Summer Math Opportunities

What could be more fantastic than the one-two combination of excellent math skills and excellent writing skills? Be sure to check out the English Department's offerings for the spring and summer terms.
The Walking Club will continue to meet during the summer. Join the Walking Club's discord server for updates about meeting time and location. For now, it meets at the Church Street entrance to the Math Atrium at 6:05 am with a return time of 7:30 am every weekday. On Sundays, they meet at 6:30 and/or 8:30 am at the Sweetwaters in Kerrytown. On Tuesday evenings they walk from 7:30 to 9 PM leaving from the Church Street Math Atrium Doors.
REU opportunity in Puerto Rico! Spend June and July researching Combinatorics and Coding Theory in the Tropics. Wow!
The Southeast Center for Mathematics and Biology at Georgia Tech will run a 2023 Summer Undergraduate Workshop, July 31- August 4, on the topic: Cell to Datum: How We Interpret Biological Structures Using Mathematics. Apply here soon.
Budapest Semester in Mathematics Education has extended the application deadline for their summer program to April 17.
Asian Languages and Cultures is offering spring/summer Korean, Chinese, and Japanese classes
The K-20 Programs team in Engineering's Office of Culture, Community and Equity is hiring staff to support their high school summer engineering programs. There are a number of different positions open, and you may apply here. If you have any questions, please contact Eric Aiken.
Michigan's Comprehensive Studies Program (CSP) is looking to hire Summer Bridge Scholars Program Course Assistants. The application form may be found here.
In response to the record number of applications to their summer 2023 8-week work-based experiential education programs, City Internships has created additional availability in their core destinations. Interested students are encouraged to apply here.
This summer the Polymath program will run between June 20 - August 13, taking place entirely online. Each participant can decide what they want their level of involvement in the program to be. Applications are due April 1.
Have you scored an internship for the summer term, but really need some cash to help make ends meet? The LSA Internship Scholarship for current students provides scholarships for spring and summer terms to qualified LSA students who have demonstrated financial need as determined by the Office of Financial Aid.
The MaCSS Scholars Program is hiring an undergraduate assistant for their summer institute (May 22 - June 16). They are looking for a student with strong coding chops, experience with mathematical proof, and teaching or tutoring experience to join their instructional team. The participants in the summer institute are math, statistics, and computer science majors at UM in the early stages of their major coursework; many are transfer students. The dates are May 22 - June 16. See way more details in their job description and application form. Please submit your application by March 25.
The Summer Institute in Survey Research Techniques Diversity Fellowship is a two-week program (July 10-21, 2023) geared toward upper-level undergraduates offered through the 2023 Summer Institute for Survey Research Techniques. They will hold information session on Monday, March 20, 2023 from 3-4pm. Advanced registration is required.
UNC Charlotte is hosting a math REU. The application is open from March 1-March 15 and details may be found at https://Charlottesville/math-research/.
Willis Towers Watson (WTW) has full time and internship opportunities for Mathematics, Statistics, or Economics majors. Look here for postings.
Join the Math Corps at U(M)! The Math Corps helps to make the world a better place. It is a free summer camp for middle school students and high school mentors from the Ypsilanti area. We are looking to hire some college students to serve as College Instructors or College Assistants during our camp, which will run July 11 - Aug 12, 2022 (in person!). More info can be found in the application - apply by April 15!! Please email Sarah Koch with any questions.
The Society for Industrial and Applied Mathematics (SIAM) is accepting applications for the SIAM-Simons Undergraduate Summer Research Program, which will provide research, networking, and mentorship opportunities to U.S. students from underrepresented groups.
The annual Wolfram Summer School will be held June 25–July 12 at Bentley University in Waltham, Massachusetts, USA. Students, educators, researchers and entrepreneurs alike will benefit from spending three weeks working closely on a project with senior developers and Stephen Wolfram himself. Apply here.
KAIST Advanced Institute for Science-X(KAI-X) will host a Summer KAI-X Research Internship Program! Third and fourth year students interested in fields including Physics, Chemistry, Mathematics, Biology, and Medical Science are invited to participate in this program.
Sophomores: the D.E. Shaw Discovery and Latitude Fellowships for 2023 will be taking place in New York City this May. Participants will have the opportunity to apply their analytical skills in discussions with investment professionals, attend lectures given by senior leaders and outside speakers, and interact with a cross-section of D.E. Shaw's employees. Participants will receive a stipend, accommodations, and travel to and from New York City. Apply by March 17.
