Utbildningsplan. Masterprogram, matematik Master's Programme, Mathematics, 120 credits 120,0 högskolepoäng. Utbildningens mål. Kunskap och förståelse

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1 Utbildningsplan Masterprogram, matematik Master's Programme, Mathematics, 120 credits 120,0 högskolepoäng Gäller för antagna till utbildningen fr o m HT12. Utbildningens mål The main objective of this programme is to educate skilled mathematicians, well prepared for advanced industrial positions or continued graduate studies. Kunskap och förståelse A Master of Science in Mathematics will: have a good broad knowledge in mathematics as well as a significantly deepened knowledge within the chosen area of specialization, have a good ability to in an independent manner apply mathematical theories and solution methods, be able to formulate and approach new problem settings in a scientific manner, by having a creative, critical and systematic attitude towards mathematics. Färdigheter och förmågor A Master of Science in Mathematics will be able to: work out solution strategies to important classes of mathematical problems, knowing the capabilities and limitations of different methods and tools, work efficiently in a teamwork environment in groups with different compositions, communicate results and conclusions in a competent and intelligible manner, both orally and in writing, follow and participate in research and development related to the chosen specialization. Värderingsförmåga och förhållningssätt A Master of Science in Mathematics will be able to: critically judge a situation and in an independent manner acquire the information and knowledge that is necessary to establish a qualified standpoint, have the ability to identify the need for further knowledge in the field and take responsibility for keeping their personal knowledge up to date. Complete information on the degree requirements can found in the local degree policy of KTH, see /regelverk/utbildning-forskning/grundutbildning/examina Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Sida 1 av 4

2 Utbildningens omfattning och innehåll Mathematics is a two-year (120 university credits) master programme on the advanced level (second cycle). The instruction language is entirely English. The programme consists of a basic curriculum followed by five tracks: (i) mathematics, (ii) mathematical statistics and financial mathematics, (iii) computational mathematics, (iv) optimization and systems theory, and (v) discrete mathematics and theoretical computer science. The courses in the basic curriculum are compulsory and constitute about half of the course work. To obtain sufficient depth in a track, a student is normally required to complete courses worth at least 18 university credits among the profile courses for the track in question. Behörighet och urval General eligibility requirements A completed Bachelor's degree, corresponding to a Swedish Bachelor's degree (180 ECTS), or equivalent academic qualifications from an internationally recognised university. Students in their final year of undergraduate education may also apply to KTH and if qualified, receive a conditional acceptance. Specific eligibility requirements The prerequisites for the Master's programme in Mathematics is a Swedish or foreign degree equivalent to Bachelor of Science of 180 university credits, with at least 45 university credits in mathematics. The students are required to have documented solid knowledge corresponding to adequate university level courses in analysis, linear algebra, numerical analysis, differential equations and transforms, and mathematical statistics. Applicants must provide proof of their English language proficiency which is most commonly established through an internationally recognised test. Seehttp:// The specific requirements may be assessed as not fulfilled if 1. the average grade is in the lower third on the grading scale used (above pass level) 2. the degree awarding institution is not considered to meet acceptable quality standards by the authorities of the country in which the institution is located 3. the degree does not qualify for admission to equivalent Master level in the country where the degree is awarded see Selection process The selection process for The Master of Science programme in Mathematics is based on a total evaluation of the following selection criteria: university, grade point average (GPA), course work related to the programme (mathematics in a wide sense), and references. Complete information on the eligibility requirements can be found in the local admission policy of KTH, see Utbildningens genomförande Utbildningens upplägg The academic year at KTH is divided into four periods. Each period lasts approximately seven weeks with at least 33 days of study. Each period is followed by an exam period consisting of two extra days and at least 5 exam days. In addition to the four regular exam periods, there are three additional re-examination periods: after Christmas, after May, and immediately preceding the first study period of the academic year. The academic year lasts for a duration of 40 weeks. Teaching activities may, if necessary, be scheduled outside the academic year. Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Sida 2 av 4

