The Internship Network in the Mathematical Sciences

Resources Needed

This section summarizes the resources needed to run a program providing career assistance to graduate students in mathematics. It has the following components:

An assessment of Potential Additional Resources is also given. Of course, a smaller program serving a single institution could operate with fewer resources.

Software and Physical Infrastructure

The program relied on the following infrastructure components to support its activities:

Personnel

To meet the demand of up to 90 students per year, the INMAS team was composed of two (part-time) PIs, two part-time program coordinators, and on-demand instructors and teaching assistants. The time commitment from PIs, including grant management, consisted of a few hours per week in addition to the overall program coordination and full participation in all training activities. The program coordinators had similar roles in addition to coordinating all summer internships. This involved outreach to up to a thousand companies for each hub, and sending hundreds of resumes once the participating companies were identified. The student mentorship role was assumed jointly between PIs and program coordinators. PIs and program coordinators also participated in the development and delivery of the training material, primarily on projects and Python programming. The statistical methods and machine-learning training modules were primarily developed by additional instructors.

Financial

A good portion of the INMAS budget went to cost-sharing the students’ remuneration for the INMAS-sponsored internships. During the last year of the program (2025), interns were paid $15/hour or more by the host companies while INMAS matched that amount in the form of a lunp-sum stipend. The internships were typically around 10 to 12 weeks at 40 hours per week, so roughly $7k of INMAS funding was allocated per student per summer. For a program of 20 internships per year, one would need an annual budget of about $150k for stipends.

The other big-ticket items in the INMAS budget were salaries for the program coordinators, payments to the instructors, teaching assistants, external consultant for , and teaching reductions for the PIs. Finally, reimbursements for travel, lodging, and meals for students participating in the training sessions constituted another important component of the budget.

Potential Additional Resources

We believe that significant potential synergies with existing resources could be exploited by people looking to set up a program at their institution:

Tasks and Activities

Operating a year-round program such as INMAS requires careful scheduling of resources aimed at accomplishing specific tasks and activities. Below, we break down the activities conducted by the INMAS team and list them in chronological order as they take place in the annual calendar.

Node Selection and Outreach

One of the premises of the INMAS program was that sharing and pooling resources between universities could greatly improve the chances of success for a program aimed at facilitating the transition of graduate students to BIG careers. Successfully recruiting and training student participants from a department at another institution relies on several specific elements:

  1. The existence of a local champion to help promote the program within the institution.
  2. A sizable population of graduate students to recruit from.
  3. The participation of more than one student per year from each institution, in order to create a cohort that supports learning.
  4. Easy and affordable transportation to get participating students to the hub institution where in-person technical training takes place.
  5. Financial support for activities involving students from the institution.

The INMAS model provided the infrastructure, staff, and most of the financial support. For future models with more limited resources, the contributions of personnel from the participating organizations, potentially through rotating roles, could offer a creative approach to lowering costs and pooling resources between nearby universities.

Program Coordination

The annual INMAS schedule ran over the course of two semesters, with training sessions starting in October and ending in March, followed by an internship (for up to two-thirds of participating students) that took place during the summer. Training sessions were typically run outside normal school hours to minimize the interference with regular activities such as classes and TA/RA duties. Professional development sessions were usually 1-2 hours long and were run remotely during weekday evenings. Except for the first year of the program, during which COVID-19 happened, technical training workshops were generally delivered in-person over weekends, starting at dinner time on Friday night and ending at midday on Sunday. This schedule allowed non-local students to travel to and from the hub. Bringing students from many different universities together in the same location also enabled networking opportunities for the students, an opportunity we explicitly encouraged them to take advantage of.

A calendar of participant activities was advertised through the website, so that students applying to the program could evaluate their full availability required to participate in the program. A typical annual calendar looks as follows:

Date Activity Description  
  early September Recruiting Send email to nodes, information sessions
  late September Application Deadline Last day to apply to program
  mid-October Welcome session Present program activities and rules for participating (remote)
  late October Technical workshop #1 Fundamentals of Python programming (in-person)
  early November Professional development A Resume preparation (remote)
  mid November Deadline to provide draft of resume Last day to submit draft of resume
  all November Mentoring One-on-one meetings to provide feedback on resume and career goals (remote)
  late November Technical workshop #2 Statistical methods (in-person)
  early December Deadline for final resume Deadline to submit final resume
  mid-January Technical workshop #3 Machine learning (in-person)
  early February Professional development B Preparing for interviews (remote)
  late February Professional development C Networking and effective communications (remote)
  late February Technical workshop #4 Projects and teamwork (in-person)
  April Professional development D Internship guidelines (remote)
  mid-May Internships start Typical start date for internships
  late August Internships end Typical end date for internships
  September Due date for internship reports Summary of internship work

