EPN-V2

TRFE1000 Mathematics 1000 Course description

Course name in Norwegian
Matematikk 1000
Study programme
Bachelor's Degree Programme in Software Engineering
Weight
10.0 ECTS
Year of study
2020/2021
Course history

Introduction

Ved å arbeide med emnet, vil studentene opparbeide innsikt i deler av matematikken som står sentralt når man skal modellere tekniske og naturvitenskapelige systemer og prosesser. Temaene som tas opp, inngår i ingeniørutdanninger over hele verden. Temaene er nødvendige for at ingeniører skal kunne kommunisere faglig, effektivt og presist, og for at de skal kunne delta i faglige diskusjoner. Arbeidet med emnet vil gi øvelse i å bruke matematisk programvare for å gjøre studentene i stand til å utføre beregninger i jobbsituasjon. Emnet bygger på FO912A.

Required preliminary courses

Ingen utover opptakskrav.

Learning outcomes

Etter å ha gjennomført dette emnet har studenten følgende læringsutbytte definert i form av kunnskap, ferdigheter og generell kompetanse:

Ferdigheter

Studenten kan

  • anvende den deriverte til å modellere og analysere dynamiske systemer
  • stille opp og beregne størrelser hvor integraler inngår
  • drøfte ideene bak noen analytiske og numeriske metoder som brukes for å løse første ordens differensiallikninger
  • sette opp og løse differensiallikninger for praktiske problemer
  • drøfte numeriske metoder for å løse likninger
  • løse likninger med komplekse koeffisienter og komplekse løsninger
  • bruke grunnleggende regneoperasjoner for matriser som multiplikasjon, addisjon og invertering
  • løse lineære ligningssystemer ved reduksjon til trappeform og invertering

Kunnskap

Dette krever at studenten kan

  • regne ut eksakte deriverte og antideriverte ved å bruke analytiske metoder
  • med utgangspunkt i definisjonene bestemme tilnærmede numeriske verdier av den deriverte og av det bestemte integralet og vurdere nøyaktigheten av disse verdiene
  • bruke den deriverte og deriverte av høyere orden til å løse optimaliseringsproblemer, problemer med koblede hastigheter og til å regne ut lineære tilnærminger
  • forklare hvordan man kan bruke det bestemte integralet til å regne ut størrelser som areal, volum, buelengde og arbeid
  • løse separable og lineære differensiallikninger ved hjelp av antiderivasjon
  • gjøre rede for hvordan retningsfeltet til en førsteordens differensiallikning kan brukes til å visualisere løsninger til likninger
  • finne numeriske løsninger av initialverdiproblem ved hjelp av Eulers metode
  • løse likninger ved for eksempel halveringsmetoden og Newtons metode
  • regne med komplekse tall
  • gjøre rede for sammenhenger mellom lineære ligningssystem og praktiske problemstillinger

Generell kompetanse

Studenten kan

  • overføre et praktisk problem fra eget fagområde til matematisk form, slik at det kan løses analytisk eller numerisk
  • skrive presise forklaringer og begrunnelser til framgangsmåter, og demonstrere korrekt bruk av matematisk notasjon
  • bruke matematiske metoder og verktøy som er relevante for sitt fagfelt
  • bruke matematikk til å kommunisere om ingeniørfaglige problemstillinger
  • gjøre rede for at endring og endring per tidsenhet kan måles, beregnes, summeres og inngå i likninger

Teaching and learning methods

Undervisningen organiseres i timeplanlagte arbeidsøkter. I arbeidsøktene skal studentene øve på fagstoff som blir presentert. Noe av undervisningen vil foregå som øving i problemløsing, hvor bruk av numerisk programvare naturlig vil inngå. Innholdet i øvingene omfatter diskusjoner og samarbeid samt individuell øving i å løse oppgaver. Mellom de timeplanlagte arbeidsøktene er det nødvendig å arbeide individuelt med oppgaveregning og litteraturstudier.

Course requirements

Følgende arbeidskrav er obligatorisk og må være godkjent for å fremstille seg til eksamen:

  • Tre av fire individuelle innleveringer må være godkjent.

Assessment

Ny eksamen våren 2021: Individuell skriftlig hjemmeeksamen på 4 timer.

Eksamensresultat kan påklages.

[Eksamen tidligere:]

Individuell skriftlig eksamen under tilsyn på 3 timer

Eksamensresultat kan påklages.

