Graduate Program Overview

The department offers Ph.D. degrees in both mathematics and statistics as well as M.S. degrees in applied mathematics and statistics. We are committed to excellence in research and teaching in a friendly and diverse academic environment.

People

Life in the Department

Options and requirements

Alumni Testimonials

Zoi Rapti is currently an Associate Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign. Her main research focus is on mathematical biology with applications to infectious diseases. She mostly uses differential equations, both ordinary and partial, and sometimes stochastic models to describe these disease systems. Recently she has become interested in the analysis of epidemic time-series from a data-analytical point of view. She still remembers fondly her time at UMass Amherst.

The applied mathematics and analysis professors and, in particular, my advisor Panos Kevrekidis made those five years at UMass both enjoyable and productive. After visiting other graduate programs in the US, I appreciate even more the small size of the graduate program and the attention graduate students were receiving at the UMass program. Having a private office as a graduate student now seems like a true luxury! Having professors that constantly encourage their students to talk to visitors, attend national conferences, write manuscripts and be willing to write recommendation letters and notes to colleagues on their behalf, had long-lasting effects on my career.

Julie Rana enrolled into our PhD program after graduating from Marlboro College, a small liberal arts college in Vermont. Her thesis "Boundary divisors in the moduli space of stable quintic surfaces", written under supervision of Jenia Tevelev, won the department's distinguished thesis award. Dr. Rana's research interests are in algebraic geometry, which studies shapes defined by polynomial equations using an array of algebraic, topological and analytic techniques. After graduating from UMass and teaching for two years as the Math Fellow at Marlboro College, Dr. Rana held a postdoctoral position at the University of Minnesota in Minneapolis. She is now a tenure-track Assistant Professor at Lawrence University in Appleton WI, where she lives with her husband and their twins Isha and Akash, who were born while she was a graduate student.

The best part of grad school at UMass was the community of women graduate students and lecturers in the math department. I honestly don't think I would have finished without their support. I also loved the Valley Geometry Seminar and the Geometry Reading Seminar. Although I was lost most of the time (especially for the first couple of years), I was inspired by the talks at VGS, and really appreciated the opportunity to give talks at the reading seminar.

Bright Antwi Boasiako enrolled into our regular MS statistics program in 2016 after completing a BS in Actuarial Science in 2015 from the Kwame Nkrumah University of Science and Technology (KNUST), Ghana. He graduated in 2018 and his current position is Actuarial Assistant in New York Life Insurance Company.

One of the things that surprised me the most about the Statistics program at UMass was the welcoming attitude of the faculty, this made it easier to tap into their broad knowledge base and experience. I think it is a thing with the department, everyone I encountered was nice! The program itself has a very strong theoretical foundation of statistics with an opportunity to practice through Statistical Consulting. The consulting bit was extremely helpful. It provided an opportunity to work on real-world problems, and at the same time give back to our community. It was also a great way to learn important soft skills such as communication, professionalism and teamwork through client and team meetings. We were always motivated and empowered to take lead roles in such deliberations. Working in a Life Actuarial role, my training at UMass helps me take a data driven perspective of my day-to-day, in connection with actuarial models, to better understand the mechanics of my job and gain more insight into findings. I feel like I'm my own little consultant at my desk and I owe that to the great work by the faculty and staff at the department!

Holley Friedlander is an Assistant Professor in the Department of Mathematics and Computer Science at Dickinson College. She came to UMass after completing a Bachelor of Arts in Mathematics at the University of Vermont. Her research is in number theory, arithmetic geometry, and combinatorial representation theory.

As a prospective student, I wanted a supportive program with close faculty-student interaction. The wide range of research offerings at UMass relative to the size of the graduate program allowed me to get to know faculty and explore areas through topics courses and seminars prior to choosing a research focus. I continue to reap the benefits of the many opportunities I had as a student to build my professional network, including the entire semester I spent at the Institute for Computational and Experimental Research in Mathematics (ICERM). The teaching assistantship program gave me experience without overloading me with work, and I have no doubt that my work as instructor of record at UMass and involvement with the Undergraduate Math Club (for which I was awarded the Department?s Distinguished Teaching Award) helped me land my first position as a Visiting Assistant Professor at Williams College. In the years since graduation, the number theory group, especially my advisor Paul Gunnells, has continued to provide mentorship and support my career.

Boxuan Cui enrolled into our Fifth Year MS statistics program in 2010 after graduating from UMass Amherst with an BS in Mathematics. In 2012, he graduated statistics program with an MS and he is currently Data Science Manager at TripAdvisor. Boxuan has a grateful memory of the two years in the MS Statistics program at UMass Amherst.

The MS Statistics program offers a great blend of theoretical and applicable coursework. Throughout the program, students not only get to understand complex theories, but are also able to apply the knowledge to real-world problems. In addition to the standard statistics courses, I find the cross disciplinary research, independent study and the statistical consulting service extremely helpful in preparing me for my future career. From data analytics to presentation/communication skills, from coding to prototyping solutions, I have acquired most essential skills to succeed as my career progresses. As a fresh graduate, these also opened doors for various interview and networking opportunities. During my study in the program, there were also regular colloquium and seminars. Students were encouraged to attend and participate, so that they can stay up-to-date with the latest research. These meetings also broadened my views and field of interests, so that I could better understand my personal aspiration, and choose relevant courses to further my learnings. To conclude, I am grateful for everything the MS Statistics program had offered me. It was a key to my next journey after academia, and I couldn't feel more fulfilled having graduated from UMass Amherst, and from this program.

Dr. Isabelle Beaudry graduated from UMass Amherst with a PhD in Statistics in 2017 and currently she is an Assistant professor, Statistics Department at Pontificia Universidad Católica de Chile.

My journey as a PhD statistics students began in 2011 after practicing as an actuary for a number of years. The Department of Mathematics and Statistics at UMass Amherst was among my top choices of program because of one of the research areas, that is, statistical methodological for Social Sciences. In addition to the research interests match, selecting this Department to pursue doctoral studies turned out to be a very satisfying experience for a wide variety of unexpected reasons.

In addition to the solid, modern and engaging curriculum designed to help students prepare for academic and professional careers, the Department provided me with various opportunities to develop the skills needed to become an academic. Examples of these opportunities included teaching my own courses, participating in the writing of a number of grant proposals, mentoring students, peer reviewing papers, etc. These skills have helped me secure an academic position in one of the highest ranked universities in Latin America.

The Department also promotes interdisciplinary research. For instance, the Computational Social Science Institute is one of the initiatives in which various professors and students from the Department participate. This Institute was of particular interest to me due to its research focus, but more importantly, it provides students exposure to multidisciplinary research which highly contributes to the training of well-rounded academics and professionals.

One of the main reasons for my positive experience is the incredible dedication of the Faculty members and Personnel from the Department. The professors are available to the students and really go the extra miles to make sure optimal conditions are in place for the students to learn. For instance, regular working groups are organized where students may present their work and hear about others’ work in a friendly environment. Also, I will be forever grateful for the extraordinary support I received from everyone in the Department when I suffered a huge loss in my life.

In summary, I am really appreciative of all the amazing individuals in the Department I have met and who all contributed to the successful completion of my studies as well as the quality of the education I received.

Dr. Xiangdong Gu enrolled into our MS statistics program in 2010 and graduated with an MS in 2012. Currently he is working as Lead Data Scientist at MassMutual Financial Group. Dr. Gu has a very fruitful experience in the MS Statistics program at UMass Amherst.

The best thing about this program is that it prepares students not only with extensive practical skills that can be directly applied to real world projects but also with solid theoretical background to understand how things work and solve problems in greater depth. The department is very supportive for students to gain practical experience through industry internship, research assistantship and teaching assistantship (I want to highlight that there are many RA/TA opportunities available even for MS students). Professors here are knowledgeable, helpful and approachable. Students out of this program can easily find industry jobs or enter PhD programs for further study.

Ngoc Thai graduated from UMass Amherst with a MS in Statistics in 2013 and she is currently a data scientist at Harvard Pilgrim Health Care where she builds statistical models from large claims and clinical databases to help identify effective interventions for care management programs. More recently she has also started pursuing a PhD in Population Health at Northeastern University where her research interests focus on social determinants of health and health economics.

I owe a lot of what I have been able to do in both industry and advanced study to the Statistics program. In my opinion there are two attributes of the program that were instrumental in preparing me to work as a statistician: the strong curriculum and various faculty-guided research opportunities.

The broad curriculum that spanned both theory and applications provided a solid foundation for my work. I studied not only foundational material such as the theory of statistical inference and generalized linear models, but also more specialized topics such as Bayesian Inference and Network Analysis. I am pleasantly surprised at how often this material ties into to my current projects.

The department also provided me with valuable opportunities to apply what I learned in the classroom to real-world projects, both through my consulting work with the Five College Consortium and other research opportunities such as the MS final project. For my final project I worked on a social network study with two other graduate students under the guidance of two very engaged faculty members, which was a great opportunity to learn from experts in their fields and collaborate with fellow grad students. Not only did this experience help build my ability to conduct a statistical research study, it also improved my interpersonal skills when working in a team, both of which are highly valuable skills for a statistician. I was also able to showcase this research experience during my job interviews which garnered positive feedback from hiring managers.

