Evaluation of the education and degree programmes of the university of helsinki 2001-02

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Self-evaluation report of the Departments of Mathematics, Physical Sciences, Chemistry and Computer Science

Helsinki, November 2001




Appendix 1 Student organisation statements 45
Appendix 2 Theses 54
Appendix 3 Degrees in 199-2001 72


This report deals with the degree programmes in the exact natural sciences, which in this case include Mathematics, Physical Sciences, Chemistry, and Computer Science. These are disciplines in which concepts and knowledge are organised deductively (usually on the basis of empirical material) into a systematic hierarchical structure. The disciplines also aim at mathematical modelling and creative, yet methodical, problem solving. Studies in the disciplines involve a great number of practical skills, which are developed through laboratory work, problem-solving and computer courses carried out in small groups. These methods considerably increase the cost of education.
Basic education aims at the MSc degree, which is the de facto basic degree in Finland and consists of a minimum of 160 credits. Two minor subjects, which together account for a minimum of 45 credits, are an essential part of the degree. After many years of absence, the lower 120-credit academic degree, corresponding to the Bachelor’s degree in many countries, was reintroduced into the degree structure in the late 1990s in accordance with international degree structures. However, Finnish qualification requirements (for example, those of subject teachers) often do not recognise the lower degree, and students of exact (natural) sciences rarely complete it. About half of the lower degree consists of the major subject, leaving a considerable share for minor subjects and “other studies”. Owing to the hierarchical knowledge structure of the disciplines, this degree may not offer enough depth of studies or sufficient professional skills. Postgraduate studies mainly aim at a Doctoral degree within 4-5 years of the Master’s degree. It is also possible to complete a lower Licentiate degree after approximately two years of postgraduate studies.
The common problem of exact (natural) sciences is their weak position in the Finnish school system, which leads to there being too few talented and motivated students. As a result, a large number of students drop out after the first year of studies. Some of the main reasons for interrupted studies include students using their study right to prepare for entrance exams in other faculties or universities, as well as the fact that some students obtain two study rights and later drop one of them. Particularly in Computer Science, the heavy recruiting of businesses has also led to students leaving their studies. To improve the situation, the departments have worked to enhance tutoring, increase instruction that improves study skills, organise alternative teaching in the Open University, and change the selection method so as to emphasise motivation and the role of the major subject. These measures have led to a slight improvement. The regulation allowing first-year students to accept only one study right has also had a favourable influence. In the case of students that started their studies in 2000, the situation looks more promising. The number of students continuing with second-year studies has now increased considerably.
The Faculty of Science conducts ongoing development work concerning teaching and the degree programmes. The report “Development of Teaching at the Faculty of Science 1998-2000” is appended to this self-evaluation report.
In 1996-2000, the Ministry of Education granted an additional appropriation to the departments as part of the national LUMA development programme for the development and extension of teaching, particularly that related to teacher training.
This self-evaluation report was drafted by a working group appointed by the Department and consisting of Hannu Honkasalo, Professor; Tapani Hyttinen, Academy Research Fellow; Saara Lehto, student; Jussi P. Nieminen, student; Kalevi Suominen, Professor; Hans-Olav Tylli (Chairman), Academy Research Fellow.
1. Overview
The educational goals of the Department of Mathematics include providing basic and postgraduate education in Mathematics to enable graduates to work in a variety of expert and educational tasks requiring mathematical skills in different sectors of society. Other goals include the provision of systematic education and supervision to those aiming at a career in research. The Ministry of Education and society in general have continued to emphasise the importance of mathematical skills and education to the IT sector and school instruction, among others.
An annual average of 46 MSc degrees, 5 Licentiate degrees and 3 Doctoral degrees were completed in 1996-2000. The number of MSc degrees, in particular, has considerably increased since the early 1990s. The Department’s long-term goal is to raise the number of MSc degrees to an annual 65–70 (provided that enough financial resources are available). The Department also wishes to increase the number of postgraduate students. The Department of Mathematics offers one of the most extensive programmes of instruction measured in completed credits at the University of Helsinki (Table 1 on p. 10).
The development of instruction focuses on teacher training (the Department aims to meet the increased demand for teachers), financial and insurance mathematics, and computer-aided mathematics, for which a new 5-year professorship was recently established. In 1997-2000, the Department of Mathematics was able to increase the amount of instruction and make it more efficient thanks to the so-called LUMA funding. The instalment of FIM 1.7 million, which was not received in 2001, has proved to be difficult to compensate for. The Department’s degree paths were renewed in 1999.
One of the central goals is to support the teaching provided in the Department’s internationally successful fields of research. As of 2002, the Department will house a centre of excellence for analysis and mathematical physics. Supporting the instruction provided by the centre will demand considerable investments from the Department starting with basic education.
The departmental library has a selection of mathematical research journals of international top quality, which other Finnish departments of mathematics turn to when needed. While the library’s book collection is more of a research nature, its textbook selection has also grown considerably in the past years.
2. Content of education and degree programmes
The major subject studies in the MSc degree of Mathematics consist of intermediate and advanced studies. The intermediate studies are largely the same for all major students of Mathematics; common courses include Differential and integral calculus I (parts I.1 and I.2), Linear algebra I and Differential and integral calculus II. These and other intermediate courses aim to enhance the students’ skills in core mathematics needed at the later stages of studies.
At the advanced stage, the degree programme in Mathematics is divided into four sub-programmes, two of which are further divided into four specialisation areas each. This division was implemented in autumn 1999, with the intention to provide as wide a coverage as possible of all the typical career choices available for mathematicians. The sub-programmes and specialisation areas include the following:
General Mathematics sub-programme