Permitted exam materials and equipment

The program is a full-time program over two years that consists of a lecture-based component with a scope of 90 credits and an independent project, the master’s thesis, with a scope of 30 credits. The master’s degree program will prepare students to meet society’s need for up-todate, forward-looking expertise in sustainable and smart urban analytics and transport planning. In this master program, the students will achieve knowledge in both the fields of Transport- and Urban Planning.

The courses are organized in a systematic way. The transport courses provided in the first semester will provide students strategic and technological knowledge of the state-of-the-art transport system and the challenges it is facing. Moreover, basic research skills will also be provided to help students to handle more methodological courses in the second semester. During the second semester, the widely applied analytic and modeling method will be provided to students with the focus on human activity and needs. Their knowledge will be expanded from the transport system to the whole city. Students will have in-depth skills and concepts of urban analytics and regional science. In the second year, students will select their expertise and conduct a master thesis based on everything they learned in the first year.

Transport planning concerns the evolution of transportation networks and transport planning strategies. The study program focuses on providing the students with more detailed knowledge of the history, trends, problems, and opportunities in land use and transportation. The program incorporates substantive knowledge in transport demand and travel behavior, land use and transportation policy and planning, street design and urban space, and implications for a sustainable urban future. The study program also aims to provide updated skills on new technology in this field as well as knowledge in innovations in equitable and sustainable urban mobility.

Urban planning is analyzing and understanding the evolution and challenges of urban development, as well as urban and land use planning. The study program focuses on providing the students with solid, theoretical knowledge and applied skills in urban systems, management of urban design and human factors in sustainable cities. Climate change and increased focus on resource use and environmental impacts thereby entail a greater focus on the choice of urban design. The study program focuses on providing the students with more detailed knowledge of town-friendly planning and green policy. The study program also aims to provide updated skills on new technology in this field as well as knowledge in innovative and sustainable urban planning.

In the third semester, students have the option to choose in-depth knowledge in either smart mobility or in urban analytics. Students who choose to specialize in smart mobility will take the Urban Mobility elective, and students who choose to specialize in urban analytics will take the Space Syntax elective. The elective courses give students necessary knowledge in these areas, and experience applying the skills and methods learned in the first and second semester to specific problems in Transport and Urban planning. After completing the elective, students will then complete a master’s thesis in the fourth semester. The master’s thesis will then give the students further practice in applying their knowledge and skills to relevant issues through more comprehensive project work.

The study program focuses on teaching students how to use advanced computer programs and simulation tools to solve complex problems relating to sustainable urban and transportation problems, so the development of digital skills is an important integrated part of all the courses. This also helps make the program cross-disciplinary, including elements of computer science, analytic disciplines (like modeling, simulation), artificial intelligence, machine learning etc., because that is what the industry needs today

The study program also aims to qualify candidates with the competence to participate in research work in the field. The two courses Research Methods and Research Ethics (5 ECTS) and Advanced Research Methods (5 ECTS) underpins the master’s thesis and provides an introduction to qualitative and quantitative research methods, ethics, and academic writing and dissemination of results

The master’s thesis is an independent, supervised research or development project in the core areas and represents further specialisation in either transport or urban planning.

The structure of the programe:

The master’s degree program consists of eight compulsory courses, two elective courses in addition to a master’s thesis. The course portfolio is composed so that the compulsory courses ensure academic and professional breadth, at the same time as the students are given an opportunity for in-depth study and specialisation through elective courses and the master’s thesis.

The choice of elective courses for the third semester (Transport and Urban Planning) is made at the end of the second semester. The whole fourth semester is dedicated to the master’s thesis. It is natural that the master’s thesis builds on the project work that forms part of the specialization topic in the third semester. The topic of the thesis can either be linked to a client’s issue or to relevant research projects in the department.

In order for students to be able to present the master’s thesis, all courses from the first year of the study program must be passed.

Students are encouraged to contact relevant enterprises in the region for the purpose of gaining practical training and experience in the fields through a summer job or similar, and to establish cooperation on project assignments.

Grading scale

The work and teaching methods in the program includes group work, cross disciplinary projects, lectures, exercise sessions including digital labs, presentations, field work and discussions. The students will be involved in peer feedback which will be part of the learning process. The scheduled study activities shall be motivating and inspiring for the students and induce nonorganized academic work. The work methods are intended to stimulate cooperation, individual activity, reflection and fresh thinking. Contact with business and industry through external lecturers and projects in addition to ordinary tuition is intended to give the students a relevant and motivational approach throughout the study program.

