Contents

• Introduction
• Program Overview
• Learning Outcomes
• Application to the Program
  • Standard Applications
  • Transfer Applications
  • Application Decisions
• Program Timeline and Milestones
• Advising and Special Committees
  • First-Year Faculty Advising
  • Finding a Permanent Advisor
  • Special Committee Constitution
• Mentoring in CAM
  • Mentoring Networks
  • Faculty Mentoring Framework
  • Individualized Development Plans
  • Peer Mentoring Program
    • Peer Mentor Expectations
    • Peer Mentee Expectations
• Courses
  • Enrollment Expectations
  • Prerequisite Courses
  • Responsible Conduct in Research (RCR)
  • CAM Core Courses
    • A. Computational Methods
    • B. Mathematical Analysis
    • C. Differential Equations and Dynamical Systems
    • D. Stochastic Methods
    • E. Optimization and Discrete Mathematics
    • F. Algorithms and Complexity
    • G. Algebra and Logic
  • Minor Requirements
  • Special Masters in CS
  • Minor in Applied Mathematics
• Student Progress Reviews
• A and B Exams
  • A Exam
  • B Exam
  • Outcomes of Exams
• Dissertation
• Leaving the Program
• Life at the Center
  • CAM Space
  • Computing Resources
  • CAM Wiki
  • Colloquium
  • Bill Sears Blitz
  • First-Year Seminar
  • SIAM Student Chapter
  • Association for Women in Mathematics
  • Other Events
• Funding
  • What Funding Covers
    • Tuition
    • Student Health Plan (SHP)
    • Stipend
  • Types of Funding
    • Fellowships
    • Teaching Assistantships (TAs)
    • Graduate Research Assistantships (GRAs)
  • Funding Responsibilities
  • Outside Employment
  • Summer Support Options
  • Conference and Travel Grants
• Administrative Matters
  • Residency and Leave
  • Academic Standing
  • Petitions and Other Forms
• Other Cornell Resources

Introduction

The Center for Applied Mathematics was created in 1964 “to encourage the application of mathematical knowledge in the physical, biological, and social sciences.” The first director was Bill Sears, an aerodynamicist educated under von Karman at Caltech, who was returning to academia after time spent in industry at Northrup. The center started with 20 members from math, engineering, physics, and chemistry. Today, we have over a hundred members, from an even broader array of disciplines, but still are guided by that original mission of encouraging the application of mathematical knowledge across a wide range of disciplines.

The range of possibilities for graduate study encompasses the areas of specialization of all of the faculty members in the field, who currently number more than one hundred. The faculty members are drawn from fourteen departments in the College of Engineering, the College of Arts and Sciences, the College of Agriculture and Life Sciences and the Samuel Curtis Johnson Graduate School of Management. There is opportunity for further diversification on the choice of minor subjects.

Program Overview

Research degrees at Cornell fall under the Graduate School, which is organized around different fields of study. Most fields are associated with one or more academic departments, but the graduate Field of Applied Mathematics is associated with the Center for Applied Mathematics, a research center under the Office of the Vice Provost for Research. We informally refer to both the graduate field and the research center as “CAM.” The Graduate School maintains a broad set of support programs and policies around issues common across academic fields, but leaves field-level policy issues to the fields. This handbook describes the field-level policies for CAM.

CAM only offers PhD study, though students may opt for an MS in applied mathematics at the time of their A exam. The program is based on a solid foundation in pure mathematics, which includes the fundamentals of algebra and analysis. It involves a grounding in the methods of applied mathematics and studies of scientific areas in which significant applications of mathematics are made. The field has a broadly based interdepartmental faculty that can direct student programs in a large number of areas of the mathematical sciences.

Many specialized or interdisciplinary programs can be designed for individual students, including, for example, a variety of possibilities in biomathematics.

The dissertation is normally a mathematical contribution toward the solution of a problem arising outside mathematics.

Students are admitted to the Field of Applied Mathematics from a variety of educational backgrounds that have a strong mathematics component. About 40-50 students are enrolled in the program, which usually requires 4-6 years to complete. A typical CAM class size is about eight students, though the target size depends on funding, advising capacity, and space. More statistics about the Applied Mathematics degree program are available from the Graduate School Dashboard.

Learning Outcomes

A graduate student in Applied Mathematics is expected to demonstrate both mastery of knowledge in mathematics and its applications, and ability to create new mathematical knowledge and innovative ways to apply mathematical tools to important problems in science, industry and society. Each student is expected to demonstrate the following proficiencies.

• Make substantial original contributions to applied mathematics. This includes ability to identify new important and promising research problems; ability to think independently, critically and creatively; ability to complete research work by bringing it to the stage where it can be published and be used by the others.

• Maintain ability to acquire new knowledge by keeping up with the new developments in the field through professional publications and professional meetings.

• Ability to communicate effectively research findings and plans. This includes ability to present results in the format of technical papers and have them published in professional journals and conference proceedings; ability to explain complex ideas to peers in technical presentations; being aware of funding opportunities and ability to write effective research proposals and obtain research funding.

• Dedication to advancing science through effective teaching, advising, mentoring and service to professional community.

• Awareness of the ethical standards in the field, and ability to maintain and advance these standards.

See also the statement on doctoral proficiencies from the Graduate School.

Application to the Program

Standard Applications

Applications to the CAM PhD program are due in January. Applications are only accepted for the fall semester. The online application system is managed by the Graduate School, and a non-refundable application fee of $105 is required along with the application to cover the cost of processing. Fee waivers are available for students with financial need and for students who have participated in a variety of programs designed to provide educational and/or career support to students from historically underrepresented identities. A list of eligible programs is available on the Graduate School application fee page.

The application materials include:

• Basic information: Typical application information such as nationality, GPA, schools attended, etc.

• Transcripts: Accurate unofficial transcripts for each school you have attended. There is space in the field for listing three schools. A student who has attended more than three schools should upload those transcripts in the writing sample portion of the application.

• Statement of purpose: A statement of purpose is required and can be uploaded directly into the application. The statement should ideally include information about areas of mathematics that interest the student and field members the student might like to work with.