Algebra and topology path

Analysis path

Mathematical physics path

Mathematical logic path

Applied Mathematics sub-programme

Applied mathematics path

Stochastic modelling and data analysis path (together with the Rolf Nevanlinna Institute)

Computer-aided mathematics path

Financial and insurance mathematics path

Computer Mathematician sub-programme (jointly with the Department of Computer Science)

Teacher of Mathematics sub-programme

The sub-programmes and specialisation areas are not fully separated from each another even at the advanced stage (this would be impossible to implement due to resource availability, in addition to which, the different paths still require much of the same skills in core mathematics). It is rather a question of how the different subfields of mathematics are emphasised. The number of sub-programmes and the related course offering at the Department of Mathematics is the most versatile of all Finnish universities. The sub-programme for teachers produces a significant share of the Department’s MSc degrees (some 52% in 1996-2000). The number of graduates in other options and paths has also increased. The Department of Mathematics at the University of Helsinki differs from other Finnish universities in also educating a considerable number of mathematicians other than teachers. This requires more resources, as the studies in mathematics of teachers consist of 75 credits, whereas the requirements in other paths is usually 93 credits. In addition, the Rolf Nevanlinna Institute has supervised some theses, and licentiate and doctoral dissertations, as well as arranged individual special courses.
The degree programme in Mathematics also offers the opportunity to complete the lower BSc degree. The number of BSc graduates has remained low although it would be an excellent intermediate goal for students aiming at the MSc degree. The BSc should be marketed more actively to students. A clear problem in this respect is, however, that working life does not value the BSc degree, because the students’ average skills in Mathematics are still insufficient at that stage (one of the reasons being the big share taken up by minor subjects).
The Department of Mathematics offers a substantial amount of instruction in (minor subject) studies to other disciplines, particularly to students of the Physical sciences, Chemistry and Computer science. Minor subject teaching accounts for an average of 45–50% of the Department’s credits (Table 1 on p. 10). In recent years, students of Computer science have become the biggest group of minor subject students. This has brought about a change in minor subject teaching, which was implemented in autumn 2001 after lengthy discussions. The Approbatur I and II courses solely aimed at minor subject students were dropped (these courses were originally designed for students of Physics and did not meet the needs of students of Computer science). Minor subject students can now put together a study module in Mathematics (approbatur 15-34 credits, cum laude min. 35 credits, laudatur min. 70 credits) relatively freely using any of the available intermediate-level courses in Mathematics. Students majoring in other disciplines are offered courses specifically designed for their needs, which makes it easier to achieve the goals set for minor subject studies in Mathematics. This also makes it easier to integrate the minor subject teaching of Mathematics with instruction in the major subject.
The degree requirements and curriculum for the following academic year are prepared on the basis of discussions between the professors in charge of the various sub-programme s, the other teachers of the Department, and the members of the steering group. The curriculum is designed to offer a wide range of intermediate and advanced-level courses, to find the best possible lecturers for the courses, and to keep the annually altered range of special courses for advanced and postgraduate studies sufficiently versatile and interesting. The last goal, in particular, is clearly hampered by the insufficient basic funding of the Department.
3. Practical organisation of education
Teaching and study culture
Education in Mathematics has traditionally been based on individual work (such as constructing proofs and solving problems) aiming at achieving personal skills in Mathematics. A central challenge to the teaching in Mathematics (also from an international perspective) is how to construct the lectures to better serve learning and to be more motivating. Students often feel that lectures do not take into consideration the skills and knowledge of an average student: lectures may proceed too fast or the exercises for the problem-solving classes are too difficult. The Department has launched several projects that aim to promote student-orientedness even further than usual (examples include essays in the basic courses of the sub-programme for teachers, a “problem seminar”, and workshop activities). The aim is to share successful experiences with others and attempt to inspire as many teachers as possible by giving them new ideas for their work. Workshop experiences, for example, will be introduced into Differential and integral calculus I during 2001- 02.
Attempts have been made to complement traditional study guidance (course-related problem-solving exercises, supervised groups in Differential and Integral calculus I, study guidance provided by assistants) with new forms of guidance. The Department has experimented several times with teacher tutoring, but the resulting experiences have been controversial (while guidance has met with approval, participants have felt that it may not optimally correspond to the needs of first-year students). The Department plans to implement a supervised problem-solving workshop (the lack of suitable facilities has been an obstacle). The student organisation arranges comprehensive tutor group activities for new students in the first-year autumn, which aim to integrate students into the study community and provide a flexible start for studies.