This summer the Polymath program will run between June 20 - August 13, taking place entirely online. Each participant can decide what they want their level of involvement in the program to be.
The Center for Computation & Technology at Louisiana State University is accepting applications for its 2023 REU Program in Computational Sciences.
UNC Charlotte is hosting a math REU program. The application is open from February 1 to March 15 and details can be found here.
The Honors Program hires Academic Peer Advisors every summer. Check out this page for more information.
The International Center also hires Academic Peer Advisors for the summer. Here are last year's advisors. I'm not sure of their hiring process, so I suggest you contact the International Center if interested serving as a peer advisor.
Google announces its 2023 Summer of Code. This is a global, online program focused on bringing new contributors into open source software development. Contributors work with an open source organization on a 12 (or more!) week programming project under the guidance of mentors.
Professor Ryan T. White of the Department of Mathematical Sciences at Florida Institute of Technology (FIT) in Melbourne, Florida would like for you to apply for their REU on Statistical Models With Applications To Geoscience. There are some cool projects here.
U(M) Mathematics alum Ruthi Hortsch reports that BEAM is hiring counselors and teaching assistants for the summer. At BEAM you will become part of a close-knit community, doing all kinds of interesting and engaging math with kids who are realizing they love math. BEAM is hiring nationally for their residential programs (with transportation, housing, and food provided). Take a look at their summer hiring website for more information.
Join the Math Corps at U(M)! The Math Corps helps to make the world a better place. It is a free summer camp for middle school students and high school mentors from the Ypsilanti area. We are looking to hire some college students to serve as College Instructors or College Assistants during our camp, which will run July 10 - Aug 11, 2023. More info can be found in the application - apply by April 14!! Please email Sarah Koch with any questions.
The Institute for Social Research's will again run its Summer Institute program on Survey Research Techniques.
I've been asked to remind you: The 2023 Undergraduate Big Data Summer Institute will run from June 20 to July 28. The application is now open and they are being evaluated on a rolling basis.
The University of Nebraska-Lincoln really wants you to apply to their Summer Research Program. They offer many different opportunities.
Have you scored an internship for the spring and summer terms, but really need some cash to help make ends meet? The LSA Internship Scholarship for current students provides scholarships for spring and summer terms to qualified LSA students.
Have you scored an internship in Europe, but need some cash to make it happen? Then check out the Summer Grants for Research and Internships in Europe and Eurasia.
Are you a junior considering pursuing a graduate degree in IT, data analytics, or cyber security? Carnegie Mellon University's IT Lab: Summer Security Intensive (scroll down!) is a paid summer fellowship offering courses in security policy and technology implementation.
Breakthrough Collaborative has summer teaching internships at many locations across the United States.
Reminder: The Michigan REU continues to accept applications. Applications are due tomorrow: February 3.
Reminder: The Michigan Math and Science Scholars camp is still looking for summer counselors; this is an excellent way to support yourself and stay in beautiful Ann Arbor. Applications are now being accepted.
I've been asked to remind you that next May the Institute for Advanced Study (think Einstein) is hosting a Women and Mathematics program on Patterns in Integers: dynamical and number theoretic approaches.
The Edge Program invites women who will be attending math graduate school in the fall to join them in Providence for four weeks this summer. The goal of the program is to strengthen the ability of women students to successfully complete graduate programs in the mathematical sciences, with particular emphasis on women from underrepresented groups. Applications are due February 15.
The REU Modern topics in pure and applied mathematics will be held at the University of Maryland in Summers 2023 and 2024. Application Deadline: February 20.
The Michigan REU continues to accept applications. Applications are due February 3.
The U.S. Food and Drug Administration (FDA) has a whole slew of summer research opportunities. Check them out here. I think you apply for them here.
Are you interested in the social, behavioral, and economic sciences? Then perhaps the 2023 Summer Research Initiative (SRI) at the University of Maryland, College Park is for you.
I've been asked to remind you that the Institute for Pure and Applied Mathematics (IPAM) at UCLA runs the Research in Industrial Projects for Students (RIPS) program for students, including international students, in math and related disciplines who wish to work in teams on real world research projects proposed by a sponsor from industry or a national lab.