• Personal statement: The personal statement should provide the admissions committee with a sense of the student as a whole person. It should complement rather than duplicate the content of the academic statement of purpose.

• Letters of recommendation: At least three letters of recommendation are required. Additional letters are allowed. Recommenders may submit their letters online. Once an application is submitted, recommenders receive an automated email soliciting their letter. Applicants will be prompted for recommender contact information before submitting their applications.

• Test scores: GRE scores are not accepted.

• Language scores: With very few exceptions, international applicants must demonstrate English language proficiency by submitting IELTS (International English Language Testing System) Academic or TOEFL (Test of English as a Foreign Language) scores to the graduate school. Scores are valid only if dated within two years of the application deadline. Minimum scores and exception policies are detailed on the Graduate School web page.

• Supplemental documents such as undergraduate research papers, awards, etc, can be included in the writing sample of the application.

The admissions committee begins reviewing applications in mid-January and continues throughout February.

Transfer Applications

Students already enrolled in a program with the Cornell Graduate School may apply to transfer between fields. Students who want to transfer into CAM under this mechanism, should consult with the Director of Graduate Studies (David Bindel) and (if relevant) with their academic advisor.

Because transfer students receive center support and resources the same way that incoming students do, transfer requests are considered by the admissions committee at the same time as regular applications. Requests should be ideally be supported by an advisor from the field of applied mathematics.

Application Decisions

Decisions are communicated to applicants until the end of March. Applicants offered admission will receive an admission letter and a deadline for when they need to inform CAM about their enrollment decisions (usually April 15). Early notifications are appreciated, as they help us in planning for the upcoming year. Deferral by a semester or two is sometimes allowed. To request a deferral, applicants should write directly to appliedmath@cornell.edu.

When international students respond that they will enroll at Cornell, they are sent an I-20 form.

Program Timeline and Milestones

A PhD in Applied Mathematics typically takes 4-6 years depending on several factors. These factors include the level of preparation prior to beginning the program, graduate committee recommendations, motivation to end graduate study quickly, and faculty availability, among other issues. Students begin their program with primarily taking classes and end it with primarily research, with the years in between being a mix of the two. During the first two years a student typically takes two or three classes a semester.

Five years is the average time period for completion of PhD, with many students continuing into their sixth year. Below is a time table based on five years.

• Year 1
  • Before fall arrival, incoming students are assigned a provisional advisor.
  • Students take classes both semesters, chosen in consultation with the provisional advisor. A normal course load for a beginning graduate student is three courses per term.
  • Ideally, students select an advisor to replace the provisional one in the spring, and begin to consider who they will ask to be on their special committee.
• Year 2
  • Take classes both semesters.
  • By the end of the fall semester, the student must choose a special committee (minimum of three members including the Chair). The committee request is submitted online in Student Center. The advisor, the DGS, and GFA will receive an email to sign off on the request.
  • Begin exploring research topics for the coming spring and/or summer.
  • During the spring semester, research should be underway.
• Year 3
  • Prepare for the Admissions to Candidacy (A) exam and consult with the Chair which classes you should be taking before becoming more involved in research. During the spring or summer (must be before semester 7 begins), the student must take the A exam.
• Year 4
  • Research and finish up any remaining required classes.
  • Begin thinking about and pursuing employment opportunities.
• Year 5
  • Research.
  • Actively pursue employment opportunities during the fall semester. Don’t wait until spring to start!
  • Take the B exam (thesis defense).

Advising and Special Committees

First-Year Faculty Advising

All first-year graduate students are formally advised by the CAM director. This means that the CAM director is responsible for signing the “advisor” slot in any university forms that a first-year student might need signed. CAM students (first year and beyond) are also welcome to come to the director to ask questions or seek advice.

Beyond the director, each incoming CAM student is assigned a provisional advisor for the first year. The provisional advisor should check in with the student at least twice a semester until the student finds a permanent advisor (which may or may not be the provisional advisor). Some topics of discussion for these meetings might include:

• Course selection
• Time management
• Seminars and colloquia
• Applying for fellowships
• Seeking advisors
• TA duties
• Adjusting to life in Ithaca
• Physical and mental health
• Relating to other students
• Any concerning behavior encountered (unethical behavior, biased speech)

Finding a Permanent Advisor

A committee chair (thesis advisor) must be selected by each Ph.D. student before the end of the second semester (i.e., before the end of Academic Year 1). Because applied math is an “orphan” graduate field without an associated a department, the faculty affiliated with applied math have a wide range of departmental homes; and CAM PhD students are integrated with exciting initiatives across campus in biology, engineering, computing, finance, and more. Because the CAM PhD program touches so much of campus, choosing an advisor can be an intimidating task! Fortunately, there are several formal and informal mechanisms to help students find an appropriate advisor:

• Discussion with faculty mentors: The director and the provisional advisor are meant to serve as a resource for students looking for possible advisors. In many cases, faculty members may have some idea who is looking for students (and who is not), and can help point a student to a few prospective matches.

• Discussion with CAM students: The first-year mentors and other CAM students often know how field members have worked out as advisors for other students, and can be a valuable source of information.

• Bill Sears Blitz: The Center has a fall poster session and “blitz session” of one minute talks from students and faculty about their current research. This can be a good opportunity for new students to learn about prospective advisors (and vice-versa), as well as giving older students a peek into the broader CAM research portfolio.

• CAM events: Students and faculty have opportunities to socialize at post-colloquium refreshments, picnics, and other CAM events.

• Classes and seminars: One standard way that students get involved in research is to take a class from a prospective advisor, or to get to know a prospective advisor from interactions in a colloquium or area seminar.

• Knocking on doors: Even without any other excuses for interacting, it’s possible to send an email to a faculty member expressing interest in their research! If the email gets ignored, it’s also possible for a student to show up at the faculty’s office (particularly if it is during advertised office hours).