Alternative

An in-house program, based at a single institution, could easily integrate the training workshop material into the students’ regular schedule, for example by running a weekly extended seminar with learning and lab time combined. Such a method would eliminate the costs associated with travel, lodging, and meals that INMAS incurred from running the workshops over weekends at a central location. Or, if multiple institutions partnered to create an INMAS-like program, one could imagine having traveling instructors for the year, each responsible for delivering a specific module of the training at the multiple institutions.

Program Advertisement

The program was advertised through the following instruments:

  1. A website describing the program and its goals, activities, and calendar of events.
  2. Emails to all graduate students in participating departments, to describe the program and explain how to apply.
  3. Information sessions held online, with plenty of time for Q&A. Program alumni (students who had participated in previous years) were invited to participate too, so that they could share their experiences with prospective students. The majority of questions asked during the information sessions were addressed to the alumni.
  4. Optional on-site visits by INMAS personnel to the node departments, in order to publicize the program to students and run Q&A sessions. As in the online sessions, former students proved to be good ambassadors for the program.

Program Application Process

Depending on the number of applicants for such a program, the application process could be coordinated using different tools. For a small pool of applicants, a simple email address with a webform might suffice; in the first year of our program, we used a Google form. For larger cohorts, we found it more convenient to utilize online workflow management software from Monday.com (“Monday”), which enabled us to gather and organize student information and then carry it through the year’s activities. If a program were integrated within the regular curriculum of an institution, the application process could simply leverage existing record-keeping systems.

We used the workflow management tool also for the internship application process and internship progress monitoring. Using Monday’s form feature, all student application data were instantly stored in a database, easily viewable in aggregate form and linked via the student’s email to any future records associated with the student.

In addition to demographic and contact information, the form asked students to describe:

Participant Selection Process

This section describes the criteria used for selecting the participating students.

Priority was given to students who were more advanced in their PhD program, because early-year students are focussed on coursework and qualifying exams, and also they are generally not thinking ahead seriously to career options.

A modest amount of prior programming experience was required e.g. a one-semester undergraduate course.

The number of applications per institution varied each year, based on the nodes’ commitment to recruiting. Our acceptance rate was around 50-70%, which resulted in each branch of the program accepting between 35 to 50 students per year into the training program. We anticipated placing roughly 60% of these accepted students into INMAS-sponsored summer internships, with the remainder of each cohort either finding their own internships or getting summer TA or RA positions.

While there were some hard criteria which the students needed to satisfy, efforts were made to evaluate each application from a human standpoint with consideration for individual circumstances. Selection criteria included the following:

Professional Development

Four dedicated professional development sessions, given online and each roughly 90 minutes in duration, served as the backbone of the program’s training on professional skills (which are sometimes wrongly referred to as ‘soft skills’). These sessions addressed the following topics:

Each of the three first modules included follow-up actionable items to be completed by the student. As a strong emphasis of the program was to make the students take responsibility for their own careers, none of these follow-up items were collected or graded, but they were rather presented as SMART goals to them. Nonetheless, subsequent discussions on the progress achieved on these tasks took place during the in-person workshops, and/or during one-on-one online meetings with program coordinators.

Resume Preparation

This session provided guidance on crafting a good technical resume. It was encouraged that the document be a single-page, information-dense, and search-engine optimized (SEO) resume. A challenge faced by many students, and which the INMAS program aimed to address, is the gap between the students’ mathematical backgrounds and the diverse areas where they might see themselves employed. Thus, an emphasis was placed on re-framing the student’s theoretical mathematical experience in terms of their leadership skills, capacity to innovate, and technical experience.

Students submitted draft resumes before the second in-person workshop. These drafts underwent revisions during one-on-one sessions interspersed with the workshop, or during subsequent one-on-one meetings online, with a final version submitted in time for the start of the internship application process.

Students were encouraged to apply to as many external positions as they could on their own. To help manage their expectations, the concept of best-fit in contrast to best student was presented to them, as a way of distinguishing the job application process from the selection process used for getting into graduate school.

We found that students really enjoyed receiving feedback on their resume and were extremely receptive to the feedback received, often requesting a follow-up meeting.