I feel very fortunate to be able to utilize my statistical training in my work in healthcare research which was something I had hoped to do before the MS degree. This was made possible in large part due to the foundation and direction that the program gave me, and for that I am really thankful.

Kostis Gourgoulias is currently a Research Scientist, assisting the research division at  Babylon Health with the goal of making healthcare affordable and accessible to every human on Earth. His day-to-day work is split between research work on the mathematics behind generative modelling, amortized inference, and machine learning methods, as well as the development of prototypes for the products at Babylon. He graduated in 2017 with a PhD in (applied) mathematics, jointly supervised by Professor Katsoulakis and Professor Rey-Bellet. His thesis, titled “Information Metrics for Predictive Modelling and Machine Learning”, was awarded the distinguished thesis distinction from the Department of Mathematics and Statistics.

I had great fun during my PhD studies in the department. I remember when I first read the acceptance letter (which I still have!) about how intellectually stimulating the studies in Amherst will be -- I now think that is an understatement! Apart from the standard curriculum, I had the opportunity to take classes discussing ideas at the forefront of research in applied mathematics, where we would study and present published work to the rest of the class.

The close collaboration of the Mathematics and Statistics department with other disciplines made venturing out and meeting Professors from other departments simple (the department has strong ties with biostatistics, physics, computational social science, computer science, etc., through the work of the faculty) and the applied math seminar always had interesting and varied topics from the frontier. In fact, I was often given the chance to talk to some of the speakers over lunch or dinner, which gave me unique insights into the life after the PhD -- a lot of my fellow graduate students took advantage of this too!

I felt like the department supported me throughout the creative process of writing the PhD; I had a lot of attention from the computing centre and other faculty. I never felt uncertain about my funding and communication regarding logistical issues, such as travel funding or summer assistantships, was always clear.  When I, with a few friends from biostatistics, engineering, evolutionary biology, and CS, decided to start our own data science group (http://gridclub.io) so that we could practice more in the problems that are of interest in industry, the department had a modern stance and supported the endeavour wholeheartedly.

After the PhD I was able to extend my research around statistical inference in the age of super-expressive models, like deep neural networks, etc.,  and to me, that speaks to the strong background knowledge I acquired by the people in the department and the insightful directions of my advisors. I think it’s a great place for a prospective student to carry out PhD research.

 

People

The permanent faculty teach most of the graduate courses and provide formal and informal supervision of graduate students' careers. Students also learn a great deal from interacting with each other both in and out of class. The department also has at any time a number of temporary postdoctoral visiting assistant professors. They are usually from one to three years past their Ph.D., and provide a useful bridge between students and areas of current research.

The Department currently has 91 graduate students, of whom approximately 27% are women and half are from outside the U.S. We embrace the diversity of our department and community, see our statement on equity, inclusion and diversity. The UMass chapter of Association for Women in Mathematics provides resources and networking opportunities for women-mathematicians. We actively seek to increase the proportion of women and of minority students. Foreign students with strong mathematical preparation and a good command of spoken English are encouraged to apply.

Life in the Department

The early part of a graduate student's time will be spent on coursework. These courses provide the background necessary for further study in mathematics, and prepare students for the qualifying exams. A diverse group of "topics" courses are offered every year to introduce students to areas in which our faculty are currently working. Students can also take directed reading classes with faculty.

Outside of formal class instruction, there are other ways students can participate in the mathematical life of the department. There are a wide variety of seminars covering the range of pure and applied mathematics and statistics, and students are encouraged to attend them to become more familiar with current research. Talks in the department colloquium are meant for a general mathematical audience, and so are generally more accessible to graduate students, and seminars such as GRASS and Reading Seminar in Algebraic Geometry are specifically aimed at graduate students.

Our graduate students are funded as Teaching Assistants. The Teaching Seminar helps students to become excellent instructors. Graduate students run a Math Club for undergraduate students.

Options and requirements

Mathematics and statistics form separate programs within the department; students are admitted either to one program or the other, and permission is required to change programs. The M.S. in pure mathematics is normally only offered to students on the Ph.D. track; we do not generally admit students whose objective is a masters' in pure mathematics. The applied mathematics M.S. program is formally a separate program, with its own requirements and admissions process. It is possible to apply for both the Ph.D. and M.S. in statistics with the same application.

 

A complete description of the requirements for each of these degrees can be found in the Graduate Handbook.

More information about graduate options in statistics can be found here.

Information on a fifth year MS in Statistics for Five College students can be found here.

For more information about the applied math master's program, click here.

Applied Mathematics M.S. Program

This is a two-year professional degree program designed to prepare students in the mathematical sciences for a career in contemporary industry or business. The students receive thorough training in applied mathematics and scientific computing, exposure to mathematics-related subjects in science and engineering, and experience in a group project. The program's graduates have been successful in securing desirable positions with companies ranging from small, local firms to large, international corporations.

Director: Qian-Yong Chen

On this page:
Program goals and structure
Student experiences and employment
Group projects
Application and admissions
Possible interdisciplinary courses
Center for Applied Mathematics and Computation

Program goals and structure

The Master's Degree Program in Applied Mathematics is specially designed to prepare graduates for a successful career in today's industrial/business world. Accordingly, the program is structured into the following three components:

  • a core of graduate courses in applied subjects within the Department of Mathematics and Statistics;
  • a selection of advanced courses in other departments including, but not limited to, these;
  • a group project in which an applied scientific problem is undertaken in a colloborative effort.

The graduate courses in the Department concentrate on Analytical Methods, Numerical Methods, and Probability/Statistics. These two-semester courses sequences give the student a thorough background in advanced applied mathematics.

The elective courses outside the Department are determined depending on each student's interests and preparation. In recent years, they have been chosen from Computer Science, Engineering (Industrial, Mechanical, Electrical), Physics, and Management Science. These courses expose the student to the use of practical mathematical tools by scientists and engineers.

The group project is the most novel component of this program. It is intended to emulate industrial teamwork on a large, technical problem. Through the combined efforts and diverse talents of the group members, a mathematical model is developed, a computer code is implemented, and a final report is written. In the process, the students learn how to start solving a new and hard problem, how to make a professional presentation of their work, and how to collaborate effectively with their coworkers.

Student experiences and employment

How is student life in the program? A comradery develops naturally among the students through their common coursework and the group project class, which meets weekly as a seminar and requires joint work outside class. There are around ten students in the program in any given year. This size allows the students and the faculty to interact easily and frequently. Also, the second-year students often share their experiences and contacts with the first-year students.

Where do the graduates go? While a few find the program useful for developing their mathematics prior to pursuing other advanced degrees, most graduates find jobs in industry. Typically, these jobs are in high-technology firms, often falling under the label of software development. Some recent graduates are employed by large, well-known companies: DEC, GTE, Hewlett-Packard, MIT Lincoln Labs, Pfizer. Others work for smaller, local firms, such as Artios (Ludlow, MA) and Amherst Process Instruments (Hadley, MA).

How do the graduates fare on the job market? It appears that many employers prefer to hire candidates having strong mathematical training together with good programming skills, rather than those with other, more specialized, degrees. And, indeed, all the recent graduates from the program have secured good jobs upon completion of the program. Many have received several attractive offers.

What do the recent graduates have to say? Feedback from our graduates underscores the value of program, and the group project in particular, as preparation for the workplace. Here are a few examples of their comments:

A 1993 grad now at Lincoln Labs writes, "One thing I would like to mention is that even though I may be using more computer skills than math, I feel that my math background has helped a lot. When I was hired, my boss told me that she preferred someone with a math background who could program than a computer science major. I think that was the key for me. Also, the applied math group project is a great idea because it teaches you to work as a group and prepares you for the "real world"."

One of our 1994 alumni, who worked for a while at Fuji Capital Markets Corporation before returning to school, recalls, "Well I remember some words from my boss at FCMC : He told me that, 'A good background in mathematics and programming makes you a very valuable person for an Investment bank or a Capital Markets firm like Fuji Capital Markets. Usually people are either one or the other. If you combine both and have good conversational skills, that's exactly what employers are looking for.' And that is exactly what we tried to learn in the Master's Program : get a thorough math background, learn to program and communicate."

An alumna from 1995, now working at GTE, states, "I think the best selling point is the project. Not so much in terms of what the project is about, but rather the fact that you're working in a group where you have to deal with people not getting their portion of the project done, and project management issues. The team aspect is emphasized a lot at GTE and also I think in other companies. The C coding is also very important; even little things like the RCS configuration management tool are good things to talk about (We're using one now called ClearCase, and tho' I didn't know exactly how to use it, at least I knew the principles behind why we needed such a thing.)."

A 1994 graduate reports, "I am currently a Statistician/Quality Engineer for the Hewlett-Packard Company. The Applied Math Program at UMASS was great for me. I found it very flexible. I was able to choose many classes that built on my previous engineering degree. The faculty at UMASS are also very supportive and are available for the students. I never had a problem trying to get advice on any matter. In addition, the faculty realizes that students will be looking for a job after the program and they give the students many opportunities to make contacts and explore various professional paths."

A 1990 alumna who later received her PhD in meteorology writes, "The best thing about the applied math program is the solid theoretical background it gave me and the 'hands-on' application of that knowledge in a project. I also enjoyed enormously the course I took outside the department in fluid dynamics, which set the foundation of my current research work."