Applied mathematics students must have a committee chair who is a member of the field of applied mathematics. In cases where a student would like to do research with faculty not in the field, there are two standard options:

• The student can ask the CAM director about the possibility of nominating the faculty member to the field of Applied Mathematics. This takes some time, and so such requests should be broached well ahead of the deadline for appointing a committee chair.

• The student can formally work with a CAM field member who serves as the committee chair, but work on research with other non-CAM faculty members. These types of co-advising relationships are not uncommon in CAM.

Finding a good advising match is important, and it takes time. It is fine not to match advisors immediately, and it is fine not to work with the first advisor attempted. Cornell provides extensions to give students a way to take the time they need — but at the same time, it’s best not to delay the search too much!

Special Committee Constitution

The committee chair will aid the graduate student in selecting a Special Committee, which shall consist of a minimum of three faculty members and which will directly supervise the graduate study and research of a student. The committee chair, who is also the thesis advisor, represents the major field of applied mathematics. The other faculty members represent two minor fields; one of these must be mathematics and the other is a field outside mathematics. This committee must be formed before the end of the third semester.

A Special Committee Selection and Change form must be submitted to the Graduate School to establish a committee or change/add committee members. This can be done online through Student Center.

Selection of a Special Committee (including the thesis advisor) is a mutual agreement between a student, the chosen faculty members and the DGS. During the pursuit of the degree, changes in circumstances may cause the student and/or faculty members to desire the termination of this commitment. Students may make changes to their special committee any time before the A exam; changes after an A exam require special approval.

Different students have different levels of engagement with their special committees. The field of applied math does not require any formal meetings of the committee except at A exams and B exams, and some students have little interaction with their committee members outside of these exams. For other students, the committee members may act as collaborators or co-advisors, helping jointly mentor the student along with the thesis committee chair.

Mentoring in CAM

The first year of graduate school is a critical period for students as they learn to navigate Cornell and to manage competing demands from coursework, research, and teaching duties. In addition to the start-of-year orientation activities, first-year students are matched with both faculty and peer mentors who can help provide guidance throughout the year.

After the first year, the advisor and the special committee play an official role in guiding students through the PhD degree requirements. But students need more than advisors who will get them through the finish line; they also need mentors, invested in the academic and professional success of the student/mentee through graduate school and beyond. Ideally, in addition to supervising a student through the degree program, an advisor will be one of a network of mentors helping the student thrive.

Mentoring Networks

While the advisor can be an invaluable mentor, they ideally should be part of a broader network of mentors who help students thrive. Different mentors can provide different perspectives and functions: from building a broader research network, to helping a mentee become a better teacher, to helping define future career goals. Students will want to form relationships with faculty members who can recommend them for positions, senior students who can help them navigate Cornell and CAM, postdocs who can provide another perspective from their own PhD experiences, and others. Advisor and special committees play an important formal role in guiding students through the PhD program, but it is worthwhile cultivating a broader network of mentors beyond the committee as well.

Faculty Mentoring Framework

Cornell supports the Faculty Advancing Inclusive Mentoring (FAIM) framework for faculty/student mentoring, based on a strengths-based and identity-informed approach to support mutual growth, development, and success. The FAIM web site includes resources and tools for building mentoring relationships by:

• supporting mentors and mentees as they develop an understanding of one another’s expectations, cultures, values, and motivations
• helping mentors and mentees develop a mentorship plan customized to their preferences and aligned with their respective strengths, needs, and goals;
• providing practical resources and tools that can be adapted to a particular mentoring context.

The FAIM web page includes a number of resources, including core mutual expectations documents to help mentors and mentees establish, communicate, and refine their shared expectations about the relationship. Various funding agencies, including NSF, now require mentoring plans for sponsored research projects; FAIM also provides a mentoring template plan for proposals.

Individualized Development Plans

Starting in 2024, each graduate student and postdoctoral scholar receiving substantial support from an NSF award must have an Individual Development plan, updated annually and certified to exist in PI reports. The goal of these plans is to identify academic and career goals and what can be done to progress toward those goals. The NSF does not specify a particular format for the IDP, but one well-developed IDP framework is the Science Careers Individual Development Plan (myIDP). Ideally, CAM students should revisit their IDP and discuss it with their advisors at the time of the annual student progress report (SPR).

Peer Mentoring Program

The Peer Mentoring Program offers formal support to CAM students in their first year by pairing them with established CAM students who can help them navigate their transition into CAM. First-year students are matched with one or two peer mentors before the beginning of their first semester. The role of the mentors is to enhance the first-year experience by providing support, encouragement and information to their mentees. Mentors may have suggestions about work-life balance, adjusting to life in CAM or Cornell, advisor/advisee relationships and more. Mentors may serve as both personal and professional support for their mentees. In addition, Peer Mentor Program group events are held throughout the year and include fun activities as well as practical workshops.

Over the summer, a match-up survey is sent out to all incoming CAM students and to prospective peer mentors. In mid-August a welcome email is sent out to mentors and mentees with their matches. Mentors and mentees meet throughout the year, and larger group activities are organized 1-2 times per semester. After each semester, a feedback survey is sent to mentors and mentees. Questions or comments can be sent to the program coordinators

Peer Mentor Expectations

• Make a good faith effort to meet with your mentee in-person at least once per semester.
• Attend at least one group activity per semester.
• Direct your mentee to the Director of Graduate Studies (David Bindel) or the Administrative Manager (Philip Rusher) for answers to questions you cannot answer.
• Check in on your mentee’s morale and progress or goals, both academic and research-related, at least twice per semester.
• Facilitate connections and build community between your mentee and other graduate students and faculty when appropriate.
• Respond to your mentees and the mentoring program coordinators in a timely fashion.

Peer Mentee Expectations

• Make a good faith effort to meet with your mentor in-person at least once per semester.
• Attend at least two group activities per semester.
• View your mentor as your go-to person for questions or concerns but also feel free to reach out to other CAM students.
• Respond to your mentors and the mentoring program coordinators in a timely fashion.