Sage Corps thought you might be interested in its summer internship program that places interns in a tech startup abroad.
Columbia Business School is seeking outstanding applicants for its 2023 Summer Research Internship program. They have had good luck with students of math from Michigan. The highly selective program provides an intellectually stimulating environment and exposes students to the world of business research.
If you are in the Honors Program, then please note that you may apply for an Honors Summer 2023 Fellowship until February 17.
Carnegie Melon is hosting a Summer Undergraduate Applied Mathematics Institute.
The 2023 Undergraduate Big Data Summer Institute will run from June 19 to July 28. The application is now open and they are being evaluated on a rolling basis. Math students who participated (and got paid!) in the past report that they enjoyed the experience.
Wolfram, the developer of Mathematica, will host a three week summer school from June 25 to July 15. Participants will learn how to apply Wolfram technology and work on individual research projects.
Interested in business research? The Columbia Business School is accepting applications for its Summer Research Internship program. Apply by March 1.
The Philosophy Department at Carnegie Mellon University is hosting a Summer School in Logic and Formal Epistemology. Tuition and housing are provided to participating students.
The Michigan Math and Science Scholars camp is still looking for summer counselors; this is an excellent way to support yourself and stay in beautiful Ann Arbor. Applications are now being accepted.
The Summer Institute for Training in Biostatistics may be running programs at different campuses in 2023. For sure, they are running one at Boston University. Apply soon or risk being overlooked.
The Mathematical Sciences Research Institute (MSRI) in Berkeley, CA is hosting a summer program for undergraduate students on the topic of Topological Data Analysis. While there, you could take a Math T-shirt photo with the beautiful Helaman Ferguson sculpture, The Eightfold Way.
The Michigan REU continues to accept applications. Applications are due February 3.
The Institute for Pure and Applied Mathematics (IPAM) at UCLA runs the Research in Industrial Projects for Students (RIPS) program for students, including international students, in math and related disciplines who wish to work in teams on real world research projects proposed by a sponsor from industry or a national lab. They have sites in LA and Singapore.
Paid 10-week internship at MSU: Research areas may include: computational chemistry, computational education research, computational genomics, computational neuroscience, computational mathematics, machine learning, climate modeling, remote sensing and image processing. Housing and subsistence support provided. Additionally, participants receive a stipend.
Applications to the Program for Research in Markets and Organizations (PRIMO), a 10-week summer research opportunity with faculty at Harvard Business School, are now open!
Applications to serve as a counselor at various math camps are due beginning now. For example:
Notre Dame's Center for Mathematics will hold a week long school on Rationality and Hyperbolicty from June 12to June 16. The Program is pitched at beginners.
The Summer Undergraduate Mathematics and Statistics Accelerator (SUMSA) is an eight week mathematics and statistics bootcamp for undergraduates which will take place June 12-August 4, 2023. The program’s aim is to help prepare students for the rigors of graduate school through lecture series and problem sessions taught by experienced postdocs and advanced graduate students from the University of Chicago. It will cover core material in linear algebra, advanced calculus, metric spaces, probability, statistical modeling, and data science.
Microsoft's Explore Microsoft summer internship is for first and second year students.
The Perimeter Institute for Theoretical Physics is now accepting applications for the Perimeter Scholars International Start (PSI Start) program. This is for students intending to start PhD work in 2024 in Physics.
The Michigan REU is now accepting applications.
The Fields Undergraduate Summer Research Program welcomes carefully selected undergraduate students from around the world for a rich mathematical research experience in July and August.
We have no Math T-shirt pictures from the Michigan of the East. You could change this by attending the Summer Program in Quantitative Sciences at the Harvard School of Public Health.
San Diego State University Summer 2023 Mathematics Research Experiences for Undergraduates will run June 11 -- August 5.
MSU's Advanced Computational Research Experience for Students (ACRES) is a paid 10-week internship in areas including computational chemistry, bioinformatics, computational biology, astrophysics, topological data analysis, machine learning, climate science, remote sensing and image processing.
The University of Nebraska-Lincoln Summer Research Program encourages you to consider its wide-ranging programs.
Along with the lists of REUs mentioned in previous missives (e.g. at the AMS and at the NSF), you might find this site useful while researching potential REUs. It includes brief descriptions and information about dates (like application deadlines).
