## Mathematics and Physics (MAFY)

**Mission statements for the CL program's four branches**

The branch specific courses fulfill three purposes. They should

• provide sufficient breadth and depth in the natural sciences and technology for the engineering degree

• factually cover the information contained in the upper secondary and late primary school curriculum

• in keeping with the subject didactic courses, prepare for a deeper understanding of the key issues and learning in the subject area

**The goals for the common subject Mathematics**

Courses in mathematics provide a sound basis for professional activities as a teacher in upper secondary school and as Master of Science in engineering. The training is comprised of courses developed specifically for the program as well as courses common to most other engineering programmes, the latter are often read together with the co-study programmes.

After completing training in the CL programme, the student will be able to

• describe, use and apply basic concepts, theorems and methods in linear algebra, differential and integral calculus of one and several variables, discrete mathematics as well as probability theory and statistics,

• demonstrate an understanding of the concepts of ordinary and partial differential equation, and how such equations arise in mathematical modeling and how to use and account for common analysis and solution methods,

• implement evidence and mathematical reasoning, and to communicate these both orally and in writing,

• demonstrate knowledge of real analysis and abstract algebra bases,

• use and apply mathematical knowledge in mathematical modeling,

• plan, implement and interpret computer-aided algebraic and numerical calculations central to the engineering profession and for educational math assignments,

• describe some important features of the historical development of the mathematical concept of the world,

• grasp and account for the central parts of school mathematics with confidence and flexibility,

• apply knowledge and skills to teaching and learning within secondary school courses in mathematics

**Mathematics / Physics**

Having completed training in the Mathematics / Physics - branch of the CL program the student should be able to

... explain and use basic principles and relations in the fields of thermodynamics, electrical circuits, electrostatics and magnetism, waves and optics

... carry out physics experiments in both classical and modern physics, both alone and in groups, including readings and error estimation

... master basic engineering methodologies such as estimations, reasonability assessments and dimensional analysis

... formulate relevant mathematical and physical relations and models using vector algebra, vector analysis as well as partial differential equations and solve these

... perform basic calculations in mechanics, especially in the areas of particle dynamics, statics, rigid bodies and shocks

... show an understanding of the foundations of modern physics; relativity, quantum physics, atomic and molecular physics, nuclear physics and solid state physics

... report on sustainable energy options for the future and associated technical and social aspects

... in an educational way communicate information within the technical / physical areas, both orally and in writing

... relate her/his knowledge and skills to teaching and learning in upper secondary school physics courses Fysik 1, 2 and 3

CL students co-study physics courses mainly together with students of the program in Engineering Physics. This applies to basic courses in physics, thermodynamics, mechanics and electricity as well as courses in modern physics and mathematical methods of physics. The elective courses provide opportunities for specialization within the desired area on the second level. The studies during the first year in basic chemistry and energy / environment complement the scientific knowledge breadth. The compulsory courses are thus designed to cover well the subject knowledge for teaching upper secondary school physics courses.

The high mathematics content of the CL program ensures excellent potentialfor the studentto succeed inher/hisstudies,andduring the fourth and fifth yearthere is also opportunity to choose advanced courses in mathematics.

## Mathematics and Chemistry (MAKE)

**Mission statements for the CL programme’s four branches**

The branch specific courses have three functions. They should

• provide sufficient breadth and depth in natural sciences and technology for an engineering degree

• cover the information contained in the secondary school curriculum with regard to the main subject of the branch

• prepare for a deeper understanding of the key issues and learning in the subject area, in keeping with the main subject didactic courses

**The goals for the common subject Mathematics**

Courses in mathematics provide a sound basis for professional activities as a teacher in upper secondary school and as Master of Science in engineering. The training is comprised of courses developed specifically for the program as well as courses common to most other engineering programmes, the latter are often read together with the co-study programmes.