Courses

A normal course load for a beginning graduate student is two or three courses per term. The Director of Graduate Studies in conjunction with the student’s provisional advisor will assist first-year students in determining the appropriate courses to meet individual needs. All requirement courses must be taken for a letter grade. Only courses at the 5000 level or higher may be used toward graduate credit. Some courses are cross-listed with undergraduate course numbers (typically 4000 level) and graduate course numbers (typically 5000 level); in this case, students must enroll in the graduate-level version to receive credit toward their degrees.

Enrollment Expectations

Students on ordinary status (e.g. not on leave of absence) are required to enroll in a minimum of 12 credits per semester. Students not enrolled in sufficient courses must be enrolled for research using either Graduate School or, if available, departmental course numbers assigned for that purpose. Graduate School research courses will be automatically adjusted at the end of the group period to bring total credits to 12.

Prerequisite Courses

Prerequisite to the graduate program are familiarity with analysis and algebra at the advanced undergraduate level (e.g., MATH 4130-4140 and MATH 4330-4340). Students lacking either prerequisite (which may be determined by their special committee chair and/or the CAM Director of Graduate Studies), should take the appropriate courses within their first two years of study. No more than two of these courses can count towards meeting other CAM degree requirements.

Responsible Conduct in Research (RCR)

Every graduate student is required to complete a short course on Responsible Conduct of Research, to be finished by the end of the second registered semester. This online training addresses issues of authorship, peer review, plagiarism, and research misconduct. Students who are supported on NSF funding are required to take a longer course on RCR within 60 days of the start of the support period.

CAM Core Courses

For advancement to candidacy, a student is required to take at least eight courses in mathematics and its applications that are approved by her/his special committee, at least four of which must be numbered 6000 or above. Course credit cannot be transferred from other institutions to satisfy this requirement. Suggested areas for these courses are given in the list of Focal Areas for Applied Mathematics. The courses must include an advanced course in computational methods (focal area (a)). In order to achieve breadth in Applied Mathematics, courses from at least three other Focal Areas should normally be included. Should a course be listed under more than one focal area, then it will count towards only one such area as chosen by the student’s Special Committee. Courses must be taken for a grade, and students should maintain an overall GPA of at least 3.0 as a prerequisite for good academic standing.

The program allows great flexibility in the selection of courses. Most students design their own course sequences, subject to requirements, to meet their own interests. Courses are typically chosen from the math department and many applications departments.

The seven major Focal Areas for the field of applied mathematics are listed below, along with examples of recommended courses for completing the requirements in each focal area. In addition to the listed example courses, appropriate courses containing substantial mathematical content, offered by any department, may be taken to satisfy field requirements in mathematics and its applications, subject to approval by the student’s Special Committee.

A. Computational Methods

• CEE 5745/6745: Inverse Problems: Theory and Applications

• CEE 6300: Spectral Methods for Incompressible Fluid Flows

• CEE 6720: Introduction to Finite Element Method

• CS 5223: Numerical Analysis: Linear and Nonlinear Problems

• CS 6210: Matrix Computations

• CS 6220: Data-Sparse Matrix Computations

• CS 6241: Numerical Methods for Data Science

• MAE 6230: Computational Fluid Dynamics

• MATH 5250: Numerical Analysis and Differential Equations

B. Mathematical Analysis

Not both 6110 and 6210; not both 6220 and 7130

• MATH 6110: Real Analysis

• MATH 6120: Complex Analysis

• MATH 6210: Measure Theory and Lebesgue Integration

• MATH 6220: Applied Functional Analysis

• MATH 7130: Functional Analysis

C. Differential Equations and Dynamical Systems

MAE 5790/MATH 4210 must be taken with the graduate course number.

• CEE 5735/6736: Mathematical Modeling of Natural and Engineered Systems

• [CHEME 7530: Analysis of Nonlinear Systems: Stability, Bifurcation, and Continuation]

• MAE 5790: Nonlinear Dynamics and Chaos

• MAE 6010: Foundations of Fluid Mechanics I

• MAE 6110: Foundations of Solid Mechanics I

• MAE 6330: Multiphase Flow Dynamics

• MAE 6840: Asymptotics and Perturbation Methods

• MATH 6260: Dynamical Systems

• MATH 6180: Smooth Ergodic Theory

• MATH 6150: Partial Differential Equations

• MATH 6160: Partial Differential Equations

• MATH 6230: Differential Games, Optimal Control, Front Propogation, and Dynamic Programming

• MATH 6280: Complex Dynamical Systems

• MATH 6520: Differentiable Manifolds I

• MATH 6270/MAE 7760: Applied Dynamical Systems

D. Stochastic Methods

Probability, stochastic process, statistics, ML, signal and image processing, etc. Note that most BTRY 6000-level courses are not suitable.

• BTRY 7180: Generalized Linear Models

• CS 6780: Advanced Machine Learning

• CS 6783: Machine Learning Theory

• CS 6784: Advanced Topics in Machine Learning

• CS 6788: Advanced Topic Modeling

• ECE 6230: Stochastic Systems: Estimation and Control

• ECE 7620: Fundamentals of Data Compression

• ECE 7630: Information Theory for Data Transmission, Security, and Machine Learning

• MATH 6710: Probability Theory I

• MATH 6720: Probability Theory II

• MATH 6730: Mathematical Statistics I

• MATH 6740: Mathematical Statistics II

• MATH 7740: Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning

• ORIE 6500: Applied Stochastic Processes

• ORIE 6510: Probability

• ORIE 6540: Advanced Stochastic Processes

• ORIE 6570: Stochastic Dynamic Programming

• ORIE 6580: Simulation

• ORIE 6700: Statistical Principles

• ORIE 6750: Optimal Learning

• ORIE 6780: Bayesian Statistics and Data Analysis

• STSCI 6520: Statistical Computing I

• STSCI 7170: Theory of Linear Models

E. Optimization and Discrete Mathematics

• MATH 5410: Introduction to Combinatorics I

• MATH 5420: Introduction to Combinatorics II

• MATH 6230: Differential Games, Optimal Control, Front Propogation, and Dynamic Programming

• ORIE 6300: Mathematical Programming I

• ORIE 6310: Mathematical Programming II

• ORIE 6320: Nonlinear Programming

• [ORIE 6325: Interior Point Methods for Mathematical Programming]

