The objective of the department’s Master’s program is to produce graduates who achieve a mastery of some of the modern developments Applied Mathematics and Statistics.

The current University Catalog contains a detailed description of the department’s courses, programs, and requirements and a list of the current faculty and their interests. The purpose of this handbook is to present supplemental information; it should be read along with the departmental listing in the Catalog.

The Master of Science in Engineering (M.S.E.) in Applied Mathematics and Statistics ordinarily requires a minimum of two semesters of registration as a full-time resident graduate student. To obtain departmental certification for the master’s degree the student must:

**1. **Complete satisfactorily at least eight one-semester courses of graduate work in a coherent program approved by the Department Head.

(a) Most 3- or 4-credit AMS Department 600-level and 700-level courses are satisfactory for this requirement. (553.604, 553.689, and research/internship courses may not be counted.)

(b) Certain courses in other JHU departments are also acceptable, and must be *fully approved in advance*. At most 3 courses outside the department may be counted toward the 8 (or 10) courses used toward Master’s degree requirements. Non-JHU (transfer) courses may not be used toward degree requirements.

(c) JHU courses listed as 2-credit courses (with the exception of research/internship courses) may count only as one-half course. JHU Public Health courses may count only as one-half course. JHU 1-credit courses may not be used.

**2.** Meet either of the following options:

(a) Submit an acceptable research report based on an approved project (see *Research/Master’s Thesis* below); or

(b) Complete satisfactorily two additional one-semester graduate courses (with the same restrictions listed in section 1) and as approved by the faculty advisor and Department Head.

**3.** Satisfy the computing requirement (see *Information for Computing Certification* below).

**4.** Complete an area of focus by taking three courses in one of the following areas:

(a) Probability Theory.

(b) Statistics and Statistical Learning.

(c) Optimization and Operations Research.

(d) Computational and Applied Mathematics.

(e) Discrete Mathematics.

A list of courses that can be counted toward each area of focus will be maintained and updated every year by the department (see *Area(s) of Focus Approved List of Courses* below for the current version). Some courses from other departments can be eligible to count toward area of focus. They can be used within the three-course limit specified in point 1) above.

**5.** Complete training on the responsible and ethical conduct of research. (WSE Responsible Conduct of Research.)

**6.** Complete training on academic ethics.

**7.** Students in the AMS MSE program are strongly encouraged to register in EN.553.801 Department Seminar in at least one semester of their program.

**An overall GPA of 3.0 must be maintained in courses used to meet the program requirements. At most two course grades of C or C+ are allowed to be used, and the rest of the course grades must be B- or better.**

Substitutions and exceptions are permitted at the discretion of the Department Head.

Each candidate for the master’s degree must submit for approval by the department a program stating how the degree requirements will be met. This should be done during the first semester of residence and again each semester upon registration. Please note that any changes to an approved program will require new approvals. If you make any change(s), you will need to submit a revised form, which will need new electronic approval. It should not be assumed that changes to your program will be approved during your final semester of study before requesting certification for the Master’s degree. Click here to access the form.

Students are evaluated at the end of each semester, and failure to make what is considered satisfactory progress in the program is grounds for being placed on Academic Probation or dismissal. The *Advising/Evaluation* section of the handbook below provides additional information.