Brown University is a great location for Math T-shirt pictures. The Undergraduate Summer Research Program at Brown University on Mathematical Modeling of DNA Self-Assembly is designed for a select group of 18-22 undergraduate scholars.
SIAM has a list of contact information for internships, the ASA maintains a very long list of internships in the statistical sciences, and the AMS maintains a listing of internships and co-ops.
A comprehensive list of mathematical REU programs in the U.S. may be found at this AMS web page. The NSF maintains a listing of the REUs it funds, and there are many in areas other than math.
There are various internships with the United States government available, but they don't make them easy to find. Go here and read the section titled "How do I know a job is open to Students & recent graduates?". Then follow instructions. Also try here.
And here is yet another listing of research/internship opportunities.
Professor Ryan T. White of the Department of Mathematical Sciences at Florida Institute of Technology (FIT) in Melbourne, Florida would like for you to apply for their REU on Statistical Models With Applications To Geoscience. There are some cool projects here.
The Edge Program invites women who will be attending math graduate school in the fall to join them for four weeks this summer. The goal of the program is to strengthen the ability of women students to successfully complete graduate programs in the mathematical sciences, with particular emphasis on women from underrepresented groups. Applications are due February 15.
The electronic Computational Homotopy Theory (eCHT) online research community is sponsoring an online REU in Summer 2023. One of the REU leaders is the amazing Kyle Ormsby.
The Perimeter Institute for Theoretical Physics is now accepting applications for the Perimeter Scholars International Start (PSI Start) program. This is for students intending to start PhD work in 2024 in Physics.
The Michigan REU is now accepting applications.
MSRI in Berkeley is a math center with an amazing view. If you'd like to visit, then check out their 2023 program on topological data analysis.
Applications to serve as a counselor at various math camps are due beginning in January. For example, the following camps need counselors:
The Weizmann Institute of Science's annual Kinetic-Getz International Science School accepts outstanding undergraduate students to participate in summer research projects in mathematics and computer science, physics, chemistry and life sciences. It is an enrichment program designated for undergraduate students from all over the world, who are majoring in the Sciences, to experience science first hand by becoming part of a research group at the Weizmann Institute.
If you are in honors, then check out (a) the Honors Summer Fellows program and (b) their grant program to support current research projects.
The Scripps Institution of Oceanography in La Jolla, California wants students of mathematics to know about its ten-week summer internship opportunity in the Marine Physical Laboratory.
The David Harold Blackwell Summer Research Institute at UC Berkeley is a six-week competitive summer activity designed to provide research experience to talented undergraduate students. Students will conduct research in Applied Probability, Analysis, or Theoretical Computer Science, under the supervision of faculty members who are experts in these areas.
There are various internships with the United States government available, but they don't make them easy to find. Go here and read the section titled "How do I know a job is open to Students & recent graduates?". Then follow instructions. Also try here.
The Fields Undergraduate Summer Research Program welcomes carefully selected undergraduate students from around the world for a rich mathematical research experience in July and August.
Next May the Institute for Advanced Study (think Einstein) is hosting a Women and Mathematics program on Patterns in Integers: dynamical and number theoretic approaches.
Park City is hosting an undergraduate summer school on the topic of Quantum Computation. Apply by January 31.
The University of Nebraska-Lincoln wants you to apply to their Summer Research Program. They offer many different opportunities.
A comprehensive list of mathematical REU programs in the U.S. may be found at this AMS web page.
The NSF maintains a listing of the REUs it funds.
Here is another listing of research opportunities.
And here is yet another listing of research/internship opportunities.
The Department of Homeland Security sponsors a summer internship program for students majoring in homeland security related science, technology, engineering and mathematics disciplines.
The Michigan REU will be accepting applications beginning November 25.
NYU's Pathways into Quantitative Aging Research Summer Program is now accepting applications.
Southeast Toyota Finance is looking to hire a summer Data Science Intern.
The University of Minnesota - Twin Cities wants you to join their REU in astronomy and physics. Details are here.
The Florida Institute of Technology is hosting an REU on statistical modeling with applications to geoscience. Applications for Summer 2023 are open until March 10, 2023.