Nearly all courses have traditionally evaluated learning with mid-term and final exams, which often include extra points collected in problem-solving classes. Evaluation methods now also include essays and seminars, which can be used to complete courses in their entirety or only parts of them.
The nature of the interaction and cooperation between students and teachers depends on the courses and teachers in question. Interaction is closer at the advanced stage of studies than at the intermediate stage, where courses often have more than 200 participants. While the Department’s teachers take care of teaching independently, they work within the course framework familiar to all.
Workloads seem to be in good proportion to the credits awarded in the Mathematics degrees. This issue has not raised any considerable discussion among teachers and students.
Compared to the number of students in the Department, the SOCRATES/NORDPLUS student exchange is relatively small scale (an average of four of the Department’s students annually participate in the programme; the Department has entered into SOCRATES exchange programme agreements with 10 universities and also has one agreement for a teacher exchange programme). Study-related social issues, particularly financing, are the main obstacle to extending exchange activities. The Department places foreign exchange students (an average of 3/year) as flexibly as possible in the courses they are interested in (the situation will improve as the number of classes held in Swedish and English increases). The same applies to foreign undergraduate students, whose number, however, is small. Foreign postgraduate students are placed directly in one of the research teams. Recognition of studies completed abroad (or elsewhere in Finland) is flexible (thanks to the general similarity between modules in Mathematics).
The Department’s teachers have different educational approaches both in terms of their point of view and their specialisation (expertise). In recent years, the Department has had excellent opportunities for educational reforms and experimentations. Ongoing projects include workshop activities and the renewal of educational instruction (for example, in educational psychology) for future teachers. The Department is also involved in research in learning.
Teaching and learning environments
The teaching material in most basic courses consists of lecture notes with widely varying print quality ranging from photocopies of the lecturer’s own notes to a textbook given out by a publisher. In some cases, lecture notes have been partly outdated, but their mathematical content is usually of very high quality. There has been a lot of discussion about increasing the use of international (mainly English) textbooks, which would be useful for students’ language skills. The disadvantages of using international books include their high price and the difficulty of seamlessly linking their contents. Students have also considered the use of Finnish material to be important particularly at the early phases of studies. The Department is also improving the availability of lecture material on the Internet.
Approximately 1-2 basic courses are held every term in both Swedish and English. The lectures are scheduled so that the course is not lectured in Finnish during the same term. This ensures that the Swedish and English lectures are also attended by Finnish-speaking students (the number of Swedish and English-speakers is relatively small, but experiences of this practice have been positive). Teaching in advanced and postgraduate studies is often provided in English if participants include foreign students. The Department’s research seminars are often held in English.
As for teaching tools, the blackboard is generally felt to be superior to many other methods, such as overhead projectors or whiteboards. The Department has launched an ambitious project (including a 5-year professorship) related to the use of computers. One of the problems, however, is the small number of computer labs, caused by inadequate facilities and financial resources.
The aim is to distribute teaching evenly across and within the different terms, as well as over the various days of the week. This is also required by the scarce teaching facilities and their appropriate use. Apart from a few intensive courses, the Department of Mathematics has not arranged any actual summer courses. The Open University offers some basic courses in Mathematics. Summer exams offering students the opportunity to take final exams in all courses are arranged in June and August. The Department also actively participates in the continuing education of subject and class teachers (usually arranged during weekends or in the summer).
The big basic courses are held in facilities outside the Department, some of which are satisfactory (the lecture rooms in Porthania), and others inadequate (for example, lecture room 1 on Vuorikatu 20; the other options being even worse). Smaller intermediate and advanced-level courses are held in the Department’s own lecture rooms (four), which are satisfactory as such, although their limited number makes sensible scheduling of teaching groups difficult. Most of the problem-solving classes are held in the four lecture rooms on Vuorikatu 20, which, while equipped with the bare minimum, are located in the vicinity of the Department.
The Department of Mathematics has inadequate facilities, made evident by the crowded office spaces of teachers and researchers (many rooms accommodate 2-3 people), as well as the lack of work spaces for students, in addition to the small number of computer labs. The Department hopes that the move to Kumpula in 2004 will alleviate these space-related problems.