To work as an expert researcher in urban or mobility design and planning requires a high level of expertise in the use of advanced computer programs and simulation tools (ICT tools) for problem-solving. Computer exercises and tasks that require the use of advanced ICT tools are therefore one of the main work methods used in the study program.

Research and teaching are also integrated throughout the study program. The teaching is to be constantly updated to encompass new knowledge, and research articles are part of the syllabus. Furthermore, the students will participate in research-related discussions and be included in ongoing research and development through projects that are part of the study program.

Project-based learning relating to urban and mobility design and planning tasks is used to give the students practice in work on complex issues. The study program will prepare the students for work methods used in the industry, through group work and project assignments in cooperation with partner companies in the industry. The projects are intended to develop the students’ ability to formulate and analyze research questions using scientific methods. Projects are normally carried out in groups, and the students will also thereby develop their ability to listen to others, exchange knowledge and discuss solutions in cooperation with others. Project work shall culminate in reports written on the basis of a template for scholarly articles/reports.

The master's thesis shall take the form of independent, supervised research or development work in one of the key subject areas of the study program.

The master's thesis must follow at least one scientific approach, and the result must contain elements of new knowledge or new methods. Each student or group of students will be assigned an internal supervisor who will ensure that the project complies with research ethics principles and help students to formulate the research question and ensure quality in the collection and analysis of data. The master's thesis shall be a written report based on research principles and methods.

Examiners

Both the language of instruction and the course literature are in English, making the study program well-suited for international students and student mobility. The study program is structured so that it is possible for the students to take one semester abroad, in the third or fourth semester. These will also be the semesters for exchange students from abroad to join the master program at OsloMet for one semester.

Internationalization in this master program is four-fold by taking an approach from different angles. This master’s program educates and prepare students for an international competitive job market with (1) language of instruction in English to equip the future graduates to work in practice and academia world-wide with (2) international state-of-the-art knowledge in the field of mobility with digital skills and urban analytical techniques and tools, (3) using comparative Norwegian and international case studies in courses and (4) the program is taught by national and international trained instructors including English native speakers and academics who have long-standing experience in lecturing in English.

With student mobility, students have the opportunity to gain experience abroad at a foreign academic institution which will offer complementary courses being very relevant for the students at the master program in Transport and Urban Planning, and the courses OsloMet will offer on the master program in Transport and Urban Planning will be of interest to students attending these selected universities.

OsloMet is part of the Erasmus program for student exchange and has entered into several Erasmus+ agreements with relevant universities and university colleges.

Students can gain approval and recognition of up to 30 credits on application.

OsloMet has a dedicated web page with supplementary information about student exchanges: https://www.oslomet.no/en/study/exchange-students

Requirements:

An average grade C or better in previously completed courses. An exchange agreement with the desired university or college must be in place before the student can apply. Acceptance from a receiving institution to an exchange-stay with the necessary academic relevance.

Application deadline: One semester prior to the planned stay.

Overlapping courses

Required coursework means compulsory assignments or activities that must be approved within a given deadline in order for students to be able to get the course validated. The coursework requirements in this study program are linked to written assignments and compulsory attendance to some labs. The coursework requirements are described in more detail in the individual course descriptions.

Coursework requirements are set in order to promote the student’s progress and development and to ensure his/her participation in necessary elements of the program. Required coursework can also be set to ensure that students achieve a learning outcome that cannot be tested in another way.

Required coursework is assessed as approved or not approved. In the event of delays in study progress, previously approved coursework remains valid for two years, provided that the course has not changed.

Valid absence documented by e.g., a medical certificate does not exempt students from meeting the coursework requirements. Students who fail to meet the coursework requirements within the deadline due to illness or for other documented valid reasons should as far as possible be given a new chance. If another attempt at meeting a coursework requirement is not possible because of the nature of the subject/course, the student must be prepared to meet the coursework requirements on the next possible occasion. This must be agreed with the person responsible for the course on a case-by-case basis. This may result in delayed progress in the program.

If a work requirement is assessed «not approved», students have maximum two chances to retake the work requirement. A work requirement that three times is assessed «not approved», will result in loss of the right to get this course validated.