3 The first year in the programme is mainly dedicated to the compulsory courses in the basic curriculum. However, some courses in the specializations are also given in the first year, in order to harmonise the master programme and the final part of the five-year engineering education at KTH. The second year mainly consists of elective courses and the final degree project, although it depends on the chosen specialization. Kurser Utbildningen sker i kursform. Kurslistor finns i bilaga 1. The programme is course-based. Lists of courses are included in Appendix 1. The basic curriculum corresponds to approximately 45 university credits. In each track, there is an additional set of profile courses, of which normally at least 18 university credits have to be taken. This leaves approximately 27 university credits for optional (elective) courses. These courses may be chosen among other higher level courses at KTH, or at the Department of Mathematics at Stockholm University, relevant to the student's profile. Betygssystem För kurser på KTH används en sjugradig målrelaterad betygsskala A-F som slutbetyg för kurser på grundnivå och avancerad nivå. A-E är godkända betyg med A som högsta betyg. Betygen godkänd (P) och underkänd (F) används som slutbetyg då särskilda skäl föreligger. Courses in are graded on a scale from A to F. A-E are passing grades, A is the highest grade. The grades pass (P) and fail (F) are used for courses under certain circumstances. Villkor för deltagande i utbildningen No later than November 15 and May 15 each academic year, respectively, the students are required to make a study registration and course selection for the coming term. At least 45 university credits have to be completed during the first academic year (including the re-examination period in August) in order for the student to be promoted to the second year of the programme. Students have to make a decision about the track during the first year of the programme. Tillgodoräknanden Under certain circumstances, and in agreement with the programme director, credits for previous studies can be received according to the local policy of KTH, see Examensarbete Students admitted to the programme are required to perform an independent study in the form of a thesis project corresponding to 30 university credits. To begin the thesis project, a student must normally have completed at least 60 university credits of the total course work and 18 university credits of the profile courses in the track. The purpose of the thesis project is that the student should demonstrate the ability to perform independent project work, using and developing the skills obtained from the courses in the programme. It is the student s responsibility to find a suitable thesis project, with assistance from KTH. More information on the KTH policy on the degree project can be found at examensarbete-30-hogskolepoang-for-masterexamen-120-hogskolepoang-samt-betygssattning-av-examensarbete ?l=en_UK Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Sida 3 av 4

4 Examen Students who fulfill all the requirements will be awarded a degree of Master of Science (two years). Students must apply for the degree and also show proof of their basic degree (bachelor or similar). Complete information on the degree requirements can found in the local degree policy of KTH, see Bilaga 1 - Kurslista Bilaga 2 - Inriktningsbeskrivningar Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Sida 4 av 4

5 Bilaga 1: Kurslista Masterprogram, matematik (TMTHM), Utbildningsplan för kull HT2012 Gemensamma kurser Obligatoriska kurser (22,5 hp) DN2221 Tillämpade numeriska metoder, del 1 6,0 Avancerad nivå DN2222 Tillämpade numeriska metoder, del 2 3,0 Avancerad nivå SF1841 Optimization 6,0 Grundnivå SF2940 Sannolikhetsteori 7,5 Avancerad nivå Villkorligt valfria kurser SF2713 Analysens grunder 7,5 Avancerad nivå SF2729 Grupper och ringar 7,5 Avancerad nivå SF2736 Diskret matematik 7,5 Avancerad nivå 2 av 3 villkorligt valfria kurser ska läsas. Den som läst SF1630 ska inte läsa SF2736. SF1630 räknas som en av de villkorligt valfria kurserna. Obligatoriska kurser (7,5 hp) AK2036 Vetenskapsteori och vetenskaplig metodik med tillämpningar (naturvetenskap) 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 1 av 6

6 Beräkningsmatematik (COMP) DD2257 Visualisering 7,5 Avancerad nivå DN2265 Parallella beräkningar för storskaliga problem, del 2 3,0 Avancerad nivå DN2275 Avancerade beräkningsmetoder i flödesmekanik 7,5 Avancerad nivå DN2297 Avancerad individuell kurs i beräkningsteknik 6,0 Avancerad nivå SF2812 Tillämpad linjär optimering 7,5 Avancerad nivå SG2212 Strömningsmekaniska beräkningar 7,5 Avancerad nivå SG2224 Tillämpade strömningsmekaniska beräkningar 5,0 Avancerad nivå DN2230 Snabba numeriska algoritmer för storskaliga problem 7,5 Avancerad nivå DN2255 Numerisk behandling av differentialekvationer 7,5 Avancerad nivå DN2260 Finita elementmetoden 6,0 Avancerad nivå DN2264 Parallella beräkningar för storskaliga problem, del 1 6,0 Avancerad nivå DN2266 Matematiska modeller, analys och simulering del 1 7,5 Avancerad nivå DN2281 Beräkningsmetoder för stokastiska differentialekvationer 7,5 Avancerad nivå SF2702 Wavelets 6,0 Avancerad nivå För information om kursval på detta spår se DN2258 Introduktion till högprestandaberäkningar 7,5 Avancerad nivå DN2297 Avancerad individuell kurs i beräkningsteknik 6,0 Avancerad nivå SF2812 Tillämpad linjär optimering 7,5 Avancerad nivå DN2230 Snabba numeriska algoritmer för storskaliga problem 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 2 av 6

