Research support guide

The instructions are written from the point of view of PhD students and post docs working on inverse problems.

Authors: Matti Lassas and Samuli Siltanen.

• Terry Tao's pages on career advice.
• Terry Tao's pages on how to write papers.
• How to succeed in graduate studies - a good (American) tutorial to PhD studies.
• Survival in the Academy. The page contains The assistant professor's guide to the galaxy.
• Essay: Ten lessons I wish I had been taught (by G.-C. Rota).
• Advice for new Ph.D.s. The web page of AMS.
• AMS web page on Careers and Employment.
• A guide book for post-docs and new faculty members (the book is concentrated on biosciences but many instructions are perfectly as valid in math).
• The Chronicle of Higher Education. Especially popular in the Math. Depts. of the US. Contains articles on the different aspects of the life as an academic.

• IPIA Job Market - Pages of Inverse Problems International Association
• Mathematics Jobs Wiki.
• Job applying pages of the AMS.
  In the Post Doc phase it is advisable to consider the possibility of a long term stay abroad. Note that in the US the Post Doc system is more developed than in Finland; in the US universities, a typical researcher's contract is not longer than a few years. A vast majority of the young American scientists do several Post Docs before settling down for a tenure track. However, you ought not apply just any position abroad; it is important that the university is of high quality and/or has significant research activity in your field.
• www.mathjobs.org - Portal of AMS to apply and advertice jobs in mathematics.
• AMS Website Employment Information in the Mathematical Sciences (EIMS)
• Timeline of job search in US - How to apply for a Post Doc position in the US.
• It's April and I Still Don't Have a Job! The Panicked Scientist's Guide to Accelerated Job Searches (by Peter Fiske). The text contains a guide on organizing the applying of jobs.
• Marie Curie funds. A possible way to get to a Post Doc position abroad is to obtain EU funding. Should it so happen, the host institution must apply for a "Marie Curie" position for the visitor.
• Euro-Math-Job.
• Academic Jobs EU has also a section on Mathematics.
• Open positons in nordic countries
• jobs.ac.uk
• www.math-jobs.com

• The essay classic of Halmos on producing a good presentation.
• A short (and more modern) text on producing a good presentation.
• The guide recommended by the AMS on writing a resumé. Consider letting others review your CV to get suggestions for improvement.
• A Chronicle article on creating a webpage. Note that the evaluators/referees of your funding/job applications as well as research manuscripts will visit your website. Having your professional website recommended.

• Examples of Career profiles in Mathematics. A webpage of Mathematical Association of America.
• SIAM career page.
• An aricle in the Solmu-magazine (finnish) on Finnish mathematicians.

• Open positions in mathematics in Finland.
• A newsletter on grants. For mathematicians (and inversionists) good options include Aaltonen, Väisälä, Wihuni, Kulttuurirahasto, Magnus Ehrnrooth, Tekniikan edistämissäätiö (the foundation for advance in techology), Instrumentariumin säätiö (the foundation of Instrumentarium), the foundations of your university, the grants of the Finnish Ministry of National Security.
• Academy of Finland. Applicable are Post Doc positions (groups as well as individual scientists are permitted; start applying about 3 to 4 after dissertation), Academy researcher positions (applicable before obtaining a professorship), grants for researching abroad (that is funding an international research visit), funding for returning researcher (easy to obtain after a long stay abroad). NOTE: PhD student are not qualified to apply for setting up a graduate school (some have tried this!).
• TEKES For a Post Doc, it is worthwhile to occasionally lay an eye on new research programs. TEKES mainly provides funding for co-operation with private sector parties.
• It is recommended to read Samuli's guide on writing a funding application. It is also advisable to ask more experienced colleagues to let you read their past applications. For example FIPS and Academy applications typically contain the accumulated insight from several researcher generations. Let others read your application, and ask them to provide comments.

The aim of PhD studies, among completing the thesis, is to develop you into a professional scientist. The goal is best achieved by participating seminars and conferences, discussing about mathematics, and absorbing the "folklore" of the field of research. In practice this means:

• Typically the graduate studies are funded by: a doctoral school program, a teaching position/substitution or other employment in an institution, or a research grant (applied e.g. from a foundation). The funding situation should be discussed with the instructor right in the beginning of graduate studies.
• One should find out what seminars the group members attend, and attend them too. In the beginning, understanding the seminar talks is challenging or impossible for almost everyone. This doesn't indicate the newcomer is brainless. After few years of experience the understanding will gradually increase. It is also instructive to visit other group's seminar once in a while.
• Attending conferences (whenever financially possible) is important. Usually there is travel funds for at least domestic happenings so those can be easily attended. It is good to practice the conference talks a few times either alone or in front of a small audience. The performance can be improved by asking the training audience's suggestions for changes. When giving a talk, it is important not to exceed the predefined time limit - it is better to finish early than late. Matching the time limit is one of the reasons for rehearsing the talk.
• Discussing as often as possible with other scientists is recommendable. In this way one will hear about upcoming events and news, and will integrate well within the research group.