**Probability Theory**:

110.445 Mathematical and Computational Foundations of Data Science;

553.626 Introduction to Stochastic Processes;

553.627 Introduction to Stochastic Processes in Finance I;

553.628 Introduction to Stochastic Processes in Finance II;

553.629 Introduction to Research in Discrete Probability *(until Summer 2018 only)*;

553.633 Monte Carlo Methods;

553.720 Probability Theory I;

553.721 Probability Theory II;

553.722 Introduction to Stochastic Calculus;

553.763 Stochastic Search and Optimization;

553.764 Models, Simulation and Monte Carlo.

**Statistics and Statistical Learning:**

110.445 Mathematical and Computational Foundations of Data Science;

553.602 Research and Design in Applied Mathematics: Data Mining;

553.613 Applied Statistics and Data Analysis;

553.614 Applied Statistics and Data Analysis II;

553.616 Intro to Statistical Learning, Data Analysis and Signal Processing;

553.617 Mathematical Modeling: Statistical Learning;

553.632 Bayesian Statistics;

553.634 Elements of Statistical Learning;

553.636 Introduction to Data Science;

553.639 Time Series Analysis;

553.650 Computational Molecular Medicine;

553.669 Large-Scale Optimization for Data Science;

553.724 Probabilistic Machine Learning;

553.730 Statistical Theory I;

553.731 Statistical Theory II;

553.733 Nonparametric Bayesian Statistics;

553.735 Topics in Statistical Pattern Recognition;

553.737 Distribution-free Statistics and Resampling Methods;

553.738 High Dimensional Approximation, Probability, and Statistical Learning;

553.739 Statistical Pattern Recognition Theory & Methods;

553.740 Machine Learning I;

553.741 Machine Learning II;

553.743 Equivariant Machine Learning;

553.742 Statistical Inference on Graphs;

553.767 Iterative Algorithms in Machine Learning;

553.782 Statistical Uncertainty Quantification;

553.796 Random Matrix Theory in Data Science and Statistics.

**Optimization and Operations Research:**

553.600 Mathematical Modeling and Consulting;

553.653 Mathematical Game Theory;

553.661 Optimization in Finance;

553.662 Optimization for Data Science;

553.663 Network Models in Operations Research;

553.665 Introduction to Convexity;

553.667 Deep Learning in Discrete Optimization;

553.669 Large-Scale Optimization for Data Science;

553.761 Nonlinear Optimization I;

553.762 Nonlinear Optimization II;

553.763 Stochastic Search and Optimization;

553.765 Convex Optimization;

553.766 Combinatorial Optimization;

553.767 Iterative Algorithms in Machine Learning;

553.769 Topics in Discrete Optimization;

553.797 Introduction to Control Theory and Optimal Control.

**Computational and Applied Mathematics:**

110.445 Mathematical and Computational Foundations of Data Science;

553.681 Numerical Analysis;

553.683 Numerical Methods for Partial Differential Equations;

553.688 Computing for Applied Mathematics;

553.691 Dynamical Systems;

553.692 Mathematical Biology;

553.693 Mathematical Image Analysis;

553.694 Applied and Computational Multilinear Algebra;

553.780 Shape and Differential Geometry;

553.784 Mathematical Foundations of Computational Anatomy;

553.792 Matrix Analysis & Linear Algebra;

553.793 Turbulence Theory;

553.795 Advanced Parameterization (through Fall 2022);

553.795 Matrix Analysis and Linear Algebra II (as of Spring 2023):

**Discrete Mathematics:**

At least one of:

553.671 Combinatorial Analysis;

553.672 Graph Theory;

553.766 Combinatorial Optimization;

but the other two courses may include 553.629 Introduction to Research in Discrete Probability* (until Summer 2018 only)* and the Computer Science offerings:

601.630 Combinatorics & Graph Theory in Computer Science;

601.631 Theory of Computation;

601.633 Intro Algorithms;

601.634 Randomized & Big Data Algorithms;

601.635 Approximation Algorithms;

601.645 Practical Cryptographic Systems.

This list of courses is based on recent offerings. Not all classes are available every year, and substitute classes may be accepted if approved by the advisor and the Academic Affairs Committee.

### IMPORTANCE OF COMPUTER LITERACY AND COMPUTING COMPETENCE

Familiarity with computing is essential to applied mathematics, and students should aim for practical problem-solving capability for computing in applied mathematics. Thus, every department graduate should possess a working knowledge of the utilization of computers and the fundamentals of scientific computing. This includes, but is not limited to, such topics as: computer programming (e.g., FORTRAN or C++), numerical software packages (e.g., MATLAB), symbolic computations (e.g., MAPLE), technical word processing (e.g., LaTeX), and professional presentation (e.g., PowerPoint).