• [ORIE 6327: Semidefinite Programming]

• ORIE 6328: Convex Analysis

• ORIE 6330: Graph Theory and Network Flows

• ORIE 6334: Combinatorial Optimization

• ORIE 6335: Scheduling Theory

F. Algorithms and Complexity

• CS 5814: Introduction to Computational Complexity

• CS 6810: Theory of Computing

• CS 6820: Analysis of Algorithms

• CS 6840: Algorithmic Game Theory

• ORIE 6350: Foundations of Game Theory and Mechanism Design

G. Algebra and Logic

• CS 6117: Category Theory for Computer Scientists

• CS 6764: Reasoning about Knowledge

• CS 6766: Reasoning about Uncertainty

• CS 6860: Logic of Programs

• MATH 6310: Algebra

• MATH 6320: Algebra

• MATH 6340: Commutative Algebra with Applications in Algebraic Geometry

• MATH 6390: Lie Groups and Lie Algebras

• MATH 6810: Logic

• MATH 7880: Applied Logic

Minor Requirements

Students are required to have minors in Mathematics and in another field relevant to their doctoral research. The Graduate School requires a representative of each minor on the student’s committee; ultimately, it is up to the minor representative to judge whether the minor requirements are met. However, most fields provide guidance regarding the expected minor requirements.

The requirements for the Mathematics minor are specified on the web site for the Mathematics department. Briefly, this involves:

• Two graduate mathematics courses, at least one of which is 6000-level or higher, with an earned letter grade of B- or better. These should be taken from:
  • 5000-level: 5250 (Numerical Analysis and Differential Equations), 5410 (Intro to Combinatorics I), 5420 (Intro to Combinatorics II)
  • 6000-level: 6110 (Real Analysis), 6120 (Complex Analysis), 6150 (Partial Differential Equations), 6160 (Partial Differential Equations), 6210 (Measure Theory and Lebesgue Integration), 6310 Algebra), 6320 (Algebra II), 6510 (Algebraic Topology), 6520 (Differentiable Manifolds), 6710 (Probability Theory I), 6720 (Probability Theory II), 6740 (Mathematical Statistics II), 6810 (Logic).
  • The Mathematics field member on the special committee may approve other 6000-level courses if they have graded homework or graded exams.
• Two additional mathematics courses at the 6000-level or higher.

Note that the course requirements listed above for the CAM core may suffice to satisfy the requirements for a graduate minor in Mathematics.

Special Masters in CS

Upon passing the A exam, CAM students are eligible for the masters degree in Applied Mathematics. Some CAM students may opt instead for a different masters degree, and particularly the special masters in Computer Science. This MS program requires a formal application and a special committee member representing CS who is primarily responsible for supervising the content of the program of study as it pertains to the master’s degree. For students taking the CS masters, it is expected that substantial progress toward the requirements will have been made by the time of the A exam, though it is not necessary for all requirements to be met at the time of the A exam. The degree will not be awarded until all requirements are satisfied.

Minor in Applied Mathematics

A minor in Applied Mathematics is available to Ph.D. students from outside Mathematics and Applied Mathematics. For Ph.D. students minoring in applied mathematics, the student should successfully complete

• Four graduate courses with substantial mathematical content
• All taken for a letter grade
• Covering at least two CAM focal areas
• At least two of which are numbered 6000 level or above
• With a minimum GPA of 3.0.

The four courses taken toward a minor in Applied Mathematics should generally not also be used to fulfill requirements of other majors or minors. Courses used to fulfill requirements of other majors or minors may be considered when counting the number of CAM focal areas in which a student has taken courses. A student who transfers into CAM from another graduate program may petition the CAM representative on the Special Committee to allow at most two courses from a prior institution of graduate study to satisfy the minor requirements. Such transfer requests cannot eliminate the requirement of at least two Cornell applied mathematics courses at the 6000 level or above taken for a grade.

Master’s degree students may obtain a minor concentration in applied mathematics at the direction of an applied math field member who is a member of their special committee.

Student Progress Reviews

The Student Progress Review is an annual exchange of written feedback where advisees are asked to reflect on recent accomplishments, identify challenges, and set goals. Committee chairs then review their students’ SPR forms and give constructive feedback. Chairs may rate student progress as excellent, satisfactory, needs improvement, or unsatisfactory. The SPR document is available to the student, the special committee, and the DGS and GFA.

The SPR is required beginning the second year even if advisors already communicate on a regular basis. For students who usually only talk to their advisors about research, the SPR can be an opportunity to have a conversation both about progress through the program and about broader career goals.

Student Progress Reports in CAM are completed in the spring by students in their second year and beyond, and are due in mid-late April. The SPR should identify the student and advisor’s plans for upcoming milestones, expectations, and deadlines.

It is recommended that CAM students and their advisors collaborate on an Individual Development Plan annually as part of the SPR process. IDPs are now required for all students working on NSF-sponsored grants (see the section on mentoring below). The Science Careers Individual Development Plan is a useful tool for developing such a plan.

Conversations around a student’s progress and career plans can be difficult when change is needed. While the SPR provides a record of the outcome of these conversations for all involved, we strongly recommend that students and faculty also verbally discuss the topics of the SPR.

A and B Exams

The field of applied mathematics has two required exams, which are mandated by the Cornell Graduate Faculty Code of Legislation. The A Exam (advancement to candidacy exam) can be completed after two semesters of registration and must be completed before the start of the seventh semester. The B exam (the final examination) is taken upon completion of all requirements for the degree.

A Exam

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student’s seventh semester.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and their committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, they must demonstrate expertise beyond just mastery of basic mathematics covered in the standard first-year graduate courses. Students are not required to have completed all their major and minor coursework at the time of the A exam, but it is expected that they will have substantial progress in their courses and a plan for the completion of any remaining requirements.