Group projects

Each year a group project is completed by all of the current students. In a sense, this project class is the organizing experience for the students in the degree program. In addition, it serves as the thesis component of the M.S. degree. The second-year students are expected to take a leadership role in the project, along with the two faculty members who guide it. The first-year students gradually acquire the skills (as modelers, coders and communicators) that they will use during the next year, when they lead the project. The class meets as a weekly seminar throughout the academic year, although most of the real work occurs outside the classroom.

The projects from recent years are described briefly below. More details for projects prior to 2019 can be found at our Department Newsletters

2020-21

An Exploration of Hurricane Intensity Modeling: The hurricane is one of the severe climate disasters that influence the natural environment along the coastal area and causes an economic loss of billions of dollars every year. In recent years, the prediction of the paths of hurricanes has achieved considerable progress. However, predicting the intensity of hurricanes is still a challenging issue. In our project, we mainly focus on forecasting the hurricane intensity. The whole project includes two components. In the first part, we intend to recreate the physic-based energetics model proposed in Shen(2004). The large-scale environmental conditions and present state of the hurricane work together, determining the hurricane intensity. Besides this, a neural network is employed to compare with Shen's model. To test the consistency of the results by these models and observations, we use the data of Hurricane Dorian 2019.

Modeling Ethnosocial Conflicts: Social conflict is an inevitability of human society. Ethno-social conflicts are defined to be the peak stage in differences between individuals, groups, and at the highest level society. It is characterized by confrontation between these groups or individuals. There has been a lot of research done on the complex systems of "conflictology", since throughout history people have always been trying to answer how to describe and predict when these types of conflicts are going to happen. Our research explores the work done in the paper "Global Pattern Formation and Ethnic/Cultural Violence" using a Monte Carlo agent simulation and a Mexican-hat wavelet filter to identify areas of high risk for conflict. We examine the accuracy of this modeling on an area in Pakistan with historically high rates of conflicts and modify the analysis of high risk areas to include population density as a trigger for violence. Our findings show that even though high population density in areas with pronounced ethnic segregation is a significant contributor, identifying these areas with the wavelet filter does produce consistent results.

Mathematical Modeling of Intraocular Drug Delivery: In our eyes, the vitreous humor makes up 80% of the body. There are a number of severe diseases that can affect the vitreous or the retina. However, classical ways of drug delivery in the form of pills, injections and drops are not efficient when the target is the posterior segment of the eye. To overcome this problem, one way is to use biodegradable polymers as intravitreal implants of drug. In our project, we try to numerically simulate the drug diffusion process from an ocular implant to vitreous. Our model are based on the systems of PDEs proposed in Azhdari et al(2013), which describes how the drug concentration inside polymer and vitreous changes through time. Then we use the Crank-Nicolson scheme to numerically solve our PDE model and get our simulation results.

2019-20

A Regional-Level Dynamic Bayesian Model of Seasonal Influenza in the United States

Group Elevator Optimization with Advance Information

Simulating Wildfire Propagation Using Cellular Automata

Human Cars. Automated Drivers

2018-19

"Hearing" the Graph in a Directed Graph The first group recreate a spectral graph clustering method based on relaxation of the discretized wave equation on undirected graphs and attempt to generalize the result to the directed case. They find sufficient conditions for convergent relaxation and bound the time complexity of their algorithm based on the directed graph Laplacian. Using a conductance metric, they illustrate successful cases of directed graph clustering and investigate heuristic conditions for various graph properties under which clustering may be expected to succeed.

Cancer Growth Modeling The second group investigates the dynamics of cancer growth and treatment using a combination of statistical, analytical, and numerical approaches. Using tumor volume data collected from laboratory mice, they obtain parameter estimates for several different cancer growth models. Using the parameter estimates obtained, they then analyze the performance of different treatment regimens on slightly more complicated models, and obtain some numerical and theoretical results for different treatment approaches.

Smart Grid The third group studies the Smart Grid - an intelligent utility network that is needed to satisfy the ever increasing demand on our electric grid. At a microscale level, they use gradient boosting models to predict electrical power consumption and solar power generation for a single home. They also develop a dashboard as a visualization  tool for this analysis. At a macroscale level, they explore the cost optimization of power dispatch between various energy sources in a simplified model of the German electric grid. Through these levels of study, they aim to establish a deeper understanding of the potential requirements of a modern Smart Grid.

2017-18: Electromyography Classification Using Recurrent Systems, and Multiple Scale Modeling for Predictive Material Deformation Analysis This year the students were divided into two groups. The first group investigated the classification of Electromyography (EMG) data. They compared the classical machine learning techniques including Support Vector Machine, Classification Trees, Neural Networks (eg RNN), and Reservoir Computing framework. They found each method has its pros and cons. There is no "best" approach for balancing interpretability, accuracy, and generalization to new data sets. The second group studied the multi-scale models for material deformation while taking into the consideration of the variations in material properties at the micro scale. In particular, the representative volume elements (RVEs) were employed for the averaging over stresses etc.

2016-17: Math Systems for Diagnosis and Treatment of Breast Cancer This year’s Applied Math Master’s Project investigated the detection, classification and growth of breast cancer tumors. The goal is to create a machine learning pipeline for detection and diagnosis from mammogram images. They model the growth and treatment of tumors using a system of ODEs. Due to a lack of human data, this last part of the pipeline uses data from experiments on lab mice, and is not restricted to breast cancer.

2015-16: Non-transitive Systems in Grasslands
This year’s Applied Math Master's Project modeled the non-transitive interactions between three plant species in a prairie and explored the effects that urban development would have on species survival and co-existence. We began by studying non-transitive systems. In a transitive system, if A defeats B and B defeats C then A defeats C; a non-transitive system is one that does not follow these rules. The prototypical example is the game of Rock-Paper-Scissors (RPS), where Paper covers Rock, Rock crushes Scissors, and Scissors cuts Paper. Mathematically, non-transitive systems (often called RPS games) have been examined using discrete and continuous techniques and applied to model multi-player interactions in fields such as biology, economics, and social networking.

2014-15: Uncertainty Quantification: The Story Begins
This year’s Applied Math Masters project utilized the emerging field of uncertainty quantification to focus on a topic of concern to human health: developing a Susceptible-Infected-Removed model (SIR) for forecasting the spread of dengue hemorrhagic fever (DHF).

2013-14: From Atomic Physics and Materials Science to Financial Mathematics and Beyond
This year the Applied Mathematics Masters’ Program tackled a diverse variety of themes in the context of its yearly project: Bose-Einstein condensates in atomic physics; granular crystals in materials science; and deterministic (and potentially chaotic) models of supply-demand-pricing and inflation in financial markets.

2012-13: Multi-Agent Models
This year the Masters students in the Applied Mathematics program undertook a multi-faceted project related to the broad theme of Multi-Agent Models. This theme was chosen for two reasons. First, it offered an opportunity to model the collective behavior of complex systems arising in a range of different disciplines. In particular, three subgroups of the students studied dynamical systems from physical chemistry, biology, and finance. Second, this theme demanded a computationally intensive approach, and the students themselves expressed a desire to use the project to push the limits of their abilities as computational modelers.

2011-12: Power Grids and Energy Transmission
Energy has become an important issue across the whole spectrum of our society. Overall electricity production, one of the most important forms of energy, is often used as an indicator whether a country is industrialized or non-industrialized. The power grids used to transfer electricity from the generators to consumers have a tremendous scale and are becoming ever more complicated as more power plants are built to meet the ever increasing demand. This year the students in the Applied Math Master’s Degree Program worked on three different projects that deal with three different aspects of power grids and energy transmission.

2010-11: Numerical Optimization of Airport Traffic
For this year’s group project in applied math, the students modeled the efficiency of airport taxi way operations, with the aim of improving the scheduling of departing and arriving flights at a busy airport. This problem was suggested by a former graduate from our department, Richard Jordan (Ph.D., 1994), who is currently working for the MIT Lincoln Laboratories. Rich’s group in the Lincoln Lab is under contract from the FAA to update various aspects of airport operations by means of modern automation.

2009-10: Microscopic Traffic Flow Modeling, and Compressive Sampling
In the past year, the Applied Mathematics Masters students were divided into two groups and worked on two separate projects. The first group worked on a project about “Compressive Sampling,” which is a state-of-the-art technique to compress data during acquisition. The basic idea goes back to the 1970s, when seismologists first use the reflected waves to construct an image of the Earth’s interior structure. But the field exploded around 2004 after David Donoho, Emmanuel Candes, Justin Romberg and Terence Tao discovered that the minimum number of data needed to reconstruct an image is less than that required by the famous Nyquist-Shannon criterion.

The second group worked on a project of Microscopic Traffic Flow Modeling. Different from macroscopic models, which treat traffic flow as an effectively one-dimensional compressible fluid, microscopic traffic models are built up from the minute level of individual cars and the interactions between them. The car-following model is one such model based on the stimulus-response mechanism — the following car takes actions like acceleration or deceleration whenever there is stimulus from the leading car, like a change of relative speed or headway. Ideally, models of this kind should be able to reproduce common traffic phenomena, such as stop-and- go, platoon diffusion, or spontaneous congestion. In practical situations they could be used to predict traffic conditions on major roads and to aid traffic control procedures.

