethical and harmful online behaviour

General Competence

On successful completion of this course the student can:

• be a valuable contributor to the design, planning and implementation of new technology
• be a positive agent of change in their own profession and field of study with regards to leveraging the potential of technology
• participate in innovative processes involving new and emerging technologies and build skills in anticipating and adapting to technological change
• reflect on technology use both within their field and from an interdisciplinary perspective