The typical A exam involves an open talk of about an hour, given to the committee and to any field members and peers who chose to attend. The talk should include time for general audience questions. At the conclusion of the talk and any subsequent broad audience Q&A, the committee and any field members who wish to attend have a closed-door discussion with the student in which they may ask additional questions. After this closed-door session, the student leaves the committee to deliberate in private and decide on the outcome of the exam. The student is then called back in, and the result of the exam is communicated. The special committee is encouraged to provide feedback to the student at this point about their exam and their general research direction.

The A-Exam should be scheduled well in advance of the exam. Students should ideally reach out to their special committee 2-3 months in advance in order to choose a suitable date, particularly if there is an expectation that the exam will occur close to a deadline. The appropriate form (Schedule of Examination form) MUST be submitted to the Graduate School at least 7 calendar days ahead. CAM graduate students are eligible for a Non-Thesis Masters Degree upon successful completion of the A-Exam. In order for this to be awarded, the Committee Chair must check the relevant box on the Results of Examination Form. The form must be turned into the Graduate School within 3 days after the exam.

B Exam

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the Special Committee. When the thesis is completed, the student presents their results at the thesis defense or B exam. The B-Exam (thesis defense) is scheduled with the same form as the A-Exam and must be submitted to the Grad School at least 7 calendar days ahead. The outcome of the exam will be communicated to the student immediately after the exam. The committee will frequently request edits to the dissertation even when the student passes the B exam; these edits may be requested at the time of the B exam or in the days afterward.

The final dissertation must be submitted to the Graduate School no later than 60 days after the B exam. Enrollment in future terms is not permitted after a passed B exam. This includes summer enrollment and support. Students planning to work on their dissertation in the summer with support should take the B exam during the summer term.

Outcomes of Exams

Per Graduate School guidelines, there are three possible outcomes of the A and B exams. The results of the examination are communicated immediately after the exam, and must be filed with the Graduate School within three business days of the exam:

• Pass: When the student passes the exam, it is considered completed. The committee will generally still provide feedback, recommendations, and (in the case of the B exam) requests for amendments to the dissertation.

• Conditional pass: Under a conditional pass, the committee will provide the student and the Graduate school with conditions for passing, including a deadline for these conditions to be met. Once these conditions are met, the exam is considered passed. If the conditions are not met by the given deadline, absent mitigating circumstances such as medical emergencies, the student will no longer be considered in good academic standing and may be asked to leave the program.

• Failure: If a student fails an exam, a re-examination is only allowed with the approval of the special committee, and only after at least three months have elapsed from the time of the initial failure.

While the A and B exams should be taken seriously, most students pass these exams.

Dissertation

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the Special Committee. The dissertation is expected to be nearly complete at the time of the B exam, though the special committee may still request edits after the exam, keeping in mind that the final dissertation must be submitted to the Graduate School no later than 60 days after the B exam. Acceptance of the dissertation requires the approval of all the special committee members.

While it is not a strict requirement, a normal sign of academic progress in applied mathematics is regular publication of results. Consequently, the field expects that dissertations will generally include results of previously published or submitted research. The student should report on the status of any such papers, and their relationship to the dissertation, as part of the dissertation text.

Leaving the Program

While CAM has a high graduation rate, not all students finish the PhD program. Leaving because of a failed exam or loss of standing happens only rarely; but students decide to leave for a variety of reasons, including:

• Moving to another institution, often following an advisor’s move.
• Leaving to pursue a job opportunity, often after a period of personal leave.
• Deciding they simply are not interested in doing applied math research.
• Failing to constitute a Special Committee, or failing to reconstitute a Special Committee after the resignation of a chair.
• Failing to make satisfactory academic progress.
• Failing the A or B exam.

Students who have failed the A exam, and whose committee agrees have performed at the level of a successful final exam for a master’s degree, can leave the program with an MS in Applied Mathematics. As the reasons and circumstances behind students leaving vary greatly, and there is no “one-size-fits-all” support mechanism. Students who will be leaving the program, or who are thinking about leaving the program, you should talk to their advisors and to the CAM director about their plans. The field is committed to supporting all students, including those in the process of leaving. This means supporting the student in the usual manner (e.g. with TA support) to a natural transition point, which is usually at least through the end of the semester in which the decision is made.

Life at the Center

CAM today is a center of several applied math activities on campus. The core of the center is the graduate field of applied mathematics. But we also have a postdoc program, meant to foster interdisciplinary applied math collaborations across campus, and a colloquium series that brings a wide variety of applied mathematicians to campus. The physical heart of the program is a space on the sixth floor of Rhodes Hall where all CAM PhD students and postdocs have their desks.

CAM Space

Each student is guaranteed an individual cubicle in a shared work space environment. This set up allows for more collaboration and mentoring among students while giving a space to work and store materials. A color printer is available, and print jobs with more difficult requirements can be accommodated by working with the Administrative Manager.

Computing Resources

Incoming CAM students are provided with their own computer. This can be either a laptop or a desktop, at the request of the student.

CAM Wiki

The CAM student wiki is a website where students collaborate to gather advice and resources on careers, teaching, computing, and life in Ithaca. The wiki is only open to students.

Colloquium

The applied math colloquium meets on Fridays from 3:45-4:45, with refreshments in the CAM space afterward. The colloquium usually (but not always) meets in Rhodes 655. The talks cover a wide range of applied mathematics, and are meant to be accessible to a broad applied math audience. Students are encouraged to show up even for talks outside their immediate interest!

In addition to the talk, speakers are invited to have lunch with the students (funded by CAM). The lunch meeting is not open to other faculty, and is meant to give students the chance to have a candid conversation with the speaker about mathematics, mathematical careers, and life more generally. Individual meetings are also sometimes available for students to have technical discussions with the speaker.

Colloquium invitations are coordinated by the colloquium committee, which includes a student representative. In addition to helping with the schedule more generally, the student representative is responsible for helping find student hosts to guide the student-speaker lunch. The student representative will also help coordinate the student-selected speaker colloquium, where the speaker is invited by the students rather than by the faculty.