The requirement below is a minimal one, aimed at ensuring that students demonstrate some ability at using the computer for problem-solving through homework assignments and projects.

### TIMETABLE

It is expected that students discuss their plans to meet this requirement with their faculty advisors. As early as possible, students and advisors should agree on a program of work whose satisfactory completion would meet the computing requirement. Students with no previous background in computing should first acquire basic competence during their first year of residence, either by independent study, or by participation in an elementary course.

### CERTIFICATION AND EVALUATION

It is recommended that students meet this requirement within their first year of residence.

Students meet this requirement typically by receiving a grade of B- or better in taking an approved AMS department course.

The list of approved courses together with the years in which versions of these courses can be used to meet the requirement is:

- 110.445 Mathematical and Computational Foundations of Data Science (Spring 2020 or later)
- 553.600 Mathematical Modeling and Consulting (Fall 2017 or later)
- 553.613 Applied Statistics and Data Analysis (Fall 2017 or later)
- 553.632 Bayesian Statistics (2015 or later)
- 553.633 Monte Carlo Methods (Fall 2017 or later)
- 553.634 Elements of Statistical Learning (Fall 2024 or later)
- 553.636 Introduction to Data Science (Fall 2017 or later)
- 553.650 Computational Molecular Medicine (Fall 2017 or later)
- 553.669 Large-Scale Optimization for Data Science (Fall 2022 or later)
- 553.681 Numerical Analysis (2007 or later)
- 553.683 Numerical Methods for Partial Differential Equations (2023 or later)
- 553.687 Numerical Methods for Financial Mathematics (Fall 2017 or later)
- 553.688 Computing For Applied Mathematics (Fall 2017 or later)
- 553.689 Software Engineering for Data Science (Fall 2024 or later)
- 553.693 Mathematical Image Analysis (Fall 2017 or later)
- 553.733 Nonparametric Bayesian Statistics (2018 or later)
- 553.740 Machine Learning (Fall 2018 or later)
- 553.741 Machine Learning II (Spring 2020 or later)
- 553.753 Commodity Markets & Green Energy Finance (2013 or later)
- 553.761 Nonlinear Optimization I (2012 or later)
- 553.762 Nonlinear Optimization II (2007 or later)
- 553.763 Stochastic Search and Optimization (Spring 2018 or later)
- 553.765 Convex Optimization (2016 or later)
- 553.780 Shape and Differential Geometry (2015 or later)
- 601.675 Machine Learning (Fall 2017 or later)
- 601.682 Machine Learning: Deep Learning (Spring 2018 or later)

**Finding Research Opportunities**

To find research opportunities students should contact the faculty directly to inquire.

- Visit the Faculty page for a list of our faculty and their research interests.
- Select a faculty member or two whose work interests you.
- Be prepared to talk about what interests you about their research. On each Faculty member’s “full profile” pages are publications of their recent papers, which you can often look up in the MSE Library. Read a couple papers. While you won’t be expected to know, much less understand everything in the papers, that fact that you took interest and can discuss what you read will impress professors.
- Sometimes, professors would like to see your resume and/or transcript, so keep those handy when you make your first contact.
- Contact the faculty members of interest and express your interest in their research and that you would like to get involved in their research.
- You can reference theses written by former students at https://jscholarship.library.jhu.edu/handle/1774.2/844 or consult our librarian, Sue Vazakas [email protected].

**Master’s Thesis Timeline**

Once you have identified a thesis advisor******, you should plan on working for roughly one year to conduct thesis research and write the thesis. You should develop your timeline by working backwards from the deadline posted for your graduation term.