Study progress
Dropouts at the early phases of studies are an internationally acknowledged problem in Mathematics and this is also encountered at the University of Helsinki. According to a survey commissioned by the Department, students who have carried on with their studies for a couple of years are very likely to continue their studies and they do not experience the same kind of problems with their theses as do students of other departments. For several years, the Department has focused its attention on the decisive first-year studies and tried to find the best and most motivating teachers to hold lectures. It has also attempted to take the average students’ starting level better into consideration (the problems of Mathematics teaching in Finnish upper secondary schools have weakened the skills of new students). The Department has recently focused on the main problems of first-year studies, which has already produced good results (Appendix). The new admittance procedures introduced in 2000 helps select students who are more committed to studying Mathematics.
It is relatively common for students of Mathematics to work while studying, particularly towards the end of their studies. While this lengthens the average graduation time, it also provides students with essential work experience.
Values of the teaching, learning and academic community
The scientific skills of the personnel as far as Mathematics is concerned are of top quality: the Department has done very well in research evaluations (maximum grade 7/7 in the evaluation of research at the University of Helsinki, evaluation of the field of Mathematics carried out by the Academy of Finland in 2000). Students have often given positive feedback on the expertise of the teachers, but have been more critical about their inspirational and motivational skills.
As stated in the regulations of the University of Helsinki, all teachers do research (produce and transmit new information) in addition to teaching. The emphasis on research and teaching merits when recruiting teachers depends on the requirements of individual posts. Administrative tasks related to departmental routines have clearly increased in the past years and are unevenly distributed among staff. The department aims to distribute the supervision of theses in both undergraduate and postgraduate education more evenly among personnel.
The development of education also aims to help students cope with and commit themselves to their studies. However, students have traditionally felt that their chances to influence things are relatively limited.
Owing to the cumulative nature of Mathematics, it is difficult to create connections between basic education and the research carried out in the Department. One of the Department’s goals is to include students in the activities of research teams. As participation in research seminars is often hindered by the high level of skill required, the Department has successfully tested “student seminars” and free study circles.
Postgraduate studies
The Department of Mathematics has approximately 130 postgraduate students, some 70 of whom have handed in their postgraduate study plans in the past three years. Of these, some 35 can be considered full-time postgraduate students (Appendix). In terms of supervision, the Department clearly has the capacity to increase the current number of graduates (Appendix), and is aiming at this, for example, by integrating (postgraduate) students more closely into research teams and seminars. Supervisory activities are distributed unevenly among personnel (a more even distribution would be more appropriate). For example, younger researchers can rarely offer paid project work to postgraduate students. In addition, dissertations consisting of several articles published in academic journals should be more emphatically recommended in Mathematics in addition to the traditional monographic dissertations.
A problem group among postgraduate students consists of those working elsewhere in addition to their studies. Their contacts with the supervisors and research teams are often loose and their studies also proceed more slowly. Interruption of postgraduate studies is also a definitive problem, as students have switched to employment outside the university: the salaries offered by universities are not competitive.
4. Evaluation and feedback
Course-specific feedback given at the end of courses has been used in Mathematics since the ‘80s, with the Mathematics student organisation, Matrix ry, usually collecting the results. Feedback has influenced course planning and the development of teachers’ personal teaching skills. In spring 2001, the Department implemented an electronic feedback system. Students have also hoped for feedback surveys in the beginning and middle of courses. This would enable students and teachers to better address possible problems while courses are still going on. The students also hoped for a bigger number of open-ended questions so that they could comment on specific mathematical difficulties and problems connected to the courses.
No department-wide feedback has been systematically collected from recent graduates or employees. The employment situation of mathematicians is excellent: according to a survey conducted by the Faculty, all recent graduates in the field have found employment. The research teams and postgraduate education in the Department of Mathematics were evaluated in 1999 (University of Helsinki) and 2000 (study carried out by the Academy of Finland focusing on the field of Mathematics in Finland). Both evaluations offered a variety of ideas for the development of the Department’s postgraduate education.