Bill Sears Blitz

The Bill Sears Blitz slide and poster session is an opportunity for CAM faculty and students and community members to mingle and learn about all the interesting things that CAM members are doing. Presenters are welcome to give a poster and/or a one-minute one-slide summary in a “poster blitz” talk. This event takes place in the fall semester, and is meant both as a way for new students to learn about prospective advisors and for the rest of CAM to keep up with what is going on in the center.

First-Year Seminar

During the fall semester, first-year students should try to attend the first-year professional development seminar. Topics will vary, but are likely to include:

• Funding, fellowships, and how the money works
• Advising, mentoring, and building an academic network
• Getting the most from seminars and colloquia
• Time management
• Computing at Cornell
• Publication models and venues in applied mathematics
• How to give a talk
• Reviewing and giving constructive feedback
• Collaboration models in applied mathematics
• Career paths in applied mathematics

Non-first-year students are also welcome!

SIAM Student Chapter

CAM is home to Cornell’s student chapter of the Society for Industrial and Applied Mathematics (SIAM). As members of the SIAM student chapter, students are also eligible to free SIAM student membership

Association for Women in Mathematics

The Cornell Student Chapter of the Association for Women in Mathematics (AWM) was established in 2011 and is supported by Cornell’s Department of Mathematics. CAM students are typically invited each year.

Other Events

Throughout the year, CAM offers a number of social events for students and faculty, including a fall picnic, a holiday celebration, orientation for new students, and a graduation ceremony. In addition to formal CAM events, the CAM students also organize a variety of events. CAM students also frequently attend seminars and colloquia held in peer units across campus, from mathematics to mechanical engineering.

Funding

All full-time students in Applied Mathematics receive a full support package and are guaranteed five years of funding, subject to satisfactory academic progress and satisfactory performance in any assistantship or fellowship roles. Upon availability, students in their sixth year are also funded. CAM does not admit students who are self-funded. Please contact the CAM office for questions or clarifications.

It is important to note that while students are guaranteed funding for five years, the form of support may vary. Due to CAM’s interdisciplinary nature and faculty field structure, the actual dollars of guaranteed support often come from different departments across campus. This arrangement allows students to work closely with faculty, lab clusters, and students from different disciplines while still maintaining a home in CAM. For example, a student may hold a Teaching Assistant (TA) position for two years in Math, a Graduate Research Assistant (GRA) position for two years in Computer Science and a final year be on a Graduate School fellowship. While the funding comes from different sources, the student has received the guaranteed five years of support.

What Funding Covers

All full-time students receive a support package that includes the following:

Tuition

Fall and spring tuition is directly paid by the department supporting the student. The student is not responsible for any charge or duty in this process. The current tuition amount can be found on the Graduate School web site.

Student Health Plan (SHP)

The SHP premium is paid on a yearly basis by the department(s) supporting the student. The student is not responsible for any charge or duty in the process. Information may be found on the SHP web site. Please note that only the student’s health plan is covered in the support package. Optional dental and vision plans are available, but are not included as a part of SHP. Spousal/family insurance is available, but is the responsibility of the student. The student is also responsible for any copays or deductibles incurred as a result of using services while on the plan.

Stipend

All full-time students receive a competitive academic year stipend. Payment amounts vary according to the funding source, as does the payment schedule. All admitted students are informed of the amount of funding (pre-tax) for their first year in their admission letter. Subsequent years of funding may increase or decrease depending on the funding source. The amount received after taxes depends on individual circumstances. All international students are required to obtain an American social security card directly after having arrived in the United States in order to receive their stipend. Cornell University also offers free direct deposit.

Types of Funding

There are typically three types of funding sources: fellowships, Teaching Assistantships (TA), and Graduate Research Assistantships (GRA). All three cover the above components described in a support package. However, stipend amounts and payment schedules will vary.

Fellowships

Fellowships are highly desirable because they do not carry an extra work/effort requirement. There are numerous types of fellowships available, with most being competitive. Fellowship stipends are typically paid in two lump sums divided between the Fall and Spring semesters.

A number of fellowships are awarded by government agencies, such as National Science Foundation, Departments of Energy, Defense and Homeland Security, and others. There are also opportunities for fellowships from companies like Google, Microsoft, and Bloomberg; and there are opportunities from many nonprofits, such as the Sloan Foundation, the Ford Foundation, and the Simons Foundation.

CAM awards the prestigious Presidential fellowship to two new students every year at the discretion of the Admissions Committee. The Cornell Graduate School also offers a number of fellowships according to certain criteria. Whenever possible, the Admissions Committee (for new students) and CAM faculty and advisors (for current students) nominate appropriate candidates for these competitive fellowships.

Teaching Assistantships (TAs)

A TA is responsible for assisting a faculty member in administering a class. Duties could include grading, managing a course web site, leading discussion sections, holding office hours, etc. There are limits to the hours a student can be expected to devote to TA duties (no more than 15 hours per week on average). Please consult the Cornell Policy on Graduate Assistantships for further details and expectations. Stipends are typically paid in bi-weekly paychecks.

TA positions are a very valuable piece of a student’s experience. Being a TA helps reinforce knowledge of material and is a very attractive item to colleges and universities when considering job applicants in academia, especially for tenure track positions. While TA positions require additional work, they have a large payoff and many students very much enjoy helping others learn and become more confident in mathematics.

Graduate Research Assistantships (GRAs)

A GRA position allows a student to undertake research under the direction of a faculty member, usually the Committee Chair. Such a position allows a student to gain invaluable research experience that is helpful for their dissertation research and for finding a research or academic oriented position after earning the PhD. Stipends are typically paid in bi-weekly paychecks.

Funding Responsibilities

Many fellowships come with obligations, such as filing progress reports or participating in an internship. Students who fail in these obligations and consequently have a fellowship withdrawn are not guaranteed replacement funding from CAM.

A student who fails to meet their expectations in an assistantship (TA or GRA) will be notified in writing that their performance is below expectations and will be given specific guidance and time to show improvement. If they fail to improve, they can be dismissed from the assignment, and may be informed that they are ineligible for future appointments. In this case, the student would again not be guaranteed replacement funding from CAM.