__Sample__ timeline for May graduation:

1. September through November of previous semester should be spent on:

(a) Identifying problem for investigation

(b) Obtaining appropriate data

(c) Review of background literature

(d) Review of available methodology

2. By mid-December, the problem should have been identified and December through February should be devoted to doing the work.

3. Outline of essay should completed and approved by March 1^{st}.

4. Final draft of essay should be completed by April 1^{st} allowing for substantial back and forth with reader(s)

5. Final version of essay should be presented to reader(s) May 1^{st} to allow for minor revisions.

******The thesis advisor must hold a current faculty appointment in the AMS Department. Any duly appointed member of the AMS Department holding the rank of assistant professor or higher, including lecturers, is eligible. If you are primarily conducting thesis research with a faculty member outside of the AMS Department, you will also need an additional advisor from the AMS Department who directs, advises and supervises your efforts throughout the process of research. This advisor must also read drafts of write-ups as they are written, etc. to provide feedback. The AMS Department thesis advisor must write the Reader’s Letter, or sign as a second reader if you are primarily conducting research with a faculty member outside of the AMS Department. Any questions about faculty eligibility to serve as thesis advisor should be discussed with academic staff before starting thesis research.

**Thesis/Research Requirements**

- Students must register for their thesis advisor’s section of EN.553.809 in each semester they are conducting research. (Note that additional tuition will be charged for summer registration.)
- You should be prepared to have a conversation with your thesis advisor about research/thesis expectations that clarifies what would be considered acceptable work in order to meet the requirement. The expectations are very much advisor-dependent, so this is an important conversation. Since the thesis degree option is in place of two courses, the work/effort put into the research should be at least as much as would be done in two courses.
- A Reader’s Letter (sometimes called the Reader’s Report) must be submitted for all students receiving a master’s degree with thesis/essay. This is typically written by your thesis advisor, and sometimes a second advisor. Any duly appointed member of the AMS Department holding the rank of assistant professor or higher, including lecturers, is eligible for selection as a reader. Any questions about eligibility to serve as a reader should be discussed with academic staff.
- Your final approved thesis must be submitted to the library by the appropriate deadline. Details and formatting requirements are listed at https://www.library.jhu.edu/library-services/electronic-theses-dissertations/.
- Students may view theses written by former students via JScholarship.

### ADVISING

The primary source of advice and counseling about a student’s progress is the faculty advisor.

When a student first enters the department, the student is assigned an academic advisor. The academic advisor assists the student in selecting courses and other administrative tasks, and provides general career guidance.

### EVALUATION

The department conducts semi-annual reviews of all graduate students, and notifies each student in writing of any concerns.

At the end of each academic semester, grades are reviewed, and if a student is a teaching assistant, the supervising faculty member is asked for a written performance evaluation.

A full-time master’s student who fails, in a given semester, to receive a grade of B- or better in at least two courses in their master’s program (not counting the department seminar) will be placed on Academic Probation. For a full-time master’s student on Academic Probation, failure to pass at least two courses with a B- or better in their master’s program (not counting the department seminar) is grounds for dismissal. Also, in any given semester, whether or not a student is on Academic Probation, they may be dismissed if they do not receive *any* grades of B- or better in their master’s program (not counting the department seminar).

The Department Seminar meets weekly for the presentation and discussion of current research work. Both University scholars and invited guests appear, and a wide variety of topics is covered in the course of a year.

The department sometimes hires Master’s students as temporary TAs or office assistants, with the level of salary dependent on the duties required and qualifications of the student. Students may apply for these positions after having completed at least one semester at JHU. Temporary TA salaries are generally lower than the standard TA salary for similar duties (since the standard TA salary is viewed as primarily financial aid rather than payment for duties).

All students serving as TAs are expected to make appropriate efforts to improve their language and communication skills, which may require participating in training and improvement courses offered by the university.

The Milton S. Eisenhower Library has extensive resources of books and journals and can draw freely on large nearby collections such as the Library of Congress. The facilities of the University Computing Center are available to all students for research and instruction. The Department also has high‑capability computing resources for graduate students and faculty research in its quarters in the Wyman Park Building.