Preparing for Interviews

A professional module was developed to help students better prepare for interviews. This module contains basic preparation tips as well as practice sessions. The crafting and delivery of a good elevator pitch is an important component of this module, as this quick overview is a often the starting point of any conversation with an employer.

Students were put in small teams and asked to get intel and prepare for fictitious interviews with selected companies. Practice sessions through Zoom were organized to allow students to participate in mock interviews and provide feedback to one another. These practice activities do not require a lot of effort to organize and have considerable impact on students’ confidence and readiness to interview.

Networking and Effective Communications

A powerful skill required for finding a good position in industry or academia is networking. INMAS provided training material and practice sessions for performing informational interviews and meaningful and engaging descriptions of oneself. Dispelling the perception that networking is “schmoozing”, and providing actionable networking tasks to student participants, were the central goals of this module. The integration of tools such as LinkedIn for expanding one’s network was presented and students were asked to expand their own network using these tools through SMART goals.

Internship Expectations

This training covered some fundamental rules regarding corporate America that students might not have been exposed to while in an academic environment. Honesty, punctuality, team work, intellectual property and proprietary data were part of the topics explored during these sessions. Finally, a series of situational vignettes were presented and discussed with the group. Some of these situations represented cases we encountered in earlier cohorts, and were an excellent way to raise the students’ awareness of their ethical and legal obligations towards their summer host organizations.

Mentoring

While representing a serious time commitment, the mentoring activity had a strong impact on students and on the program. These 30-minute one-on-one Zoom sessions were scheduled through calendly or an equivalent. For 90 students, this effort represents 45 hours of meetings spread over multiple weeks. The in-person workshops also provided an additional opportunity to conduct these discussions during the weekend. During these sessions, feedback was provided on a draft resume and a series of questions were asked to the students. These questions allowed the students to practice a good elevator pitch, and to express their preference for a summer internship regarding the field of work (e.g., fintech, pharma, defense, machine learning, etc.), the location, their mobility, the work model (in-person vs remote), and so on. Just as importantly, these meetings offered an occasion to better know the students and assess their capabilities, constraints, and readiness for employment.

In addition to these planned activities, INMAS staff members made themselves available as needed to discuss career choices, guidance on receiving multiple offers, and guidance on applying to external jobs for soon-to-graduate students. These discussions were helpful to us for identifying points that we then found ourselves repeating to multiple students and integrating into the regular training material.

Technical Training

This section describes the four technical workshops that were used during the INMAS technical training. Each workshop has an associated repository on GitHub which contains a series of Jupyter notebooks, instructions, and solutions.

  1. Python Programming and its Software Stack is a short introduction to the Python programming language and its most popular packages for scientific computation (NumPy, Pandas, Matplotlib, Seaborn, etc.).
  2. Statistical methods builds on the previous module, training students to clean and analyze data using statistical methods such as simple and multiple regression, logistic regression, and hypothesis testing.
  3. Basics of machine learning provides a short introduction to many common techniques in machine learning, including neural networks.
  4. Projects are open-ended projects that focus on team work and allow students to apply the skills gained in previous modules.

Python Programming and its Software Stack

One of the challenges of the INMAS program was to provide training to a population of students entering with diverse levels of proficiency in programming. To address this challenge, multiple paths covering the material were elaborated, some of which covered the basics for beginners, while others offered more challenging modules to cater to our most advanced students. We aimed for all students to be able to code in procedural Python using popular scientific modules such as NumPy, Pandas, MatplotLib, and Seaborn. Object-oriented programming was an optional module. The material for this workshop consisted mainly of Jupyter notebooks and is available here: Technical Workshop #1.

Statistical Methods

This module consists of classroom material in PDF format with associated Jupyter notebooks for practicing the concepts. The material and notebooks cover basic concepts in statistics such as data wrangling, simple and multiple linear regressions, and logistic regressions. The workshop material and files are available here: Technical Workshop #2

Basics of Machine Learning

This relatively dense workshop covered a lot of topics in a short period. These include foundational concepts, principal-component analysis, clustering, gradient boosting, natural-language processing, deep learning, and large-language models. The material for this workshop consisted of classroom-style presentations in PDF format and accompanying Jupyter notebooks. They are available here: Technical Workshop #3.

Projects

This training workshop was by far the preferred module for students. It involved open-ended projects similar to those found on the Kaggle website. Previous modules were addressed in small teams, but the work involved in going though the notebooks still remained fairly individual. In contrast, the project training required teams to partition the tasks among members in order to achieve results in the allocated time. Presentations were made by each team at the conclusion of the workshop. The material for this workshop consisted of a short problem description and possibly some links to data. A description of some of these tasks is available here: Technical Workshop #4.