7 DN2266 Matematiska modeller, analys och simulering del 1 7,5 Avancerad nivå SF2561 Finita elementmetoden 7,5 Avancerad nivå SF2702 Wavelets 6,0 Avancerad nivå Discrete Mathematics and Theoretical Computer Science (DM) DD2352 Algoritmer och komplexitet 7,5 Avancerad nivå DD2446 Komplexitetsteori 6,0 Avancerad nivå DD2448 Kryptografins grunder 7,5 Avancerad nivå SF2715 Tillämpad kombinatorik 6,0 Avancerad nivå SF2735 Homologisk algebra och algebraisk topologi 7,5 Avancerad nivå SF2737 Kommutativ algebra och algebraisk geometri 7,5 Avancerad nivå SF2741 Enumerativ kombinatorik 7,5 Avancerad nivå För information om kursval på detta spår se DD2446 Komplexitetsteori 6,0 Avancerad nivå SF2735 Homologisk algebra och algebraisk topologi 7,5 Avancerad nivå SF2737 Kommutativ algebra och algebraisk geometri 7,5 Avancerad nivå En kurs i Kommutativ algebra och algebraisk geometri tillkommer Matematik (MAMA) SF2702 Wavelets 6,0 Avancerad nivå SF2704 Valda ämnen i matematik I 7,5 Avancerad nivå SF2705 Fourieranalys 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 3 av 6

8 SF2707 Funktionalanalys 7,5 Avancerad nivå SF2709 Integrationsteori 7,5 Avancerad nivå SF2716 Valda ämnen i matematik II 7,5 Avancerad nivå SF2720 Kaotiska dynamiska system 7,5 Avancerad nivå SF2721 Topologi 7,5 Avancerad nivå SF2722 Differentialgeometri 7,5 Avancerad nivå SF2723 Valda ämnen i matematik III 7,5 Avancerad nivå SF2724 Valda ämnen i matematik IV 7,5 Avancerad nivå SF2728 Talteori 7,5 Avancerad nivå SF2731 Elementär algebraisk geometri 7,5 Avancerad nivå SF2732 Galoisteori 7,5 Avancerad nivå SF2734 Analytiska funktioner II 7,5 Avancerad nivå SF2735 Homologisk algebra och algebraisk topologi 7,5 Avancerad nivå SF2737 Kommutativ algebra och algebraisk geometri 7,5 Avancerad nivå SF2739 Partiella differentialekvationer 7,5 Avancerad nivå SF2740 Grafteori 7,5 Avancerad nivå SF2741 Enumerativ kombinatorik 7,5 Avancerad nivå För information om kursval på detta spår se SF2702 Wavelets 6,0 Avancerad nivå SF2704 Valda ämnen i matematik I 7,5 Avancerad nivå SF2709 Integrationsteori 7,5 Avancerad nivå SF2720 Kaotiska dynamiska system 7,5 Avancerad nivå SF2722 Differentialgeometri 7,5 Avancerad nivå SF2723 Valda ämnen i matematik III 7,5 Avancerad nivå SF2731 Elementär algebraisk geometri 7,5 Avancerad nivå SF2734 Analytiska funktioner II 7,5 Avancerad nivå SF2735 Homologisk algebra och algebraisk topologi 7,5 Avancerad nivå SF2737 Kommutativ algebra och algebraisk geometri 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 4 av 6