2008-09: Modeling Climate Change
At first sight, there is no easy entry point for mathematical modelers into the extremely complex subject of climate dynamics. State-of-the-art climate predictions are based on elaborate numerical models that attempt to include all relevant physical processes in the entire Earth system. These numerical simulators, which grew out of weather-prediction technology, are generically called GCMs, meaning General Circulation Models, although nowadays perhaps Global Climate Models is a more appropriate term. Their governing equations incorporate the circulation of the atmosphere as well as its radiative physics and chemistry (carbon dioxide, ozone, aerosols), the circulations of the oceans and coupling through the hydrosphere (water vapor, clouds, glaciers, sea ice), and even aspects of the biosphere (forests, soils, marine biota). Models with this level of complexity take decades to develop, test, and tune, and they are very expensive to run. Moreover, the results and predictions that they produce are often quite hard to interpret, especially if the goal is to identify a particular mechanism and its effects.

2007-08: Cancerous Tumor, and Data Compression
This year, students in the program worked on two projects. In the first project they looked at models of blood vessel growth towards a cancerous tumor. A critical question for a patient diagnosed with cancer is whether the disease is local or has spread to other locations. Cancer cells penetrate into lymphatic and blood vessels, circulate through the bloodstream, and then invade and grow in normal tissues elsewhere. This mechanism of spreading is called metastasis. Its ability to spread to other tissues and organs makes cancer a life-threatening disease. Hence, there is naturally a great interest in understanding what makes metastasis possible for a malignant tumor. One of the key findings of cancer researchers studying the conditions necessary for metastasis is the fact that the growth of new blood vessels is critical in this respect.

In the second group project, the applied math studied data compression. In computer science and information theory, data compression is the process of encoding information using fewer bits than in the uncoded representation. A popular instance of compression is the ZIP file format. As with any communication, compressed data communication is useful only when the sender and receiver understand the coding scheme. Compression is useful because it reduces the amount of space required for storage of the original data. On the other hand, compressed data must be decompressed in order to be used, and the additional processing could be harmful to some applications. For example, a compressed video may require expensive hardware for the video to be decompressed fast enough to be viewed while it is being decompressed.

2006-07: The Mathematics of Climate
The group worked on mathematical models of global climate. The first person in history to publish a scientific paper on the physical principles that underlie climate — namely, the overall effect of solar radiation and its interaction with the Earth’s surface and atmosphere — was the famous mathematician Joseph Fourier. In the 1820s the father of the heat equation asked himself how it is that the Earth maintains an equilibrium temperature and what that temperature should be. He first wondered why the Earth is not much hotter than it is, given that it is continually heated by the Sun. He realized that the Earth balances the solar radiation it receives by emitting lower frequency (infrared) radiation back into space. But then his calculations suggested that the equilibrium temperature should be below freezing worldwide. The discrepancy lay in the fact that some gases in the atmosphere absorb the reflected radiation even though they are almost transparent to the solar radiation. Of course, these are the greenhouse gases, principally water vapor and carbon dioxide. Although science was much too primitive in Fourier’s time for him to make a thorough analysis, his simple picture of the key processes has stood the test of time, and today it underlies the urgent debate on global warming.

2005-06: The Google Search Engine and the Mechanics of Human Locomotion
The group worked on two projects. The first project was to model the search engine Google. After people type keywords in Google, it prepares a list of websites associated with those keywords. By applying the power method in numerical analysis, the students were able to simulate the page-rank processing of a network. They wrote a program, called a webcrawler, that crawls the internet site by site to determine how sites are interconnected. This created a network of 60,000 sites containing the Department of Mathematics and Statistics and its connected sites. The students then applied the page-rank algorithm to this network. The students also applied the same algorithm to other topics such as developing a ranking system of US airports that would help determine which airports are the most important according to the numbers of passengers. Once again using the power method and applying it to an actual data set obtained from the Bureau of Transportation, the students concluded that Dallas/Fort Worth International Airport is the most important airport in the US.

The second project focused on running. Undertaking this project involved input from many academic areas. The students first had to understand the physiology of the leg as well as the mechanics of how the leg moves and interacts with various forces during running. As they learned, the running process can be broken down into two phases. The stance phase is the period of time when the foot is still in contact with the ground, and the flight phase is the period of time when the foot and the body are in the air. Each phase is governed by a different set of equations derived from Newton's laws of motion. The stance phase is described by three second-order differential equations while the flight phase is described by the equations for common projectile motion found in physics. The students solved the coupled differential equations for the two phases numerically in order to simulate running.

2004-05: Pattern Formation, Tumor Growth and Turing Instability
The spots and stripes which occur on plants and animals is modeled by the group. The model is based on Turing instability or diffusion driven instability. A coupled pair of partial differential equations are used to model the pattern formation. These equations are studied analytically to understand when instabilities will occur. The equations are then solved with a finite difference method numerically in different domains with varying parameters producing spots, stripes and combinations of the two.

A simple model of tumor growth is also proposed. The model is based on the tumor releasing a chemical(TAF) and using this chemical to recruit blood vessels to proliferate in its direction and eventually vascularize the tumor. The model involved a partial differential equation for the chemical and one for the blood vessels. The equations were solved with a finite difference method numerically. The solutions were similar to what is observed.

2003-04: Traffic Flow with Cellular Automata and Kinetic Models
The group looked at different models for simulating traffic flow. The primary model was one based on cellular automata. This model uses a finite set of vehicles with a finite set of rules governing their interaction. The results gave very realistic results. The group showed that one can predict the mean velocity of a collection of vehicles depending on the density. One and two lanes were modeled along with stop lights and ramps.

The group also derived a kinetic model, one between the microscopic cellular automata and the macroscopic partial differential equation. The kinetic model produced solutions similar to the cellular automata which the differential equation is not capable of.

2002-03: Modeling of the Kidney and Lungs
The regulation of sodium chloride in the kidney is modeled. Each kidney contains over one million nephrons, the basic functional unit of the kidney. Each nephron regulates the composition of sodium chloride amongst other things. The transport of sodium chloride in the loop of Henle, which is part of the nephron, is modeled with a partial differential equation. Using analysis, the partial differential equation is studied to understand when stable and unstable solutions might occur. The equation is solved numerically using the Lax-Wendroff method. The computed solutions exhibit oscillations in the sodium concentration in time as is predicted by the analysis. This is observed in rats and humans.

The group also worked with a research pulmonologist at Bay State Medical Center looking at the amount of carbon dioxide exhaled in healthy patents and patents with asthma versus time. The group tested different methods for removing the noise from the data(smoothing the data). The group proposed several good methods that the pulmonologist could use in his work.

2001-02: Artificial Neural Networks

2000-01: Dynamic control of a multilink mechanical system

Multilink system (without desire motion)   Chin up   Stand up   -->

1999-00: Modeling and visualizing human movement via mechanics and optimal control

Image(s) from this project:
1999_00.jpg

1998-99: Quasi-geostrophic turbulence modelling using pseudospectral methods
The objective of this project is to develop a mathematical model for forcasting atmospheric pressure patterns. The common assumption is made that the atmosphere can be modelled as an incompressible fluid. The laws governing atmospheric pressure changes are then described using a Navier-Stokes equation in a rotating coordinant frame. Solutions to this nonlinear partial differential equation are obtained numerically, by means of pseudospectral method.

Image(s) from this project:
initial.gif
output200.gif
output400.gif
output600.gif
output800.gif

1997-98: Macroscopic modelling of traffic flow
Traffic flow is modelled through a hydrodynamic analogy, and the resulting nonlinear hyperbolic partial differential equation is solved numerically. In addition, on-ramps, off-ramps, and bottlenecks are modelled, and these complexities also are implemented in the computer simulation program. Then, in order to model a two lane highway, the concept of lane changing is examined. A model of lane changing from the literature is discussed, and it is argued that this formulation is incorrect. Moreover, a modified lane changing model is presented, and its validity is supported by the results of several simulations, again performed through the numerical solution of the governing differential equation. Finally, in order to illustrate the interrelationship between the effects of ramps and bottlenecks and the process of lane changing, results are presented for simulations which model ramps and bottlenecks along a two lane highway.

Image(s) from this project:
1997_8.gif

1996-97: Monte-Carlo simulation of turbulent atmospheric diffusion
The physical and mathematical diffusion of particles through a turbulent velocity field was calculated via two methods, a Random Eddy Model and Fourier Spectrum Model. The Random Eddy algorithm simulates a lattice of Rankine vortices; the Fourier Spectrum code utilizes a sum of sine and cosine terms to approximate the stream function of the turbulent velocity field. Spatial correlation experiments were performed to ensure appropriate behavior for the moving particles, as well as parameter choices. Simulations of particle emanation from a smoke stack were also performed.

Image(s) from this project:
1996_7.gif

1995-96: Acoustic radiation and propagation
The sound field of a planar generator of general shape and/or mode was calculated by using a surface integral representation of the solution to the governing Helmholtz equation. Comparisons were made with some classical formulas available either in simple, symmetric cases, or in asymptotic regimes. Interesting interference patterns in the sound intensity nearby the radiator were detailed over a range of frequencies and generator characteristics. The directivity of these sound generators was also studied.