Writing of the PhD thesis is a demanding stage of life in many respects. Below are some ways for avoiding troubled times:

• It is risky for the student to independently choose her/his subject. Such subject is likely to be too difficult. It is better to discuss with the instructor about the choice of subject. Do not hesitate to shed light on your thoughts and opinions to get the subject as motivating as possible.
• When stuck in the studies/research, do not hesitate to ask the more experienced colleagues for advice. If something is difficult for you, it has likely been difficult for someone else too.
• It is normal to feel that the research is not progressing. Stuck research should be considered as a part of the job. Such situation it improve uncertainty tolerance which is an important skill of a succesful scientist. When stuck, it is advisable to divide the problem into subtasks and solve (at least some of) them. If the research is stuck after persistent work, the research problem can often be reformulated together with the instructor.
• It is very important to find one's own working methods during the graduate studies, or at latest, as a post doc. To some, perfectionism may be a threat: too much fine tuning may delay the publication of ready works. Some others focus on too many different problems which tend to end up unfinished. A good way of working lies in the "golden mean": it is good to choose a few problems carefully, concentrate on them, and publish the results after careful inspection (even if they wouldn't solve all your research problems exhaustively).
• The well-being of group members is important to the instructors. Problems, or life change issues that affect your can be discussed with the instructor. Many problems can be resolved, or the workload can be adjusted accordingly.
• In summary, troubles can be avoided by actively communicating with others. It is good to remember that the challenges during the PhD studies are the ones that make proffessional scientists. Afterwards, it typically feels that one learned during the PhD studies a lot more than expected about science as well as about the scientific community.

After dissertation, the nature of application of funding will change. Whereas the instructor mostly takes care of the funding during the PhD studies, a post doc must learn to get funded independently. To this end, the following actions should be taken close to the end of PhD studies:

• One should decide whether to purse an academic career, or to move on to the industry. If one aims at the industry, it should be done soon after dissertation. Exceptions include the TEKES-style industrial projects that provide valuable experience on applied sciences (especially for pure mathematicians) and may create relations to companies.

In case one decides to pursue an academic career:

• One should discuss with the instructor well in advance in order to survey different possibilities. This should be done as early as possible, before talking to with the head of the department
• The plans should then be discussed with the head of the department. One should find out whether and how long lasting job opportunities there are at the department. This usually requires flexibility from you but it is important to try to achieve a clear "contract". It is good to do this as soon as possible however at latest during the preliminary examination of the PhD thesis
• One ought begin applying for funding. The rule of thumb is that the average ratio of succesful and unsuccesful applications is one-to-five. Don't let the negative decisions to discourage you since rejected applications are part of every researcher's life.
• A post doc should figure out as clearly as possible his/her research topic(s) - is it pure mathematics, does one want to collaborate with the industry, or perhaps something in between? A long term goal - finding own research area and setting up a research group - should be kept in mind.
• Collaboration and learning through it during the post doc phase is extremely important. International visits are of first-rate importance. If your current life situation prohibits you from long term visiting abroad, you must act actively to form a relation network in other ways (for example doing several short visits and attending conferences). In order to continue a research career it is essential to go abroad in near future, at least for a semester but rather for a longer time. When selecting the post doc position, one should balance in between two objectives: On one hand the target university should renowned and on the other hand there would be good to be a collaborator who has a lot of time for collaboration. Often these objectives contradict each other, and balance has to be found. Before heading abroad it is advisable to find out about adjusting to the foreign culture and related phenomena.
• The most important duty of a post doc is to concentrate on research. Developing teaching methods will become important only later on, in about 5 years. An exception consists of such post docs that aim at teaching positions. In some departments, achievements in thesis instruction are well appreciated. If you stay in such a department, reasonable participation in instructing students could be desirable - after all it does give experience on leading a research group.
• Where to find good new research problems? This question bothers many fresh PhD's. Fortunately, when collaborating with more experienced researchers they usually propose new problems. In addition, typically new problems arise on the basis of your thesis. These problems can be studied after the finishing the thesis. When your knowledge of your field of research expands, the multitude of new topic will become more problematic than the lack of them. This is one of the reasons why collaboration is important - working with an expert of a slightly differing field will help in understanding which problems are already solved. Often the high number of unsolved questions can be surprising. Due to the above and other reasons the post doc phase is usually perceived easier as writing the thesis: one is getting more and more familiar with the field because results already exist - one doesn't have to doubt anymore "do I have the quality of a scientist".
• When conducting research it is important to publish the results in as high quality journals as possible. Journal suggestions can be asked from more experienced researchers. A good, although skewed, indicator is the impact factor. In particular, the Institute of Science Impact is a well-known impact factor measurer. For example, Aalto University and University of Helsinki have the right to use the www-page of ISI where the list of impact factors is found. It is noteworthy that some impact factors (which measure only the short term impact of the published science) can give a wrong picture of some journals. The 20 years impact indicates some of the traditional prestigious journals. To keep track of the research development it is good to monitor the field in MathSciNet, and to browse preprints in ArXiv. Also attending conferences, summer schools, and seminars is beneficial. Moreover, it is advisable to register to Inverse Problems Network (IPNET) and follow the newsletter.

• The guide for a mathematician who aims to work at the industry (in finnish) is recommended for everyone with such plans.
• According to reports of The Academy of Finland the bulletins of the Ministry of Education several ministries, agencies and other civil service offices such as VTT (Technical Research Centre of Finland), The Finnish Forest Research Institute, The Finnish Marine Research Institute are interested in hiring PhD's. Thus, it is worth keeping an eye open for public sector jobs.
• For a researcher who decides to head from university to other duties, teaching in different levels is an option. Many Phd's and licenciates have worked as teachers both in universities of applied sciences as well as in high schools. Their contribution to the society has been significant and diverse. For example, some docents have been giving university level courses alongside with teaching in high school.

This is the end of our guide. If you know other sources of funding, or other suitable sources of information for inverse problems mathematicians, we kindly ask you to inform us so we can update the page.

Although some of the above-described situations seem challenging, keep in mind that experience on applying of funding as well as doing research will be accumulating. When time goes on, even the youngest graduate student can eventually develop into a research group leader. Supporting one another and providing information one's success will turn out to be a benefit for all. Let us keep on working together for a common goal in the future to make inverse problems research glow even brighter than before in the broad field of Finnish sciences.