The Institute for Pure and Applied Mathematics (IPAM) at UCLA runs the Research in Industrial Projects for Students (RIPS) program for students, including international students, in math and related disciplines who wish to work in teams on real world research projects proposed by a sponsor from industry or a national lab. The deadline for applications is February 13.
Memorial Sloan Kettering Cancer Center, Cornell University, and Weill Cornell Medicine would like for you to know that applications will soon be accepted for the 2023 computational biology summer program sponsored by an R25 grant from the NCI and the Tri-Institutional PhD Program in Computational Biology & Medicine. The application is now open.
U(M)'s Center for South Asian Studies (CSAS) is welcoming applications for its 2023 Summer in South Asia Fellowship. The fellowship provides $3,000. Students design their own program (volunteering with an NGO, doing an apprenticeship with a business, or pursue an independent project).
The Columbia Business School has been very pleased with the mathematics students who have participated in their summer internship programs, and would like to see more of you.
Blue Cross Blue Shield is hiring interns for summer 2023.
Data Glacier is looking to hire for their data science internships.
Looking for a paid STEM internship or research opportunity? Check out the Oak Ridge Institute for Science and Education (ORISE) listing.
The Department of Energy is now accepting applications for their summer internship programs.
Gotoco (www.go-to.co), set up by Oxford University students, provides English-speaking students with funded opportunities to participate in summer camps around the world, where they can work towards a TEFL certificate, make new friends, explore the world, and have a unique summer experience.
MERCK is looking to hire a summer data science intern.
Goldman Sachs is looking for current sophomores and juniors to apply for a summer analyst position. See here for more information.
Do you have a passion for biology and math? Then check out UCLA’s B.I.G. Summer Research Program in Genomics, Bioinformatics, and Systems Biology.
Point 72 Academy invites you to apply for their finance summer internship program.
Brown University is a great location for Math T-shirt pictures. The Undergraduate Summer Research Program at Brown University is designed for a select group of 18-22 undergraduate scholars.
NASA is another excellent place to take Math T-shirt photos. To learn about the many opportunities NASA has available, visit their OSSI NIFS page and click around to discover all the available opportunities.
City Internships would like for you to know that they have launched their application process for 2023 and beyond.
The Detroit Community-Engaged Research Program (DCERP) is a social justice focused fellowship program run by the University of Michigan Undergraduate Research Opportunity Program. In summer 2022, DCERP students will work full-time on research projects directed by Detroit non-profits that focus on community priorities such as environmental health, food security, early learning, youth development, human rights, public health, alternative energy, affordable housing and more! Applications are now being accepted! Visit https://myumi.ch/84dXWfor guidelines and to access the online application.
Memorial Sloan Kettering Cancer Center, Cornell University, and Weill Cornell Medicine would like for you to know that applications will soon be accepted for the 2023 computational biology summer program sponsored by an R25 grant from the NCI and the Tri-Institutional PhD Program in Computational Biology & Medicine. The application opens in early November.
StepStone Group is looking to hire Venture Capital Investments Summer Interns. Apply soon!
Hannover Re is looking to hire interns for next summer. Apply here; interviews will happen in late October/early November.
Jane Street is accepting applications for internships for next summer.
The Weizmann Institute of Science's annual Kinetic-Getz International Science School accepts outstanding undergraduate students from all over the world to participate in summer research projects in mathematics and computer science, physics, chemistry and life sciences. While it is not yet known if it will run in 2023, please keep it on your radar.
The NY Federal Reserve is now accepting applications for their Junior Analyst internships (you must be graduating in Winter 2023 or Spring 2024). Candidates should apply by November 1st.
Budapest Semesters in Mathematical Education (BSME) is a study abroad program in mathematics education. BSME participants explore the Hungarian pedagogy, in which a strong and explicit emphasis is placed on problem solving, mathematical creativity, and communication. BSME is accepting applications for the summer 2023 term. Be sure to apply through CGIS. More information here.
Girls Who Invest (GWI) is a 10-week summer intensive program which offers a tuition-free introduction to asset management, access to career development resources, and an incredible community of women and partner firms who are making an impact in finance. Apply here.
There are many internship opportunities at the National Security Agency. Applications are due around this time of year. This includes The Director's Summer Program.