Industry Outreach and Internship Generation

Outreach to BIG organizations targeted mostly industrial organizations, due to their significant relative number and the breadth of opportunities provided.

Our program found the most success in connecting with small businesses. Large organizations being generally already possessed of robust talent pipelines, and the recruiting personnel at these locations experiencing high rates of turnover, our program found it difficult to both insinuate our operations into these large pre-existing structures and to maintain lasting relationships. By contrast, our interactions with small businesses were marked by the following advantages:

We found particular success connecting with businesses receiving grants from the Small Business Administration (SBA) of the US government through the Small Business Innovatioin Research (SBIR) and Small Business Technology Transfer (STTR) programs. This roster of businesses is publicly available, and the code developed by our team to pull from that database is available under the “Scripts” folder on this Github page.

We fiiltered potential hosts by location, research topic, and grant size to create our final list of contacts. We then out first through cold-call emails introducing our program and proposing a short introductory meeting over Zoom for interested parties. The conversion rate of these cold contacts was approximately 10%, and a majority of firms with whom we met ultimately submitted an internship proposal. Initial contacts emphasized that participation with the program is free, and that there is no obligation on either party.

Interested companies were asked to submit an internship proposal on a web form hosted on Monday.com. The following information was requested:

A redacted version of this information (in which contact names were removed) was shared with the students. We were typically able to develop more internship proposals than the number of available students. While some employers chose 8 weeks for the duration of the internships, the majority preferred 10-12 weeks.

Note that many small companies have grants from US agencies that restrict them to employing US citizens only. Since the COVID pandemic, a large fraction of startup companies follow a 100% remote work model, which enabled us to seek internships beyond the regions of our node institutions.

Matchmaking and Resume Coordination

All students were encouraged to apply independently to internship positions that they found through networking connections or online ads. But the success rate of online applications is low. Students primarily obtained internship positions through INMAS.

We provided a web portal that listed internship proposals at host companies identified by INMAS, as described above. Our portal offered these positions exclusively to students in the program, which presented both an opportunity and a challenge. By dealing with a small pool of qualified applicants, the probability of finding a good match for the position was high, but at the same time, the probability of having top candidates receive multiple offers was also high. This talent-race condition had to be managed carefully to avoid wasting the resources of organizations that might interview candidates who would end up turning down the offer.

Students interested in a position filled out an interest application on the portal, specifying the position they were interested in, and their level of interest (low, medium, high). A bundle of resumes was selected by the program coordinators from among the students expressing a high level of interest, and sent to the company, which would then contact the candidates directly, if interested. From this point, the interaction is completely in the hands of the hiring organizations. Similarly, the interview process was left entirely to the hosting organizations.

If a host made an internship offer to a student, then the program coordinator would take the necessary steps to establish the proper legal and financial paperwork required for the intern to be paid. The cost of the internship would be cost-shared by the company and the INMAS, each paying the student separately. Special care was taken with international students, who require work authorization (generally CPT from their university’s international office) in order to work off-campus for the summer.

Internship Progress Monitoring

This section describes how the monitoring of internship progress was carried out during the summer. One of the program requirements was that the student had to write a short report describing the work completed during the summer. These reports were given first by the student to the host, who had the opportunity to redact proprietary material. Once signed and released, these reports were kept by INMAS for grant audit purposes. During the summer, regular emails were sent by the program coordinators to the students to ensure that everything was going smoothly. INMAS staff were available to resolve any issues that occurred during the summer; these tended to be rare events involving life issues that are are well recognized in normal work environments.

The stipend from INMAS to the student was paid in two installments, one at the beginning of the internship, and the other at the end, with the second payment conditional on receipt of the intern’s final report. Final reports were typically 5-10 pages, written in LaTeX or Microsoft Word.

Program Assessment and Outcomes

The INMAS team worked with an external evaluator throughout the five years of the project. The primary focus of the evaluation was to collect data that informed ongoing program improvements, and to identify preliminary outcomes. The evaluator collected feedback from students about their experiences in the technical and professional development workshops and internship experiences. Feedback and perceptions were also solicited from company representatives and faculty and staff from participating institutions. Brief reports were shared and discussed with INMAS staff throughout the year. A final report was submitted at the end of each year. The reports and survey instruments are available here.