Spending a summer working with a professor and other students can be very helpful for deciding on whether or not you would like to go to graduate school, and if you are already sure of your desire to apply to grad school, then such experiences are helpful for determining what your research interest might be as well as developing a better relationship with a professor who may write you a letter recommendation.
The most important step in performing summer research is finding a professor or program that is willing to take you on. If you do not need any external source of funding, then simply emailing professors at McGill and asking if you would like to work (for free) with them for the summer will usually suffice. However, this is usually not the case, as most people need funding to work during the summer. Canadian citizens have NSERC opportunities, which are incredibly competitive and fund you comfortably for four months of full-time research. Non-Canadian citizens, however, are not eligible for NSERC opportunities, so they must look for other resources for funding to do summer research.
If you are interested in doing summer research in Montreal and you are not a Canadian citizen, then there are two programs worth applying to. The first one is McGill's SURA award. Most of the information is available on the website itself, but essentially you are given a generous stipend for 16 weeks of summer research with a pre-approved professor. This award is very competitive and usually given to the very top cohort of students in the department. Funding for this program is from McGill, and in recent years has been slashed considerably (I believe there were 4-5 of these awarded a few years ago; that number is now down to 1 or 2 maximum). It is still worth applying regardless. Applications are usually due in the beginning of the winter semester, but check to make sure.
The second Montreal-based summer research funding opportunity is from the ISM (Institut des sciences mathematiques). The ISM is a consortium of the math departments from all Montreal-based universities (English- and French-language). Most information is available on the website. The ISM award varies between 2-4 months long at a value of $1250 per month (less than SURA and NSERC by a fair amount). For the ISM, you generally work with a postdoc and possibly a professor from McGill, as opposed to just working with a professor for NSERC and SURA. A few are awarded each year, and I suggest applying to both ISM and SURA if you are an international student looking for funding in Montreal. Applications are usually due in the beginning of the winter semester, but check to make sure.
(usually just for American citizens, although a few programs below exist for internationals.)
Finally, there are many opportunities for American citizens to get funded for research in the summer at a university in the States. All of these opportunities are through the National Science Foundation (NSF)'s REU program. REU stands for Research Experience for Undergraduates. The REU programs differ significantly in aim and practice from NSERCs, SURAs and ISM awards. The NSERC/SURA/ISM programs are very independent: most of the time you work on your own reading a textbook and working through proofs / problems, and meet with a professor once a week or so to go over the work you have done and any questions that came up during your independent work, and this is more-or-less how the summer goes for the first few weeks and/or months, and then you will attempt to work on some open problems. The REU programs, however, are more intense and intended to give you a thorough introduction to what graduate school in mathematics and research in mathematics is like. The REU programs are generally quite short (8-10 weeks is usual, compared to 12-16 for NSERC/etc), but very fast paced for the short amount of time you are there. You are generally assigned to work with a professor in groups of 1-5 students, and the students are assigned a specific problem to work on and attempt to produce new results in this area. It is not unusual at all for there to be a publication resulting in the work from an REU. The REU programs take place at most research-oriented universities and state schools as well as liberal arts colleges across the country. The only requirement to apply is that you are an American citizen (although there are a select few, such as UCLA's, that do allow international students to apply as well). Your traveling expenses to whatever program you apply to are generally fully covered, so that if you are based in Virginia but are accepted for a program in California, your flight costs will be covered. Stipends generally range from \$2000-4500, but this depends on the program. Residence is usually provided, or otherwise the stipend is large enough so that you have an income of about \$2500 after paying rent for 8 weeks.
There is a huge variation in the structure of REUs from program to program, and so the above description is based on my research of the many REU programs that I looked at before applying. I applied to about 8 REU programs across the country, and I have heard of people applying to as few as 1 and as many as 12. Just as for university, if you are accepted to many programs you can turn them down if you prefer one or another. Each year, the NSF provides a list of all the REU programs that are funded for the year, with a short description of the area of research the REU is geared towards, and a link to the REU website. The REU website will have all of the information on funding as well as the exact project that students will work on. I suggest looking through the programs on the list and checking out which ones you are interested in and applying to 5-8 programs. See the links below for the master list of REUs from the NSF as well as some example REU programs. Be sure to re-check the list of programs before applying; some of the programs listed may not exist in the next round. I would also suggest looking at the Computer Science and Physics REUs if you are interested in these disciplines as well.
Here are some helpful links for all of the above described.
The NSERC Undergraduate Student Research Awards (USRA) in Universities program is meant to stimulate interest in research in the natural sciences and engineering, and the pursuit of research careers in these fields. Recipients engage in a research and development activity under the supervision of a professor holding an NSERC grant. It is an opportunity to gain research experience in an academic setting, while receiving financial support for summer 2012. Value and tenure
Duration: 16 consecutive weeks on a full-time basis, in Summer 2013
Value: \$4,500 from NSERC + minimum of \$1,125 from the supervisor.
You must be a Canadian citizen or permanent resident of Canada. You must be registered at the time you apply in a bachelor's degree program. You may hold a maximum of three USRAs throughout your university career. There are other requirements too: please consult the USRA information on NSERC's website. Individual departments may set higher application cutoffs than NSERC's minimum requirements, and this award application process is competitive.
How to apply; forms; student deadlines
The checklist (required), forms, and instructions are available via the Graduate and Postdoctoral Studies webpage for NSERC USRA.
Each Faculty of Science unit has a quota of available awards, and has its own selection process and deadlines. Apply through the academic unit where you wish to hold your award (i.e., your proposed supervisor's school or department, not necessarily your own unit). Students from other universities may also apply
Here is NSERC USRA contact information. *NSERC USRA
The applications are to handed in to Mrs. Angela White, by February 22nd.
International students should download the forms for NSERC USRA and fill the form before submitting it to the department.
Undergraduate Summer Scholarships:
Undergraduate Research Supervised by Postdoctoral Fellows
Funded by the ISM and the Centre de recherches mathématiques (CRM), the Undergraduate Summer Scholarships give undergraduate students the opportunity to acquire research experience in a university or industrial environment while offering postdoctoral fellows the chance to gain experience in research supervision. Description : ISM Summer scholarships are offered to undergraduate students in mathematics and statistics who are registered in one of the ISM member universities. They allow selected candidates to carry out research under the supervision of a Postdoctoral Fellow affiliated with one of the ISM member universities.
Duration of the scholarship: 2 to 4 months
Salary: $1,250 per month for the duration of the scholarship
Financing :The combined CRM-ISM contribution is $625 per month for the duration of the scholarship. The remainder of the financing is provided by other research funds (individual researchers, research laboratories, etc.).
Deadline: The deadline for submitting an application to the ISM office is March 18, 2013.
Required documents: The following documents should be submitted to the ISM:
Candidates are encouraged, but not required, to provide a second letter of recommendation.
Other conditions :
Exceptionnally, a professor who does not have an NSERC grant may supervise a student.