Legendary Summer Math Opportunities

Information about Summer REUs

An REU (Research Experience for Undergraduates) is an excellent way to get some grit under your nails in mathematical research. Information about REUs around the country may be found at the NSF's web page; at this AMS web page; or at this SIAM page (scroll down to undergraduate). Note that deadlines fall in February and March. Also note that UCLA's RIPS (Research in Industrial Projects for Students) program is available to graduating seniors and foreign students attending US universities.

Here are some research programs that were brought to my attention in one way or another -- not all of them are on the AMS and NSF web pages discussed above:

UCLA's REU program is now accepting applications. They wanted me to let you know.
Los Alamos National Laboratories in New Mexico is sponsoring an undergraduate research program. It appears the application process closes January 10.
Michigan's REU is now accepting applications. Apply here.
The analysis and applied math groups at the University of Wisconsin are organizing an Analysis and Differential Equations REU this summer. Apply after January 27 and before February 17.
San Diego State University is pleased to invite applications to its Mathematics Research Experiences for Undergraduates which will run from June 16 to August 10. Projects in combinatorics and algebra, specifically group testing and Hadamard matrices, will be the subject of the summer.
Hope College is now accepting applications for its 8-week Mathematics Research Experiences for Undergraduates Program from June 3 to July 26, 2013. Hope College faculty members have a long history of REU success; so apply before February 22 if you are interested in one of their projects.
The Institute for Pure and Applied Mathematics (IPAM) at UCLA is running several programs that are designed to expose undergraduate students to an industrial research project that requires the application of mathematical principles to solve real-world problems:
- Research in Industrial Projects for Students (RIPS)-Hong Kong 2013 from June 9 to August 9, 2013; see their web page for application instructions.
- Research in Industrial Projects for Students (RIPS) 2013 from June 23 to August 23, 2013. This program is open to international students. Apply Online by February 12.
MIT's Lincoln Laboratory hires loads of undergraduate students into its summer research program.
Carnegie Mellon hosts a Summer Undergraduate Applied Mathematics Institute; applications due March 1.
The Rose Hulman REU would like for you to apply. Applications are due March 1.
North Carolina State sent me about a dozen e-mails about their REU; they must be proud.
Miami University (Oxford, Ohio) is hosting their Summer Undergraduate Mathematical Sciences Research Institute. They are particularly interested in having participants from traditionally underrepresented groups attend.
Brown University's Summer@ICERM Program will cover Geometry and Dynamics. Apply by February 6, 2013
(12/27: not yet for 1213) The University of Washington is again offering advanced undergraduates the opportunity to study inverse problems and PDEs. Deadline April 1.