9 SF2739 Partiella differentialekvationer 7,5 Avancerad nivå Matematisk statistik och finansiell matematik (MSFI) SF2955 Datorintensiva metoder inom matematisk statistik 7,5 Avancerad nivå SF2960 Inferensteori 6,0 Avancerad nivå SF2970 Martingaler och stokastiska integraler 6,0 Avancerad nivå SF2975 Finansiella derivat 7,5 Avancerad nivå SF2976 Portföljteori, fördjupningskurs 7,5 Avancerad nivå SF2980 Riskvärdering och riskhantering 7,5 Avancerad nivå SF2701 Finansiell matematik, grundkurs 7,5 Avancerad nivå SF2942 Portföljteori och riskvärdering 7,5 Avancerad nivå SF2943 Tidsserieanalys 7,5 Avancerad nivå SF2950 Tillämpad matematisk statistik 7,5 Avancerad nivå För information om kursval på detta spår se SF2970 Martingaler och stokastiska integraler 6,0 Avancerad nivå SF2976 Portföljteori, fördjupningskurs 7,5 Avancerad nivå SF2980 Riskvärdering och riskhantering 7,5 Avancerad nivå SF2942 Portföljteori och riskvärdering 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 5 av 6

10 Optimeringslära och systemteori (OS) SF2707 Funktionalanalys 7,5 Avancerad nivå SF2827 Fördjupningskurs i optimering 7,5 Avancerad nivå SF2942 Portföljteori och riskvärdering 7,5 Avancerad nivå SF2943 Tidsserieanalys 7,5 Avancerad nivå SF2950 Tillämpad matematisk statistik 7,5 Avancerad nivå SF2970 Martingaler och stokastiska integraler 6,0 Avancerad nivå SF2812 Tillämpad linjär optimering 7,5 Avancerad nivå SF2822 Tillämpad ickelinjär optimering 7,5 Avancerad nivå SF2832 Matematisk systemteori 7,5 Avancerad nivå SF2842 Geometrisk styrteori 7,5 Avancerad nivå SF2852 Optimal styrteori 7,5 Avancerad nivå SF2863 Systemteknik 7,5 Avancerad nivå För information om kursval på detta spår se SF2943 Tidsserieanalys 7,5 Avancerad nivå SF2970 Martingaler och stokastiska integraler 6,0 Avancerad nivå SF2812 Tillämpad linjär optimering 7,5 Avancerad nivå SF2842 Geometrisk styrteori 7,5 Avancerad nivå SF2863 Systemteknik 7,5 Avancerad nivå Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 1, sida 6 av 6

11 Bilaga 2: Inriktningar Masterprogram, matematik (TMTHM), Utbildningsplan för kull HT2012 Beräkningsmatematik (COMP) The rapid development of hardware as well as software in the information technology sector has significantly improved the ability and need for mathematics in society. The track towards computational mathematics aims at construction, analysis and application of numerical methods for mathematical models. Discrete Mathematics and Theoretical Computer Science (DM) Discrete mathematics concerns the study of discrete (often finite) structures and concepts. Discrete, mathematical and combinatorial objects are often fascinating as such, but they also have a large number of practical applications and coding theory is used in cd players. Computer science is a very wide discipline which is close to discrete mathematics. Within complexity theory, mathematics and logics are very important tools for understanding what problems can be solved efficiently. Cryptography is another area where mathematical models are used to construct secure and efficient programmes. Matematik (MAMA) The track in mathematics is intended for students who wish to acquire knowledge on mathematics at an advanced level. The specialization may form the foundation for doctorate studies in mathematics, applied mathematics or closely related doctorate programmes. There are a large number of elective courses given, many jointly with the Department of Mathematics at Stockholm University. Matematisk statistik och finansiell matematik (MSFI) The aim of the track in mathematical statistics and financial mathematics is to provide broad knowledge on the mathematical foundation of statistical methods and a number of statistical tools for modeling and analysis of situations where randomness and uncertainty must be taken into account. There is a wide range of areas where this knowledge may be applied. In recent years, modelling of financial markets has attracted significant interest. Consequently financial mathematics is, to a large extent, a natural part of mathematical statistics. Optimeringslära och systemteori (OS) Optimization and systems theory is an applied mathematical discipline motivated by applications in areas such as operations research, economics, control and signal progressing. Optimization concerns maximizing or minimizing a function subject to constraints. Many such problems arise in real life, for example an airline scheduling aircraft or a telephone company routing calls. In all these problems, the systems concept arises. Systems theory is the study of phenomena and structures of high complexity, often man-made structures. Applications for systems theory can be found in e.g. robotics, control and signal processing. Utbildningsplan för Masterprogram, matematik antagna fr o m HT12. Bilaga 2, sida 1 av 1