After completing training in the CL programme, the student will be able to

• describe, use and apply basic concepts, theorems and methods in linear algebra, differential and integral calculus of one and several variables, discrete mathematics as well as probability theory and statistics,

• demonstrate an understanding of the concepts of ordinary and partial differential equation, and how such equations arise in mathematical modeling and how to use and account for common analysis and solution methods,

• implement evidence and mathematical reasoning, and to communicate these both orally and in writing,

• demonstrate knowledge of real analysis and abstract algebra bases,

• use and apply mathematical knowledge in mathematical modeling,

• plan, implement and interpret computer-aided algebraic and numerical calculations central to the engineering profession and for educational math assignments,

• describe some important features of the historical development of the mathematical concept of the world,

• grasp and account for the central parts of school mathematics with confidence and flexibility,

• apply knowledge and skills to teaching and learning within secondary school courses in mathematics

**Mathematics/Chemistry**

Having completed training in the Mathematics/Chemistry - branch of the CL programme the student should be able to

• demonstrate knowledge of the importance of chemical thermodynamics, chemical equilibrium, molecular structure, kinetics, etc. for chemical reactions and process routes, transportation and balances,

• explain and use basic principles of organic chemistry, analytical chemistry, chemical engineering and biotechnology,

• demonstrate laboratory skills and knowledge of safe handling of chemicals, and the ability to plan, implement and evaluate experiments,

• work efficiently in groups and plan and implement projects within a given framework,

• demonstrate knowledge of the other natural sciences, mathematics and numerical methods in chemistry and the field of chemical engineering,

• identify, formulate and manage problems related to chemistry/chemical engineering in industry, society and research,

• demonstrate the ability to make plausibility assessments of different solutions and to compare and evaluate these,

• consider issues related to security, energy, environment and ethics within the profession,

• present and discuss problems, possible solutions and results both orally and in writing, and communicate information within the field of chemistry/chemical engineering in an educational way to people with or without scientific/technical background,

• have sufficient knowledge in the field to quickly acquire new skills and apply these,

• apply their knowledge and skills to teaching and learning in upper secondary school chemistry courses Kemi 1 and 2.

CL students co-study basic chemistry/chemical engineering courses mainly with students in the in the Chemical Science and Engineering programme. The optional courses provide opportunities for specialization within the desired area on the second level. The studies during the first year in basic physics and energy/environmental science complement the scientific knowledge breadth. The compulsory courses are thus designed to cover well the subject knowledge for teaching upper secondary school chemistry courses.

The high mathematics content of the CL programme ensures excellent potential for the student to succeed in her/his studies, and during the fourth and fifth year there is also the opportunity to choose advanced courses in mathematics.

## Mathematics and Technology: Energy and Environment (TEMI)

**Mission statements for the CL programme’s four branches**

The branch specific courses have three functions. They should

• provide sufficient breadth and depth in natural sciences and technology for an engineering degree

• cover the information contained in the secondary school curriculum with regard to the main subject of the branch

• prepare for a deeper understanding of the key issues and learning in the subject area, in keeping with the main subject didactic courses

**The goals for the common subject Mathematics**

Courses in mathematics provide a sound basis for professional activities as a teacher in upper secondary school and as Master of Science in engineering. The training is comprised of courses developed specifically for the program as well as courses common to most other engineering programmes, the latter are often read together with the co-study programmes.

After completing training in the CL programme, the student will be able to

• describe, use and apply basic concepts, theorems and methods in linear algebra, differential and integral calculus of one and several variables, discrete mathematics as well as probability theory and statistics,

• demonstrate an understanding of the concepts of ordinary and partial differential equation, and how such equations arise in mathematical modeling and how to use and account for common analysis and solution methods,

• implement evidence and mathematical reasoning, and to communicate these both

**Mathematics/Energy and Environment**

Having completed training in the Mathematics/Energy and Environment branch of the CL program the student should be able to

• demonstrate basic knowledge of all aspects of energy in a broad sense,

• demonstrate knowledge of the validation of energy and environmental systems using modern engineering tools such as environmental systems,