(12/27: not yet for 1213) There is a program in dynamical systems to be held in Germany -- applications due March 31.
MIT's Lincoln Laboratory hires loads of undergraduate students into its summer research program.
Professor Jun Zhang from Psychology is interested in having advanced undergraduates work with him this summer to apply mathematics to cognitive and information science. If you are an expert in Algebra (Lattice theory, pseudo-complementation, relative complement, Stone lattice,Heyting algebra, intuitionist logic, etc.), Analysis (Frames, reproducing kernel, approximation theory, sampling, measure theory, l1-space (sparsity-inducing norm), Banach algebra, etc,),Geometry (Affine differential geometry, Kahler geometry, symplectic geometry, Lagrange submanifold, etc.) or Number Theory (valuation theory, p-adic analysis, ultrametric spaces, semi-ring, max-plus algebra, etc.), then please contact Professor Zhang immediately.
Los Alamos National Laboratories in New Mexico is sponsoring an undergraduate research program. It appears the application process closes around the beginning of March.
8 Summer Institutes for Training in Biostatistics will happen this summer. Statistics is quickly emerging as the thing to do (even in 2009, but more so now). Applications are due at the end of February.
Carnegie Mellon hosts a Summer Undergraduate Applied Mathematics Institute; applications due March 1.
NASA has internships and fellowships -- it looks like deadlines fall on March 1.
The Rose Hulman REU would like for you to apply. Applications are due February 24.
(12/27: not yet for 1213) The Michigan REU is now accepting applications. Applications are due March 18th at 4PM.
North Carolina State sent me about a dozen e-mails about their REU; they must be proud. (December 8)
Miami University (Oxford, Ohio) is hosting their Summer Undergraduate Mathematical Sciences Research Institute. They are particularly interested in having participants from traditionally underrepresented groups attend. (December 15)
Awesome! An REU for everyone, regardless of citizenship: 2013 PRiME: Purdue Research in Mathematics Experience will conduct research in number theory from June 10 to August 2. Applications are due April 26.
There are many internship opportunities at the National Security Agency. Applications are due from September 1 to October 15. This includes The Director's Summer Program.

Information about Summer Internships

NASA has internships and fellowships -- it looks like deadlines fall on March 15.
An excellent opportunity for third year students: The Graduate School of Science of the University of Tokyo will offer summer research internship opportunities through UTRIP (the University-of-Tokyo Research Internship Program). You do not need to know any Japanese. Apply here by March 1.
Up to 8 Summer Institutes for Training in Biostatistics will happen this summer. Statistics is quickly emerging as the thing to do (even in 2009, but more so now). Applications are due at the end of February.
The NYC Turing Fellows Program seeks to match top computer science students with outstanding summer internships at leading New York City startups. If you are interested, then apply by February 8; however, applications are looked at beginning January first.
(12/27: not yet for 1213) Google Summer of Code is a global program that offers students stipends to write code for open source projects. If you would like to work on exciting open source projects this summer, then apply by the end of March.
Michigan's Institute for Social Research has a summer internship program that often has positions for people interested in learning data analysis skills. Aim to have your application in by mid-December.
Internship opportunities at the National Security Agency. Applications are due from September 1 to October 15. This includes The Director's Summer Program, Cryptologic Mathematics for Exceptional Undergraduate Mathematicians.
SIAM has a list of contact information for internships.
The ASA maintains a very long list of internships in the statistical sciences.
The University of Minnesota has a stub of a list.
The AMS maintains a listing of internships and co-ops.
Interested in spending your summer in Europe? Check out the CIBER Summer Internship program. If you have (lots of) experience in the life sciences, the Pasteur Foundation may be your ticket abroad. (December 8) APPLICATIONS DUE DECEMBER!
There are many internship opportunities at the National Security Agency. Applications are due from September 1 to October 15. This includes The Director's Summer Program, Cryptologic Mathematics for Exceptional Undergraduate Mathematicians.
Applications are now being accepted for the Department of Energy's Summer 2013 Term of The Science Undergraduate Laboratory Internships. While the deadline for applying is January 10, 2013; earlier is better. (January 10)
Interested in spending your summer in Europe? Check out the CIBER Summer Internship program. Applications due February 1.
It is never to early to fish for a summer internship. Sophomores, Juniors, or Seniors who are interested in working in Mathematical Biology may wish to apply to participate in a Summer Cancer Research Experience for Undergraduates funded by the National Cancer Institute’s Integrative Cancer Biology Program (NCI ICBP). The ICBP focuses on the development and implementation of computational models of processes relevant to cancer prevention, diagnostics and therapeutics by bringing clinical and basic cancer researchers together with researchers from mathematics, physics, information technology, imaging sciences, and computer science to work on key questions in cancer biology. Apply here after December 3, but before January 22, 2013.
The Columbia Business School is looking for exceptional students to participate in its Summer Research Internship program. Applications are due at the end of March.
The ASA maintains a very long list of internships in the statistical sciences.
The AMS maintains a listing of internships and co-ops.
We have only blurry Math T-shirt photos from the NSA. If you want to change this, please consider applying for one of their summer internships. The deadline is tomorrow.