Image(s) from this project:
1995_6.gif

1994-95: Models of convective turbulent diffusion
The steady-state concentration field of a pollutant introduced into a flowing, turbulent atmosphere was analyzed. A finite-difference method (alternating direction implicit) was implemented to solve the variable-coefficient diffusion equation in three dimensions, under a parabolic approximation in which the downstream variable is time-like. The plume formed by a source was computed and displayed graphically for various sheared wind-flow conditions.

Image(s) from this project:
1994_5.gif

1993-94: Optics analysis
The design of a lens system was tackled using a direct numerical approach based on ray-tracing for the geometrical optics. Optical properties (focussing, magnification) of various instruments (simple telescopes, microscopes) were examied by computing the three-dimensional pencils of rays, without the classical paraxial approximation. Then the aberrations (spherical, coma, astigmatism, ...) were quantified numerically, and an optimization code was used to vary the lens system parameters so as to minimize a given aberration.

Image(s) from this project:
1993_4.gif

1992-93: Spectral computations in fluid dynamics
The behavior of a two-dimensional viscous fluid was simulated by a direct numerical computation using a pseudospectral method. First, some simpler one-dimensional codes were written for the Burgers and Korteweg-DeVries equations, and some wave interaction phenomena governed by these equations were studied. Then, the full code for a Navier-Stokes flow in two dimensions was implemented, and various vortex interactions were displayed.

 

Applications and admissions

 

Those wishing to be considered for Fall admission should submit all application materials to the Graduate Admissions Office during the preceding Spring. Applications are reviewed beginning on February 1, with precedence given to those before that date. Later applications are considered provided that openings are available. Applicants are encouraged to visit in person, if possible, to meet the faculty and students in the program.

All applicants are expected to have a strong undergraduate preparation in mathematics, including advanced calculus, linear algebra, and differential equations. Some exposure to computer science and/or scientific computing is also desirable, as is some knowledge of another area of science or engineering. A Bachelor's Degree in Mathematics, however, is not necessary. Students with undergraduate majors in Physics or Engineering, for instance, and with sufficient mathematical background, are encourage to apply.

The program is able to offer a tuition waiver and a stipend to a limited number of students upon admission. This financial support takes the form of a teaching assistantship in the department. The duties of the students in the Master's Degree Program are usually restricted to grading or consulting for an undergraduate course, although instructing in an elementary course is also possible.

For additional information, contact the Program Director Qian-Yong Chen.

Possible interdisciplinary courses

Computer science

COMPSCI 513: Logic in Computer Science
Rigorous introduction to mathematical logic from an algorithmic perspective. Topics include: Propositional logic: Horn clause satisfiability and SAT solvers; First Order Logic: soundness and completeness of resolution, compactness theorem. We will use the Coq theorem prover and Datalog. Prerequisites: COMPSCI 250 and COMPSCI 311. 3 credits.

COMPSCI 575: Combinatorics and Graph Theory
This course is a basic introduction to combinatorics and graph theory for advanced undergraduates in computer science, mathematics, engineering and science. Topics covered include: elements of graph theory; Euler and Hamiltonian circuits; graph coloring; matching; basic counting methods; generating functions; recurrences; inclusion-exclusion; and Polya's theory of counting. Undergraduate Prerequisites: mathematical maturity; calculus; linear algebra; strong performance in some discrete mathematics class, such as COMPSCI 250 or MATH 455. Modern Algebra - MATH 411 - is helpful but not required. 3 credits.

COMPSCI 585: Introduction to Natural Language Processing
Natural Language Processing (NLP) is the engineering art and science of how to teach computers to understand human language. NLP is a type of artificial intelligence technology, and it's now ubiquitous -- NLP lets us talk to our phones, use the web to answer questions, map out discussions in books and social media, and even translate between human languages. Since language is rich, subtle, ambiguous, and very difficult for computers to understand, these systems can sometimes seem like magic -- but these are engineering problems we can tackle with data, math, machine learning, and insights from linguistics. This course will introduce NLP methods and applications including probabilistic language models, machine translation, and parsing algorithms for syntax and the deeper meaning of text. During the course, students will (1) learn and derive mathematical models and algorithms for NLP; (2) become familiar with basic facts about human language that motivate them, and help practitioners know what problems are possible to solve; and (3) complete a series of hands-on projects to implement, experiment with, and improve NLP models, gaining practical skills for natural language systems engineering. Undergraduate Prerequisites: COMPSCI 220 (or COMPSCI 230) and COMPSCI 240. An alternate prerequisite of LINGUIST 492B is acceptable for Linguistics majors. 3 credits.

COMPSCI 589: Machine Learning
This course will introduce core machine learning models and algorithms for classification, regression, clustering, and dimensionality reduction. On the theory side, the course will focus on understanding models and the relationships between them. On the applied side, the course will focus on effectively using machine learning methods to solve real-world problems with an emphasis on model selection, regularization, design of experiments, and presentation and interpretation of results. The course will also explore the use of machine learning methods across different computing contexts. Students will complete programming assignments and exams. Python is the required programming language for the course. Prerequisites: COMPSCI 383 and MATH 235. 3 credits.

 

COMPSCI 590D: Algorithms for Data Science
Big Data brings us to interesting times and promises to revolutionize our society from business to government, from healthcare to academia. As we walk through this digitized age of exploded data, there is an increasing demand to develop unified toolkits for data processing and analysis. In this course our main goal is to rigorously study the mathematical foundation of big data processing, develop algorithms and learn how to analyze them. Specific Topics to be covered include: 1) Clustering 2) Estimating Statistical Properties of Data 3) Near Neighbor Search 4) Algorithms over Massive Graphs and Social Networks 5) Learning Algorithms 6) Randomized Algorithms. This course counts as a CS Elective toward the CS major (BS/BA). Undergraduate Prerequisites: COMPSCI 240 and COMPSCI 311. 3 credits.

COMPSCI 590IV + 690IV: Intelligent Visual Computing
The course will teach students algorithms that intelligently process, analyze and generate visual data. The course will start by covering the most commonly used image and shape descriptors. It will proceed with statistical models for representing 2D images, textures, 3D shapes and scenes. The course will then provide an in-depth background on topics of shape and image analysis and co-analysis. Particular emphasis will be given on topics of automatically inferring function from shapes, as well as their contextual relationships with other shapes in scenes and human poses. Finally, the course will cover topics on automating the design and synthesis of 3D shapes with machine learning algorithms and advanced human-computer interfaces. Students will read, present and critique state-of-the-art research papers on the above topics. This course counts as a CS Elective toward the CS major (BA/BS). 3 credits.

COMPSCI 590N: Introduction to Numerical Computing with Python
This course is an introduction to computer programming for numerical computing. The course is based on the computer programming language Python and is suitable for students with no programming or numerical computing background who are interested in taking courses in machine learning, natural language processing, or data science. The course will cover fundamental programming, numerical computing, and numerical linear algebra topics, along with the Python libraries that implement the corresponding data structures and algorithms. The course will include hands-on programming assignments and quizzes. No prior programming experience is required. Familiarity with undergraduate-level probability, statistics and linear algebra is assumed. 1 credit.

COMPSCI 590V: Data Visualization and Exploration
In this course, students will learn the fundamental algorithmic and design principles of visualizing and exploring complex data. The course will cover multiple aspects of data presentation including human perception and design theory; algorithms for exploring patterns in data such as topic modeling, clustering, and dimensionality reduction. A wide range of statistical graphics and information visualization techniques will be covered. We will explore numerical data, relational data, temporal data, spatial data, graphs and text. Hands-on projects will be based on Python or JavaScript with D3. This course counts as a CS Elective toward the CS major (BA/BS). Undergraduate Prerequisite: COMPSCI 220 or 230. No prior knowledge of data visualization or exploration is assumed. This course counts as a CS Elective toward the CS major (BA/BS). 3 credits.

CICS 597C Introduction to Computer Security
This course provides an introduction to the principles and practice of computer and network security with a focus on both fundamentals and practical information. The key topics of this course are applied cryptography; protecting users, data, and services; network security, and common threats and defense strategies. Students will complete several practical lab assignments involving security tools (e.g., OpenSSL, Wireshark, Malware detection). The course includes homework assignments, quizzes, and exams. Prerequisites are CICS 290S or equivalent experience with instructor permission. 3 credits.

COMPSCI 611: Advanced Algorithms
Principles underlying the design and analysis of efficient algorithms. Topics to be covered include: divide-and-conquer algorithms, graph algorithms, matroids and greedy algorithms, randomized algorithms, NP-completeness, approximation algorithms, linear programming. Prerequisites: The mathematical maturity expected of incoming Computer Science graduate students, knowledge of algorithms at the level of COMPSCI 311. 3 credits.

COMPSCI 617: Computational Geometry
Geometric algorithms lie at the heart of many applications, ranging from computer graphics in games and virtual reality engines to motion planning in robotics or even protein modeling in biology. This graduate course is an introduction to the main techniques from Computational Geometry, such as convex hulls, triangulations, Voronoi diagrams, visibility, art gallery problems, and motion planning. The class will cover theoretical as well as practical aspects of the field. The goal of the class it to enable students to exploit a broad range of algorithmic tools from computational geometry to solve problems in a variety of application areas. Prerequisite: Mathematical maturity; CMPSCI 611 or CMPSCI 601. Eligibility: Graduate CS students only. Others with permission of instructor. 3 credits.