### PURPOSE

The computing resources of the Johns Hopkins University Department of Applied Mathematics and Statistics exist to meet the computing needs of the Department’s faculty and graduate students for the purposes of instruction and research, and to provide access to relevant information and services of the Internet computer network.

### ADMINISTRATION

We distinguish between operation (otherwise known as system management or administration) and administrative oversight. Operation is considered to consist of those tasks related to the maintenance of software, hardware, user accounts, and any other tasks which directly affect the status and performance of the physical resources. Administrative oversight will consist of the establishment and maintenance of software licenses, procurement of equipment, establishment of policies, and all other tasks not related to operation.

The computing resources of the Department are to be operated by one or more designated graduate Computer Assistants, possibly in collaboration with members of the faculty. The administrative oversight of the computing resources is the responsibility of the Departmental Research and Facilities Committee.

### AVAILABILITY

The computing resources of the Department will be available to those who are eligible for accounts on the Departmental server(s), as described below, for tasks consistent with the conditions of usage described under **Acceptable Usage** below.

All faculty, staff, and graduate students of the Department are eligible for computer accounts on the Departmental server(s). Accounts for faculty and graduate student users will be maintained through the end of the first full semester after the user’s departure. Accounts for staff members will be maintained at the discretion of the Research and Facilities Committee after the staff member’s departure.

Undergraduate students, students from other departments, and former students from the Department of Applied Mathematics and Statistics, or any other person not specifically eligible as per above may obtain accounts or extend accounts past the normal termination date, as follows. The requester must have the sponsorship of a member of the Departmental faculty. The sponsoring faculty member should present the request to the Research and Facilities Committee and Department Chair for approval, whereupon the operator(s) will be instructed to create or maintain the account as specified.

If resource quotas are enforced, those users with accounts under special dispensation as described above may be required to observe resource limits different from those of eligible Departmental users.

The Department Chair is ultimately responsible for all decisions to create or terminate accounts on the Department’s server(s). The Research and Facilities Committee recommends actions on these matters to the Department Chair. Users will be notified by e‑mail two weeks prior to termination, in order to have time to properly clean out the account.

### ACCEPTABLE USAGE

The users of the Department’s computing resources are responsible for adhering to all Johns Hopkins usage requirements, as well as all local, state, federal, and international laws.

Users are expected to observe the following:

**General**

- Accounts are issued on a person-by-person basis. Allowing anyone else to access an account is therefore prohibited, and repeated offenses may result in termination of the user’s account.
- Accounts accessing, altering, duplicating, or deleting any data belonging to other users without that user’s consent is prohibited. This includes, but is not limited to, so affecting system data files maintained by the Operator(s), such as system quota databases or password files.
- Any unauthorized and deliberate action which results in the damage or disruption of a computer system is a violation of Acceptable Usage, regardless of the location of the affected system.

**Publication (mail and Web usage)**

- Any attempt to forge the source or sender of any network traffic, including but not limited to electronic mail, Web documents, or USENET articles, is prohibited.
- Any attempt to read, write, alter, or delete another user’s electronic mail, USENET articles, etc., is prohibited.
- Sending harassing, obscene, or threatening electronic mail, USENET articles, etc., is prohibited. This includes the sending of electronic “chain letters”.
- Using network or computer facilities for any commercial or for‑profit purpose is prohibited. This

includes, but is not limited to, e‑mail advertisements, professional correspondence that is not

Department-related, and the inclusion of commercial advertising on Web pages.

**Network security**

- Attempt to gain unauthorized access to any computers or networks (Departmental or otherwise) is forbidden.
- Copying of copyrighted materials without permission is not allowed.

The reasons for these restrictions should be clear. Further information and suggestions are available online. Interested users may, for example, consult the Netiquette guide on the World Wide Web.