• describe sustainable development and relevant environmental problems at the basic level, encompassing visions, concepts and definitions and be able to describe the state of the world,

• express themselves in a professional way and communicate thoughts, ideas, visions and results to their professional environment and the community,

• reflect on and critically examine the energy and environmental area's historic and future importance to global and local community development and relationship to ecological systems,

• have a holistic approach to sustainable development of system and life cycles for products as well as technical systems based on a multidisciplinary approach and by considering different player perspectives,

• assess ethical issues and conflicting objectives concerning sustainable development and demonstrate deep insight into the engineer's role and responsibility in society, especially in regard to the social, economic and environmental aspects,

• have the skills to challenge, develop and construct problem statements about prevailing habits, thought patterns, technological and economic systems and cultural and social values,

• communicate information within energy and environmental areas in an educational way, both orally and in writing,

• relate their knowledge and skills to teaching and learning in upper secondary school courses in engineering, energy and environmental science,

CL students mainly co-study the courses in energy and environment with students in the program Energy and Environment. These courses include eg courses in energy systems, environmental systems, ecology and environmental effects, and environmental management. In addition to these they have their own course in learning and sustainable development. The elective courses provide opportunities for specialization within the desired area on the second level. The studies during the first year in basic chemistry and physics complement the scientific knowledge breadth. The compulsory courses are thus designed to cover well the subject knowledge for teaching upper secondary school technology courses and courses in energy and environmental science.

The high mathematics content of the CL program ensures excellent potential for the student to succeed in her/his studies, and during the fourth and fifth year there is also the opportunity to choose advanced courses in mathematics.

## Mathematics and Technology: Information and communication (TIKT)

**Mission statements for the CL programme’s four branches**

The branch specific courses have three functions. They should

• provide sufficient breadth and depth in natural sciences and technology for an engineering degree

• cover the information contained in the secondary school curriculum with regard to the main subject of the branch

• prepare for a deeper understanding of the key issues and learning in the subject area, in keeping with the main subject didactic courses

**The goals for the common subject Mathematics**

Courses in mathematics provide a sound basis for professional activities as a teacher in upper secondary school and as Master of Science in engineering. The training is comprised of courses developed specifically for the program as well as courses common to most other engineering programmes, the latter are often read together with the co-study programmes.

After completing training in the CL programme, the student will be able to

• describe, use and apply basic concepts, theorems and methods in linear algebra, differential and integral calculus of one and several variables, discrete mathematics as well as probability theory and statistics,

• demonstrate an understanding of the concepts of ordinary and partial differential equation, and how such equations arise in mathematical modeling and how to use and account for common analysis and solution methods,

• implement evidence and mathematical reasoning, and to communicate these both

**Mathematics/ICT**

Having completed training in the Mathematics/ICT - branch of the CL program the student should be able to

... explain and use basic principles and relationships in programming techniques, object orientation, algorithms, data structures, database technology and computer engineering,

... develop software and software systems in a structured manner, both independently and in groups,

... master basic engineering methodologies such as estimations, plausibility assessments and dimensional analysis,

... model real problems with discrete structures, objects and databases so that they can be solved with computers,

... analyze and evaluate the economic, social, environmental and ethical impact of information technology applications, and to design systems with regard to this,

... communicate information in an educational way within the information technology area, both orally and in writing,

... relate knowledge and skills to teaching and learning in upper secondary school courses in programming and media and communication studies

so that they will be able to ...

... work as teachers in mathematics, programming, media and communication studies,

... work with knowledge management in the public sector and in business,

... work with development of technological learning systems,

... work in the computer industry in their selected specialization.

CL students co-study specialization courses mainlywith students in the programmes Media Technology and Computer Science. The elective courses provide opportunities for specialization within the desired area on the second level. The studies during the first year in basic physics, chemistry, energy/environmental science complement the scientific knowledge breadth.

The high mathematics content of the CL program ensures excellent potential for the studentto succeed in her/his studies, andduring the fourth and fifth year there is the alsothe opportunity to choose advanced courses in mathematics.