In 1998, Juha Oikkonen was rewarded with the highly esteemed Eino Kaila award given to the best teacher of the University. In 2000, Marjatta Näätänen received the Mathematics award granted by the Academy of Finland for her work on awakening interest towards Mathematics among girls, as well as the Maikki Friberg award for promoting equality at the University of Helsinki.

5. Future prospects and development plans
Versatile skills in Mathematics and mathematical methods are of core importance in society. The need for education in Mathematics will continue to increase as more profound mathematical methods are introduced. The employment situation of skilled mathematicians will remain good.
In 2001, a plan was presented to integrate the Department of Mathematics, the Department of Statistics and the Rolf Nevanlinna Institute on the Kumpula campus in 2004. Many surveys have proposed the integration of the departments of Mathematics and Statistics as is common in other countries. Integration could lead to synergy benefits in teaching and it would support the teaching provided in stochastics, as well as financial and insurance mathematics. The Department has a favourable attitude towards such integration although it would lead to both administrative and practical problems concerning the minor subject teaching provided by the departments.

The development plans in the Department of Mathematics focus on the following issues:

- Developing teacher training in Mathematics, particularly in the case of major subject students but also concerning the education of class teachers

- Expanding the course offering in applied mathematics, particularly in financial and insurance mathematics

- Developing workshop and small group teaching (the basic resources of the Department are not sufficient for this)

- Making postgraduate education and supervision more efficient

6. Summary

- Versatile teaching and skilled personnel

- International top-quality research in many subfields of Mathematics

- Flexible structure of degrees

- Good employment opportunities for mathematicians

- Good competitiveness in funding of projects and research schools

- Good and up-to-date library

- Relatively high share of dropouts at the early stages of studies

- Motivational problems in the teaching of Mathematics

- Insufficient number of computer labs and IT equipment for teaching

- Integration of postgraduate students into research seminars

- Insufficient number of postgraduate degrees

- Small number of post-doctoral research positions

- Crowded work and study spaces


- Insufficiency of budget funding

- Poor visibility and valuation of Mathematics and studies in the discipline

- Weaker initial skills of new students (on the average)

- Increased part-time nature of studies

- Recruitment of younger teachers and researchers


- Trend towards more efficient and versatile teacher training

- Direct entrance system for teacher training

- New ideas concerning teaching methods

- Focus on new fields in the teaching of mathematics (for example, financial mathematics and risk theory)

- New cooperation opportunities with the IT sector

- Increase in the number of students interested in Mathematics

- Increasing demand for mathematical skills

- Plan to integrate the Departments of Mathematics and Statistics on the Kumpula campus in 2004

Matematiikkalehti Solmu http://solmu.math.helsinki.fi

Table 1
Students in Mathematics

New student admission:
1996: 257

1997: 212

1998: 201

1999: 180

2000: 201

Students having Mathematics as their major subject:

1996: 1222

1997: 1184

1998: 1135

1999: 1153

2000: 1143

Teaching in the Department of Mathematics (measured in credits):

1996: 12403

1997: 11267

1998: 13331

1999: 13074

2000: 14715


The Physical Sciences degree programme includes the sub-programmes of Physics, Physics teacher, Geophysics, Meteorology, Theoretical physics and Astronomy. Except for Astronomy, the teaching and other activities of the sub-programmes and specialisation areas take place in the Physicum building, which is common to the whole Department of Physical Sciences and located on the Kumpula campus.