COMPSCI 660 Advanced Information Assurance
This course provides an in-depth examination of the fundamental principles of information assurance. While the companion course for undergraduates is focused on practical issues, the syllabus of this course is influenced strictly by the latest research. We will cover a range of topics, including authentication, integrity, confidentiality of distributed systems, network security, malware, privacy, intrusion detection, intellectual property protection, and more. Prerequisites: COMPSCI 460 or 466, or equivalent. 3 credits.

COMPSCI 682: Neural Networks: A Modern Introduction
This course will focus on modern, practical methods for deep learning. The course will begin with a description of simple classifiers such as perceptrons and logistic regression classifiers, and move on to standard neural networks, convolutional neural networks, and some elements of recurrent neural networks, such as long short-term memory networks (LSTMs). The emphasis will be on understanding the basics and on practical application more than on theory. Most applications will be in computer vision, but we will make an effort to cover some natural language processing (NLP) applications as well, contingent upon TA support. The current plan is to use Python and associated packages such as Numpy and TensorFlow. Prerequisites include Linear Algebra, Probability and Statistics, and Multivariate Calculus. Some assignments will be in Python and some in C++. 3 credits.

COMPSCI 687: Reinforcement Learning
This course will provide an introduction to, and comprehensive overview of, reinforcement learning. In general, reinforcement learning algorithms repeatedly answer the question "What should be done next?", and they can learn via trial and error to answer these questions even when there is no supervisor telling the algorithm what the correct answer would have been. Applications of reinforcement learning span across medicine (How much insulin should be injected next? What drug should be given next?), marketing (What ad should be shown next?), robotics (How much power should be given to the motor?), game playing (What move should be made next?), environmental applications (Which countermeasure for an invasive species should be deployed next?), and dialogue systems (What type of sentence should be spoken next?), among many others. Broad topics covered in this course will include: Markov decision processes, reinforcement learning algorithms (model-based / model-free, batch / online, value function based, actor-critics, policy gradient methods, etc.), hierarchical reinforcement learning, representations for reinforcement learning (including deep learning), and connections to animal learning. Special topics may include ensuring the safety of reinforcement learning algorithms, theoretical reinforcement learning, and multi-agent reinforcement learning. This course will emphasize hands-on experience, and assignments will require the implementation and application of many of the algorithms discussed in class. PREREQUISITES: COMPSCI 589, or COMPSCI 689, or COMPSCI 683, with a grade of C or better. Familiarity with an object oriented programming language is required (assignments will use C++, but familiarity with C++ specifically will not be assumed). 3 credits.

COMPSCI 688: Probabilistic Graphical Models
Probabilistic graphical models are an intuitive visual language for describing the structure of joint probability distributions using graphs. They enable the compact representation and manipulation of exponentially large probability distributions, which allows them to efficiently manage the uncertainty and partial observability that commonly occur in real-world problems. As a result, graphical models have become invaluable tools in a wide range of areas from computer vision and sensor networks to natural language processing and computational biology. The aim of this course is to develop the knowledge and skills necessary to effectively design, implement and apply these models to solve real problems. The course will cover (a) Bayesian and Markov networks and their dynamic and relational extensions; (b) exact and approximate inference methods; (c) estimation of both the parameters and structure of graphical models. Although the course is listed as a seminar, it will be taught as a regular lecture course with programming assignments and exams. Students entering the class should have good programming skills and knowledge of algorithms. Undergraduate-level knowledge of probability and statistics is recommended. 3 credits.

COMPSCI 689: Machine Learning
Machine learning is the computational study of artificial systems that can adapt to novel situations, discover patterns from data, and improve performance with practice. This course will cover the popular frameworks for learning, including supervised learning, reinforcement learning, and unsupervised learning. The course will provide a state-of-the-art overview of the field, emphasizing the core statistical foundations. Detailed course topics: overview of different learning frameworks such as supervised learning, reinforcement learning, and unsupervised learning; mathematical foundations of statistical estimation; maximum likelihood and maximum a posteriori (MAP) estimation; missing data and expectation maximization (EM); graphical models including mixture models, hidden-Markov models; logistic regression and generalized linear models; maximum entropy and undirected graphical models; nonparametric models including nearest neighbor methods and kernel-based methods; dimensionality reduction methods (PCA and LDA); computational learning theory and VC-dimension; reinforcement learning; state-of-the-art applications including bioinformatics, information retrieval, robotics, sensor networks and vision. Prerequisites: undergraduate level probability and statistics, linear algebra, calculus, AI; computer programming in some high level language. 3 credits.

COMPSCI 690LG: Advanced Logic in Computer Science
Rigorous introduction to mathematical logic from an algorithmic perspective. Topics include: Propositional logic: Horn clause satisfiability and SAT solvers; First Order Logic: soundness and completeness of resolution, compactness theorem, automatic theorem proving, model checking. We will learn about and use the Coq theorem prover, Datalog, a Model Checker, and SAT and SMT solvers. Prerequisites: Students taking this course should have undergraduate preparation in discrete math and algorithms. Requirements will include readings, class participation, weekly problem sets, a midterm and a final project. 3 credits.

COMPSCI 690M: Machine Learning Theory
When, how, and why do machine learning algorithms work? This course answers these questions by studying the theoretical aspects of machine learning, with a focus on statistically and computationally efficient learning. Broad topics will include: PAC-learning, uniform convergence, and model selection; supervised learning algorithms including SVM, boosting, kernel methods; online learning algorithms and analysis; unsupervised learning with guarantees. Special topics may include: Bandits, active learning, semi-supervised learning and others. 3 credits.

COMPSCI 690V: Visual Analytics
In this course, students will work on solving complex problems in data science using exploratory data visualization and analysis in combination. Students will learn to deal with the Five V s: Volume, Variety, Velocity, Veracity, and Variability, that is with large data, complex heterogeneous data, streaming data, uncertainty in data, and variations in data flow, density and complexity. Students will be able to select the appropriate tools and visualizations in support of problem solving in different application areas. The course is a practical continuation of COMPSCI 590V - Data Visualization and Exploration and focuses on complex problems and applications, however 590V is not a prerequisiteandboth 590V and 690V may be taken independently of each other. The data sets and problems will be selected mainly from the IEEE VAST Challenges, but also from the KDD CUP, Amazon, Netflix, GroupLens, MovieLens, Wiki releases, Biology competitions and others. We will solve crime, cyber security, health, social, communication, marketing and similar large-scale problems. Data sources will be quite broad and include text, social media, audio, image, video, sensor, and communication collections representing very real problems. Hands-on projects will be based on Python or R, and various visualization libraries, both open source and commercial. 3 credits.

COMPSCI 691E: Interactive Machine Learning
Interactive machine learning involves an algorithm or an agent making decisions about data collection, contrasting starkly with traditional learning paradigms. Interactive data collection often enables learning with significantly less data, and it is critical in a number of applications including personalized recommendation, medical diagnosis, and dialogue systems. This seminar will focus on the design and analysis of interactive learning algorithms for settings including active learning, bandits, reinforcement learning, and adaptive sensing. We will cover foundational and contemporary papers, with an emphasis on algorithmic design principles as well as understanding and proving performance guarantees. Students enrolled in the 3 credit version of the course will present one paper in detail to the class as well as prepare notes for one additional lecture. Students enrolled in the 1 credit version of the course will prepare notes for one lecture. Lect 01=3 credits; Lect 02=1 credit.

Mechanical and industrial engineering

MIE 586 - Quantitative Decision Making
Survey in operations research. Introduction to models and procedures for quantitative analyses of decision problems. Topics include linear programming and extensions, integer programming. Required for IE graduate students who lack operations research exposure.

MIE 605 - Finite Element Analysis
The underlying mathematical theory behind the finite element method and its application to the solution of problems from solid mechanics. Includes a term project involving the application of the finite element method to a realistic and sufficiently complex engineering problem selected by the student and approved by the instructor; requires the use of a commercial finite element code.

MIE 644 - Applied Data Analysis
The basics of data acquisition and analysis, pattern classification, system identification, neural network modeling, and fuzzy systems. Essential to students whose thesis projects involve experimentation and data analysis.

MIE 684 - Stochastic Processes In Industrial Engineering
Introduction to the theory of stochastic processes with emphasis on Markov chains, Poisson processes, markovian queues and networks, and computational techniques in Jackson networks. Applications include stochastic models of production systems, reliability and maintenance, and inventory control.

MIE 707 - Viscous Fluids
Exact solutions to Navier-Stokes flow and laminar boundary layer flow. Introduction to transition and turbulent boundary layers, and turbulence modeling. Boundary layer stability analysis using pertubation methods.

Civil and environmental enginerring

CEE 511 - Traffic Engineering
Fundamental principles of traffic flow and intersection traffic operations including traffic data collection methods, traffic control devices, traffic signal design, and analysis techniques. Emphasizes quantitative and computerized techniques for designing and optimizing intersection signalization. Several traffic engineering software packages used.

CEE 548 - Finite Element Method
Application of numerical methods to solution of problems of structural mechanics. Finite difference techniques and other methods for solution of problems in the vibration, stability, and equilibrium of structural elements.

