ACIT4310 Applied and Computational Mathematics Course description

The course will provide the students with an understanding of what a mathematical model is and how we use models to gain insights into systems and processes in science and engineering. The course will train the students in using analytical and computational methods for analyzing and solving differential equations and prepare them for developing, analyzing and simulating mathematical models in their own projects. The models and methods taught in this course are generic and applicable not only in science, but also in various industrial contexts.

Aesthetics and Special Needs is one of the courses under Nordic Childhoods. It focuses on Nordic culture where nature plays an important role in society, aesthetics and in work with children. Joint events with the other Nordic Childhoods courses are integrated as overnight trips and outdoor excursions. We also visit schools, kindergartens and other institutions. We focus on play, learning by doing, experience and workshops.

Aesthetics has not been a common way of approaching children with special needs. This course tries to change this by focusing on the value of aesthetics for children with special needs. The course is interdisciplinary, and takes a holistic approach to the field.

Aesthetics are important for everybody, including children and young people with special needs. Through literature, storytelling, music, dance, drama and other aesthetic acts, we perceive and understand the world and ourselves. Through aesthetics, we perform and collaborate with others. For some children and young people who lack verbal language; have problems with emotions, communication and interaction or find it hard to take other perspectives; aesthetic communication is particularly important. The aim of this course is:

1);;to enhance knowledge about and discuss the relationship between children and young people with special needs and aesthetic expressions,

2);;to introduce ways of working in practice with different kinds of aesthetic expressions when targeting various kinds of special needs.

The course is interfaculty and explores different disciplines, and ways of conceptualising and practising aesthetics with respect to a variety of special needs.

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course the student:

• knows the relevance of a selection of mathematical models to real-world phenomena
• has a thorough understanding of how mathematical modelling and scientific computing are utilized in various industrialized settings
• has a repertoire of methods to solve and/or analyze ordinary and partial differential equations (ODEs and PDEs)
• knows how to analyze the dynamics of an ODE system
• has a thorough understanding of the definitions of a smooth manifold and the tangent space
• knows the definitions and algebra of tensors and differential forms on a smooth manifold

;

Skills

On successful completion of this course the student:

• is able to derive mathematical models from facts and first principles for a selection of dynamical systems
• can apply mathematical modelling techniques on scenarios relevant to industry
• can implement mathematical models within the context of applied computer and information technology
• is able to analyse ODE systems and use bifurcation theory to elucidate the qualitative behavior of the systems
• is able to implement and use a selection of numerical methods for solving ODEs and PDEs
• is able to give examples of smooth manifolds and prove their smooth manifold property from the definition
• is able to use the geometric concepts and tools associated with smooth manifolds in the analysis of mathematical problems within mathematics, physics and engineering

;

General competence

On successful completion of this course the student:

• is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation
• is able to discuss properties of a system using the equations of the mathematical model
• can explain and use numerical methods and interpret results of numerical simulations
• is aware of the role of smooth manifolds as one of the most fundamental concepts in mathematics and physics

The course is organized as a series of lectures and seminars where the subject material is presented and discussed. Between these sessions the students should work with problem solving, implementation of numerical methods and model simulations. The last part of the semester;students will work with a compulsory individual project supervised by the course lecturer. The project will involve studies and analyses of a mathematical model and a rather extensive implementation of the numerical solution of the model. This will;result in a report that should be 2000 - 4000 words of length plus figures.

·;;;;;;;; Literature studies/theories

·;;;;;;;; Lectures and supervision

·;;;;;;;; Excursions, workshops and seminars

·;;;;; ;; Individual and group papers/performances

·;;;;;;;; Self-study

·;;;;;;;; Project work

·;;;;;;;; Digital blog

·;;;;;;;; Dramatisation

·;;;;;;;; Stop-motion animation

;Radio theatre

·;;;;;;;; Storytelling

·;;;;;;;; Visits and practice in school, kindergartens and other institutions

·;;;;;;;; Interactive learning methods, including digital media

Appendix: progress clarification for internal students

(Applicable to;Norwegian students only).

The course is open to internal students from the Department of Early Childhood Education (full-time students) in the sixth semester. The students follow the approved course description for Aesthetics and Special Needs - Nordic Childhoods (30 ECTS).

The following clarification applies to internal students:

• Internal students must complete a five-week supervised and assessed period of practical training.;
• The exam consisting of three parts counts as the student’s bachelor’s thesis. The assignments;must be written in English.
• Internal students retain bachelor supervision resources while taking the course, and are assigned a supervisor from among the teaching staff involved in the course, as far as possible.

The internal students otherwise follow the same programme and coursework requirements as the external students which, together with the written assignments, makes up the basis for the grade awarded for the course.

Three individual and four group coursework requirements must be passed in order to sit the exam. Aesthetics and/or children and young people with special needs should play an important part in the coursework requirements.

Individual:

1. Storytelling
2. Theory presentation
3. Participation in excursions
4. Participation in International Week

Group:

1. Production of a drama
2. Production of radio theatre
3. Production of stop-motion animation
4. Blog production
5. Practical work in connection with International Week

Coursework requirements must be met by the deadlines. Coursework requirements are evaluated as pass/fail.

Valid absence documented by a medical certificate or similar is not an excuse for not meeting the coursework requirements. Students who, due to illness or other valid and documented reasons, do not meet the coursework requirements by the deadlines, may be given longer deadlines. A new deadline for meeting the coursework requirements is agreed with the relevant teacher in each case.

Students who meet the coursework requirements by the deadline, but are awarded a fail grade, shall be given another attempt to meet the coursework requirements. A new deadline for meeting the coursework requirements is agreed with the relevant teacher in each case.

The exam consists of three parts:

Part 1: Aesthetic production in group for children and young people with special needs.

Part 2: Individual reflection paper on the aesthetic production (approx. 3,000 words).

Part 3: Individual autobiographical and multimodal (for instance a film) project where the student documents and reflects on his/|her process of making an aesthetic production for children/young people with special needs (maximum 3,000 words or a film of maximum 15 minutes).

Resit or rescheduled exams

If a student fails the exam or is absent at the time of the exam for a valid reason, the student is entitled to resit the exam the following semester. The resit exam will be organised in the same manner as the ordinary exam, but the group exam will be individual. The regulations on resit and rescheduled exams are set out in the Regulations relating to studies and examinations at OsloMet. Students must register for a resit or rescheduled exam.

Grade scale A-F.

All exam aids are permitted. However, sources must be stated in accordance with the applicable rules for source references.

Part 1 will be evaluated as pass/fail.

Part 2 and 3 will be evaluated according to the ECTS grading scale, with A-E as pass grades and F as a fail grade. The criteria for the different grades will be presented to the students at the beginning of the course.

Part 2 accounts for 60% of the overall grade and part 3 for 40%.

The completion of the three parts will result in one final overall grade (A- F).