The first-year studies of all sub-programmes include basic studies in Physics and Mathematics, after which the studies of Geophysics, Meteorology and Astronomy are differentiated. As the Physics, Physics teacher and Theoretical physics sub-programmes still have much in common after this, they will be dealt with together in this report. In the first section, Department will therefore only refer to these three sub-programmes instead of the whole Department of the Physical Sciences. Geophysics, Meteorology and Astronomy will be dealt with separately afterwards.

The part on Physics, Physics teacher and Theoretical physics was prepared by a workgroup including Kari Eskola, Professor; Björn Fant, Senior Assistant; Ismo Koponen, Senior Assistant; Seppo Manninen, Lecturer; Jouni Niskanen, Senior Assistant; Heimo Saarikko, Professor; and Walter Rydman, student. The part on Geophysics was prepared by Matti Leppäranta, Professor; and Lauri Pesonen, Professor, Meteorology by Noora Korhonen, student; Sami Niemelä, Assistant; Kimmo Ruosteenoja, Senior Assistant; and Hannu Savijärvi, Professor, and Astronomy by Lauri Jetsu, Docent; Peter Johansson, MSc; and Kalevi Mattila, Professor.

I The sub-programmes of Physics, Physics teacher and Theoretical physics

  1. Planning, aims and content of education

A. Educational mission and the aims of the degrees
Under- and postgraduate education in Physics is offered in two disciplines: Physics and Theoretical physics. The Physics teacher education follows a separate path after the second year of studies. Education in the three sub-programmes aims to
* Develop experts capable of independently developing and evaluating new information in their field

* Meet society’s needs as indicated by research and feedback received from working life

* Raise Finnish skills in Mathematics and the Natural Sciences to a high level on an international scale

in accordance with the goals of the country’s government programme

* Implement measures that are in line with the University’s strategy and that aim to develop an

atmosphere which inspires high-quality learning and teaching

* Increase the number of undergraduate degrees as agreed with the Faculty.
The education for Physics teachers also needs to take into consideration the needs of schools and subject didactics.
Education in Physics provides the skills to understand and promote the fast development of information and technology in modern society. It also offers comprehensive and versatile skills to apply Physics in various fields. This can be seen in the good employment situation of physicists both in professions directly corresponding to their education as well as in other jobs. Since the labour market could currently employ more physicists than are available, no risk of excess numbers of physics graduates is in sight.
B. Influence of the aims on the degree structure and degree requirements

The degree structure offers the basic education necessary for physicists, based on which students specialise during the two last years of studies in accordance with the goals of their specialisation areas. However, the choice between general physics and theoretical physics introduces variation into the basic education due to the different emphasis that the two paths place on formalism and experimental work. As a part of specialisation, students write their theses on topics related to the work of a research group. This provides students with the opportunity to obtain a wider picture of their special field as members of a research community. Students studying to become teachers usually write their theses on topics related to the teaching of Physics, based on the latest research.

The Department also offers extensive minor subject teaching in Physics, Theoretical physics and Physics teacher studies. Part of these studies is designed jointly with other exact sciences. Cooperation with the Biosciences is also being discussed. The Department arranges courses in the basics of Mathematics and Computer Science, which are needed in the studies of Physics. Theoretical physics, for example, offers physicists and other natural scientists sufficient general and practical skills in its courses on Mathematical Methods.
The degree requirements and curriculum are prepared in the Development working group for teaching, which also has student representation. Preparations use feedback from graduates and proposals made by students. Physicists that have left the Department and moved into working life are also used as teachers in special fields (IT, Medical physics).
The Physics teacher degree includes studies in subject didactics and a teacher training period arranged by the Department of Teacher Education. The Department offers a special 20-credit study module in educational physics, which has been successfully used in the continuing education for teachers (LUMA). The studies for teacher trainees are designed jointly by the Department of Physics and the Department of Teacher Education. The education offers teacher qualifications for various educational levels.
2. Practical organisation of education

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