CEE 605 - Finite Element Analysis
Introduction to finite element method in engineering science. Derivation of element equations by physical, variational, and residual methods. Associated computer coding techniques and numerical methods. Applications.

Management

Sch-Mgmt 640 - Financial Analysis and Decisions
Basic concepts, principles, and practices involved in financing businesses and in maintaining efficient operation of the firm. Framework for analyzing savings-investment and other financial decisions. Both theory and techniques applicable to financial problem solving.

Sch-Mgmt 641 - Financial Management
Internal financial problems of firms: capital budgeting, cost of capital, dividend policy, rate of return, and financial aspects of growth. Readings and case-studies.

Sch-Mgmt 745 Financial Models
Analytical approach to financial management. Emphasis on theoretical topics of financial decision making. Through use of mathematical, statistical, and computer simulation methods, various financial decision making models are made.

Sch-Mgmt 747 - Theory of Financial Markets
In-depth study of portfolio analysis and stochastic processes in security markets. Emphasis on quantitative solution techniques and testing procedures.

Sch-Mgmt 871 - Micro Theory Of Finance
Optimum financial policies and decisions of nonfinancial firms. Theory of competition and optimum asset management of financial firms.

Applying to the Graduate Programs

Catalogs and other general information about graduate study at UMass are available from the Graduate School. More information about how to apply as well as a link to the online application can be found here. You can check whether your materials have been received here.

Please note that applications must be submitted to the Office of Graduate Admissions, not to the Department of Mathematics and Statistics, and that the Department will not even see the application if the application fee is not paid. The application fee can be waived only for U.S. applicants who qualify to receive a GRE fee waiver and submit appropriate documentation. Unfortunately, the application fee cannot be waived for international students. The application for admission also serves as an application for financial aid.

Please make sure that your application clearly indicates which degree you wish to apply for. These categories have different criteria for admission, and the applications may even be read by different people.

  • Ph.D. in mathematics (this includes students interested in applied areas): on the online application, choose Doctoral Degree and then Mathematics (Ph.D.)
  • Ph.D. in statistics: choose Doctoral Degree and then Mathematics [Statistics] (Ph.D.)
  • M.S. in statistics at Amherst campus: choose Masters Degree and then Mathematics [Statistics] (M.S.) Amherst
  • M.S. in statistics at Newton satellite campus: choose Masters Degree, then Mathematics [Statistics] (M.S.) Newton. (deadline is June 30 [domestic students] and May 31 [international students] for Fall semester for Newton only)
  • M.S. in applied mathematics: choose Masters Degree and then Applied Mathematics (M.S.)

Note that although the graduate school lists an M.S. in mathematics, we do not usually admit students who only want a Master's; you should apply to the Ph.D. program.

Applicants to the Ph.D. in mathematics can indicate specific areas or subjects they are interested in under Sub-field or specialization. Do not put statistics in this space — instead use the statistics items from the pull-down menus as explained above.

It is possible to apply for both the M.S. and Ph.D. program in statistics at the same time; choose Both Masters and Doctoral Degs and then Mathematics [Statistics] (M.S./Ph.D.).

A complete application to the Graduate school consists of the following (see here for further instructions):

  • The University's application form (either paper or online form), with the application fee paid,
  • Official transcripts from all undergraduate and graduate institutions attended,
  • At least three letters of recommendation
  • A personal statement explaining the student's interest in pursuing graduate studies in mathematics or statistics,
  • For international applicants: an International Student Financial Statement,
  • The following exam scores (all score reports should be sent by ETS using the code for UMass, which is 3917):
    • The GRE mathematics subject exam score (required for applicants to the Mathematics PhD program, except for the Statistics subfield).
    • The TOEFL score report (not required for U.S. citizens or those whose undergraduate institution used English as the primary language). Other test scores can also be used to demonstrate English proficiency. We accept any of the methods described in the English Language Proficiency Requirement here.
    • The GRE general exam scores are strongly recommended, but not required, (please see the FAQ for additional details).
    • UPDATE for Admission in Fall 2023: Because of the impact of COVID-19 on ETS test administration, the GRE subject test will  not be required in order to apply to the PhD program in Mathematics. Optionally, prospective candidates are welcome to submit their subject GRE scores in case they have taken the Mathematics test. We do require submission of a TOEFL score to demonstrate English proficiency, as described by the UMass Graduate School.
  • US citizen and permanent resident students that belong to groups under-represented in the mathematical sciences are encouraged to contact the Department of Mathematics & Statistics at the email address: math-grad-admissions@groups.umass.edu to iterate on practical details of the application, including in connection to the application fee.

Answers to some questions applicants frequently ask

Information especially for international applicants

Note that the letters of recommendation are read very seriously; we encourage sending more than two letters if they will provide a better picture of a student's achievements. See the FAQ for details on GRE scores.

All applicants are expected to have a strong undergraduate preparation in mathematics, including (at least) advanced calculus and linear algebra. Other advanced courses such as real analysis, differential equations, and abstract algebra, are highly recommended. A list of courses taken, with names of textbooks and instructors, would be a useful supplement to the application.

For the statistics option, an undergraduate degree in statistics is not required. Many of our successful statistics students have a degree in mathematics or another field such as engineering, computer science, biological sciences, together with substantial coursework in mathematics.

Deadline

To be considered for a fall teaching assistantship, all application materials should be submitted to the Graduate Admissions Office by January 10, preferably earlier in the case of foreign applicants. Most offers are made by mid-April. Except in unusual circumstances, we do not admit students for the Spring semester.

The University of Massachusetts has signed the Council of Graduate School's resolution, which says that students offered admission for the Fall semester have at least until April 15th to decide whether to accept the offer. 

Axioms - Handbook for Graduate Students

Please follow the link below to access the most recent Graduate Student Handbook.

 

Graduate Handbook: Revised September 2021

 

 

Financial Aid & Housing

Most graduate students are supported by Teaching Assistantships which provide a waiver of tuition and a 9-month stipend. Health fees are mostly subsidized, but other general fees are paid directly by the student. TA duties involve teaching one section of an elementary course each semester or equivalent work connected with a large lecture course. Summer teaching opportunities are also often available. 

For Fall 2022, new Ph.D. students will receive a TA stipend of at least $23,438. New Teaching Assistants in M.S. programs will normally receive a stipend of at least $17,288 and somewhat reduced duties. 

A number of advanced Ph.D. students hold Research Assistantships attached to grants held by particular faculty members. 

Students who are enrolled in a graduate program in Mathematics & Statistics are not eligible for receiving on-campus assistantships from any other unit on campus.

Student Housing

One of the University residence halls is reserved for single graduate students. There are about 400 unfurnished apartments owned by the University on or near campus, reserved for students who are married or have dependent children. A wide range of privately owned off-campus housing is available, including many apartments near the free bus routes.   UMass Residential Life Student Services has information about on-campus housing options, and information about off-campus housing is located at UMass Off Campus Housing Service.  Information regarding on-campus graduate housing for new students can be found here: https://www.umass.edu/living/assign/grad-students .

 

 

Graduate Option in Statistics

M.S. Option in Statistics at Newton Satellite Campus (Boston Area), Completely Flexible Program (Both In-Person and Remote), Evening Degree
Overview
M.S. Option in Statistics
The Fifth Year M.S. Option in Statistics
Ph.D. Option in Statistics
Data Science Certificate (possible to earn completely remotely/online)
Related Info

M.S. Option in Statistics at Newton Satellite Campus (Boston Area), Completely Flexible (Flexible Learning: All Courses Offered Both In-Person and Remotely)

-For information regarding this program, please see the following link:

https://www.math.umass.edu/~conlon/statmtida/

-Note: non-degree students can register for graduate Statistics courses at Newton Mount Ida starting one week before the beginning of classes each semester. See:

https://www.umass.edu/graduate/apply/non-degree-students

-See the FAQ for COVID-19 and Graduate Admissions at the following link:

https://www.umass.edu/graduate/covid-19-graduate-admissions

 

Overview of the Statistics Graduate Program

Within the Department of Mathematics and Statistics, students may choose options which concentrate in Statistics. This page summarizes the main features of the Statistics options, and contains the most up-to-date information. The information on this page supersedes the information in the Axioms (Handbook), which are in the process of being updated.

The M.S. option provides students with training in statistical applications, statistical computing and theory, preparing them for statistics and data science careers in industry, government, educational organizations, consulting firms, health care and research organizations, or for moving on to a Ph.D. in Statistics or Biostatistics. The Ph.D. option provides a combination of theory and application preparing students for positions in academia, industry or government. The Certificate in Statistical and Computational Data Science is a joint program with Statistics and Computer Science. Each of these programs is described in more detail below.

M.S. Option in Statistics

Note: the information below is the most updated information, and supersedes the Axioms (Handbook), which are in the process of being updated.

The M.S. option in Statistics is designed to prepare students for statistics and data science positions in industry, government, educational organizations, consulting firms, health care and research organizations. It also serves as a basis for future work towards a Ph.D. in Statistics or Biostatistics. This program is designed to provide the student with a background in basic theory along with experience in various applications, including computational aspects. As part of their training, students will receive comprehensive exposure to popular statistical software packages. In addition to courses offered within the department, the program allows room for the students to take statistics courses in other departments on campus.