A student who fails to meet the expectations of a fellowship or assistantship would not necessarily have to leave the program, provided they remain in good academic standing. However, a student in this case would be considered responsible for seeking their own funding without direct support from CAM (through fellowships, seeking a GRA, or even paying their own tuition).

Though students in CAM are funded by research funds and teaching assignments managed by other units, the CAM director is responsible for the negotiation for those opportunities and for the associated guarantee of funding for students in good standing who meet performance expectations in assistantships. Consequently, in processes that might lead to the termination of a student’s funding guarantees, the CAM director should be involved throughout, and the director (rather than the special committee chair) has authority over decision about future funding guarantees on behalf of the Center.

Outside Employment

Students with a university-funded fellowship, external fellowship, or GRA position may accept employment of no more than eight hours per week, if allowed in the terms of the fellowship. Students working as TAs may work up to five hours per week, so long as the combined hours of the assistantship and work do not exceed 20 hours per week.

Summer Support Options

CAM students are generally supported by sponsored research at Cornell (with an advisor or with another CAM field member) or by internships in industry, national labs, or elsewhere. Internships are a valuable way to gain experience in sectors beyond academia and to learn about different types of problems and career paths. This is the most common form of summer support apart from sponsored research funding provided by an advisor. CAM students are encouraged to consider internships as an option even if they have summer research funding from an advisor.

Some fellowships include summer support, but not all; in particular, the Cornell first-year fellowships include only the fall and spring. CAM students may also receive summer support through teaching positions or by helping to run summer programs. The CAM director and administrator will advertise options and try to help students arrange suitable summer support.

In emergency situations, CAM has a limited amount of support available directly through the center. This is meant as insurance for when other options fall through, and it is not appropriate for students to rely on center funding as a planned summer funding mechanism. Students should expect such support to come with significant non-research work on behalf of the center, as well as a requirement to work from Ithaca apart from university holidays and vacation time as stipulated by Cornell Policy 1.3. The support may be pro-rated based on student travel plans.

There is no tuition charged if a student enrolls in research over the summer (June-August). However, the student is responsible for tuition if they enroll in a class and are expecting to receive a residency unit.

Conference and Travel Grants

The Graduate School offers limited funding for presenting at conferences or undertaking research in other locations. Please refer to the Graduate School web site for details and procedures.

Administrative Matters

The graduate field of Applied Mathematics is part of CAM; but, as with all graduate fields at Cornell, is administratively a part of the Graduate School. Many graduate fields are embedded in departments and colleges and interact with the broader leadership (the chairs and deans) of those units. Though CAM cooperates with several other colleges and their departments to provide funding for TA lines and postdoctoral scholars, it does not belong to any of Cornell’s colleges. Instead, it is one of the centers governed by Cornell’s Office of the Vice Provost for Research and Innovation (OVPRI). Hence, most “local” administration that CAM students will see involves the CAM director and administrative manager.

The CAM Director also serves as the Director of Graduate Studies (DGS) for the field of applied mathematics, and the Administrative Manager serves as the Graduate Field Assistant (GFA). The GFA and DGS manage the affairs of the field and sign graduate student forms and petitions, as well as serving as the first point of contact between students and the Graduate School. The CAM administration is also generally the first point of contact between graduate students and the other academic units on campus, such as the departments that provide TA lines for CAM students.

Residency and Leave

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the Special Committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes four to five years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

Students may request different types of leave of absence status during their program for a variety of reasons, whether personal (e.g. health reasons), professional (e.g. internships), or administrative (e.g. students working after filing their dissertation, but before conferral). Health leaves are available up to a maximum of four years; personal leaves are for up to 12 months, renewable for a maximum of four years. Parental accommodations are also available in the form of either six weeks of paid accommodation (eight weeks for the birth mother for a C-section) OR up to two semesters of reduced load status, depending on circumstances. Students considering a leave of absence should carefully read the associated Graduate School policies.

In absentia status is available for students conducting approved research 100 miles or more away from the Cornell campus while under the guidance of the special committee. This sometimes happens, for example, when students move with an advisor to a different institution (whether the move is permanent or for a sabbatical). To be eligible, students must first have completed two semesters of registration at a Cornell campus.

Academic Standing

Students are expected to meet graduate school milestones or work through approved petition processes. Students who have formed a special committee are also expected to meet the expectations of their committee.

When a committee chair deems a student’s progress less than satisfactory on the SPR (either “Needs Improvement” or “Unsatisfactory”), the DGS will work with the student and the advisor on a plan to address issues.

Students who receive an “Unsatisfactory” rating on their SPR have made little or no progress in the preceding one or two semesters, and are not considered to be in good academic standing with the Graduate School. In this case, the DGS will work with the student, advisor, and Graduate School on a detailed improvement plan, which is approved by (and then enforced by) the graduate school.

Petitions and Other Forms

Petitions and other forms are available from the graduate school web site. These forms include standard processes used by every student (scheduling exams and registering the results of those exams, filing a dissertation), as well as petitions for change of status or for extensions on program milestones. For guidance on graduate school petitions and forms, students should communicate with the Administrative Manager.

Other Cornell Resources

The Graduate School web page has a wealth of information for prospective and current students. In particular, the Graduate School resources page has pointers to numerous resources around Cornell for academics, health and wellness, safety, managing as an international student, student life, etc.

Mental health challenges are common in graduate school, and students should know about Cornell’s resources:

• For mental health information: https://mentalhealth.cornell.edu
• For 24/7 mental health assistance, including Talk & Text lines: https://mentalhealth.cornell.edu/247-help
• For mental health care options at CAPS (Counseling & Psychological Services): https://health.cornell.edu/services/mental-health-care
• Let’s Talk drop-in Zoom consultations are 3-4:30 PM on weekdays: https://health.cornell.edu/services/mental-health-care/lets-talk

For any concerns about unethical behavior, biased speech, etc, resources students should know about are the Office of Institutional Equity and Title IX, Office of the University Ombudsman (https://www.ombudsman.cornell.edu) and the bias reporting center (255-1426, report_bias@cornell.edu).