Information about Summer Programs

Toronto's Fields Institute will be hosting the Fields-Mitacs Undergraduate Summer Research Program in July and August of 2012. Students, who need not be Canadian citizens, will work on research projects in groups of three or four. Some projects will be related to the Fields Thematic Program on Inverse Problems and Imaging, the Focus Program on Geometry, Mechanics and Dynamics, and the Legacy of Jerry Marsden, and the Thematic Program on Forcing and its Application. You have until April 30th to apply.
PIMS (the Pacific Institute for the Mathematical Sciences) together with Simon Fraser University is offering the PIMS-SFU Summer School for Undergraduates in Algebraic Graph Theory. This program for Canadian and International students provides excellent math T-shirt photo opportunities, as well as an intense introduction to the mathematics linking graphs and algebra. Applications are due March 30.
Notre Dame's Undergraduate Summer School will offer a week long Introduction to Topological Invariants in Low Dimensions from May 21 to May 26. The Program is pitched at beginners and requires only the completion of 215 and 217. All expenses paid! Apply by March 31. I remind you that we have no pictures of a Math T-shirt with Touchdown Jesus.
The Statistical and Applied mathematical Sciences Institute (SAMSI) is sponsoring several workshops to introduce undergraduate students to research in applied mathematics and statistics
For female students in their third year of study, George Washington University and the NSA are hosting a Summer Program for Women in Mathematics(applications due March 1).
Next May the Institute for Advance Study (think Einstein) is hosting a Women and Mathematics program on 21st-Century Geometry; applications are due February 20.
For female students in their first or second year of study, Carleton College is hosting the Summer Mathematics Program for Women Undergraduates (applications due February 7).
Los Alamos National Laboratories in New Mexico is sponsoring an undergraduate research program. It appears the application process closes January 10. (January 10)
An excellent opportunity for those who are in or who have recently completed linear algebra (with proofs): Cornell is again running its Summer Math Institute (SMI) from June 8 – August 3, 2013. This program is a kind of hybrid between research and course work -- and its director, Ravi Ramakrishna, is awesome. Apply by February 15.
For female students in their third year of study, George Washington University is hosting a Summer Program for Women in Mathematics (applications due March 1).
Next May the Institute for Advance Study (think Einstein) is hosting a Women and Mathematics program on 21st-Century Geometry; applications are due February 20.
For female students in their first or second year of study, Carleton College is hosting the Summer Mathematics Program for Women Undergraduates (applications due February 15).
In May the Institute for Advance Study (think Einstein) is hosting a Women and Mathematics program on Combinatorics and Graph Theory; applications are due February 20.
First and Second Year students: The International Summer School for Young Mathematicians will take place July 2-12 at Jacobs University in Bremen. This is a fantastic opportunity to take some photos of your math T-shirt as well as learn mathematics with your peers from around the world. Applications are due March 20.
Notre Dame's Undergraduate Summer School will offer a week long Motivic Invariants and Singularities from May 20 to May 25. The Program is pitched at beginners. All expenses paid! Apply by March 31.

Information about Math Camps

Applications to serve as a counselor at various math camps are due beginning in January. For example:

applications for MathPath are due January 31.
applications for PROMYS are due in mid March.
applications for Canada/USA Mathcamp are due soon -- unfortunately, you must be an alumnus/a to apply.
The Johns Hopkins University Center for Talented Youth (CTY) is seeking instructors and teaching assistants for its summer programs. CTY offers challenging academic programs for highly talented elementary, middle, and high school students from across the country and around the world. Apply soon.

Miscellaneous.

The School of Education (SOE) is again offering undergraduate Michigan students with an interest in teaching and service a chance to serve in its Elementary Mathematics Laboratory (EML) summer program. SOE reports that they have had excellent students from mathematics in past year, and would be happy to take some more. Information about the program follows my signature.