Prerequisites: Students entering the M.S. option are expected to have had Linear Algebra and Calculus up through Multivariate Calculus (this is typically covered by a three-semester sequence in U.S. schools).

The requirements for the M.S. option in Statistics involve coursework, a project and qualifying exams.

Courses

The student must complete 30 hours of coursework with grades of C or better, including at least 24 hours with grades of B or better (pass or fail grades cannot be used to satisfy this requirement). In addition, the student must have at least an overall B average.

The required 30 hours must include

  1. Stat 625: Regression Modeling,
  2. Stat 607-608: Probability and Mathematical Statistics I, II,
  3. Stat 535: Statistical Computing,
  4. At least five other courses which are either Statistics courses numbered 526 or above, from within the department, or some courses outside the department numbered 500 and above subject to prior approval by the Statistics coordinator.

Basic Exam

Students completing the M.S. option in Statistics are required to pass two of three basic exams we offer: applied statistics, probability, and statistics, which are based on ST625 and ST535, ST607, and ST608, respectively. The Basic Exam is given twice a year, in January and in August.

Project

The project is completed under the guidance of a faculty member. This project must have prior approval of the Statistics coordinator and involves 3 credit hours which may be used to satisfy the 30 hour coursework requirement. The project can take many forms; an expository report on a particular area, an examination of methods through simulations or a detailed statistical analysis of real data. A final report is required. This requirement is typically satisfied by the successful completion of the project seminar course Stat 691P.

The Fifth Year M.S. Option in Statistics

This section explains how a Five College student can complete the M.S. option in Statistics in a fifth year.

Entering the fifth year M.S. option in Statistics

In order to enter the fifth year M.S. option in Statistics, students need to

  1. Start taking graduate courses in the fall of their senior years, typically Stat 535, Stat 607, Stat 608, and/or Stat 625. Since
    1. no credits may be counted toward both the M.S. option in Statistics and the baccalaureate degree, and
    2. at most nine credits of graduate work taken while enrolled as an undergraduate may be counted toward the M.S. option in Statistics,
    students who would like to pursue the fifth year M.S. option in Statistics should prepare to take at least 129 total credits (120 for the baccalaureate degree and 9 credits of graduate work) after their senior years.
  2. apply by February 1 of their senior years to the regular M.S. option in statistics program by following instructions here.

Finishing the fifth year M.S. option in Statistics

After being accepted into the program, students

  1. need to take additional 21 credits and fulfill the requirements for the regular M.S. option in Statistics in the fifth year
  2. may use courses taken as an undergraduate to fulfill the requirements of the M.S. option in Statistics, although no more than nine credits may be counted toward the M.S. option in Statistics. For example, if a senior takes all four Stat 535, Stat 607, Stat 608, and Stat 625 graduate courses, the student can use one of the four to count toward both the credits for the baccalaureate degree and the requirement for the M.S. option in Statistics.
  3. are not obligated to finish the program in the fifth year, although financial assistantship, if any, is only guaranteed for the fifth year

Please note that students who are interested in the fifth year M.S. option in Statistics should start planning during the fall of the their junior year and contact the Coordinator of the Statistics Program if there are any questions.

Ph.D. Option in Statistics

The Ph.D. option in Statistics prepares students for academic positions or positions in Academia, or as applied statisticians in industry or government. Entering students are expected to have had Linear Algebra, Calculus and Advanced Calculus. Typically an incoming student in the Ph.D. option in Statistics will have had an introductory course or two in Statistics at the undergraduate level. Student seeking the Ph.D. option in Statistics must complete the following: coursework, qualifying exams, language requirement and dissertation.

Coursework

  1. The student must complete successfully 36 hours of coursework, including Math 523 (or Math 623, or Math 605), Stat 535, 607, 608, 625, 705, and 725.
  2. The student must also complete five elective courses, including two 600 level statistics courses, and 3 courses of the student’s choice, which require prior approval by the statistics coordinator.

Qualifying Exams

There are two tiers of exams, Basic and Advanced, which are intended to measure a student's overall mastery of standard material. The exams are administered during the week preceding each semester (August and January).

Basic Exams: The student must pass three Basic Exams at the Ph.D. level: the Applied Statistics exam, and the Basic Probability and Basic Statistics exams, which cover the material from Stat 535 and Stat 625, Stat 607 and Stat 608 respectively.

Advanced Exams: The student must pass the Advanced Exam in advanced statistics and the oral literature-based exam. The advanced statistics exam version I is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 705. The advanced statistics exam version II is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 725. The two versions are offered in alternate years depending which of Stat 705 and Stat 725 is offered in a year.

For the literature-based exam, students need to choose a topic from the list of topics in the Axioms and form an exam committee that includes the primary faculty of that topic and two secondary faculty. Students are then given reference papers on the chosen topic to read. The exam is in the form of oral presentation and responding questions in front of the exam committee. A student may select a non-standard exam topic, in which case, the student must have the agreement of their committee members on the topic and the reading list.

In order to take the literature-based exam, a student is responsible for forming an exam committee by the end of September for a January exam, or by the last day of spring classes for an August exam. Decisions on passing the exam are by unanimous consent of the exam committee. A student who does not pass will have one more chance to pass the literature-based exam. The second attempt may be on the same or a different topic.

Dissertation

After passing the Advanced Exam, the student becomes a Ph.D. option in Statistics candidate. The student must write a satisfactory dissertation and pass a final oral examination (primarily a defense of the dissertation), and must satisfy all other requirements of his or her dissertation committee. The student is required to register for a minimum of 18 dissertation credits.

Data Science Certificate (possible to earn completely remotely/online)

The Certificate in Statistical and Computational Data Science is offered jointly between Statistics and Computer Science. The Certificate can be completed in one year and requires 5 courses total, with a minimum of 2 courses in each of Statistics and Computer Science.

It is possible to earn the Certificate completely remotely/online; pease see the following link: https://www.math.umass.edu/~conlon/statmtida/datascience.html

For more information on the Certificate, please see the following link:

https://ds.cs.umass.edu/academics/certificate-data-science

 

Related Information

 

Financial Aid and Housing

Statistical Consulting Center

Computing Facilities

Recent Courses

 

 

Recent Graduate Courses

The following is a list of some graduate courses that have been offered over the last five years. In general, courses numbered 600-699 are basic graduate courses preparing students to take the basic part of the qualifying exams, while 700-799 are more advanced courses. We have listed 500-599 courses that are most often taken by students in the Applied Math Masters and Statistics Master’s programs, but 500-599 courses are open to graduate students and advanced undergraduate students. The exact topics covered by each of these classes may vary from year to year. Statistics courses are listed separately from mathematics courses.

Courses marked with an asterisk (*) are special topics courses, designed by the instructor to lead graduate students to deeper study of a particular area that might lead to thesis research. The other courses are offered at least every other year, and many are offered every year.

Courses were held at the UMass Amherst Campus unless otherwise noted.

Detailed course descriptions can be found on the Course Descriptions page, by selecting the desired semester from the drop-down box, then clicking the change button.

 

Recent Mathematics Courses

Semester Course Number Course Title
Spring 2022 Math 612 Algebra II
Spring 2022 Math 624 Real Analysis II
Spring 2022 Math 646 Applied Math & Math Modeling
Spring 2022 Math 652 Int Numerical Analysis II
Spring 2022 Math 672 Algebraic Topology
Spring 2022 Math 691Y Applied Math Project Sem
Spring 2022 Math 697AC* Analytic Combinatronics
Spring 2022 Math 697U* Stochastic Processes & Appl
Spring 2022 Math 705 Symplectic Toplogy
Spring 2022 Math 708 Complex Algebraic Geometry
Spring 2022 Math 725 Intro Functional Analysis I
Spring 2022 Math 797LD* Low Dimensional Toplogy
Fall 2021 Math 605 Probability Theory 1
Fall 2021 Math 611 Algebra I
Fall 2021 Math 623 Real Analysis I
Fall 2021 Math 645 ODE and Dynamical Systems
Fall 2021 Math 651 Numerical Analysis I
Fall 2021 Math 671 Topology I
Fall 2021 Math 691T S-Teaching in Univ
Fall 2021 Math 691Y Applied Math Project Seminar
Fall 2021 Math 703 Topics in Geometry I
Fall 2021 Math 713 Intr-Algebraic Number Theory
Fall 2021 Math 718 Lie Algebras
Fall 2021 Math 731 Partial Differential Equations I
Fall 2021 Math 797E ST-Homological Algebra
Fall 2021 Math 797NS ST-Networks and Spectral Graph Theory
Spring 2021 Math 621 Complex Analysis
Spring 2021 Math 624 Real Analysis II
Spring 2021 Math 646 Applied Math and Math Modeling
Spring 2021 Math 652 Int Numerical Analysis II
Spring 2021 Math 672 Algebraic Topology
Spring 2021 Math 612 Algebra II
Spring 2021 Math 691Y Applied Math Project Seminar
Spring 2021 Math 697FA* Math Foundations of Probabilistic Artificial Intelligence II
Spring 2021 Math 697U* Stochastic Processes and Applications
Spring 2021 Math 704 Topics in Geometry II
Spring 2021 Math 797RM* Moduli Spaces / Reprsnt Theory
Spring 2021 Math 797W* Algebraic Geometry
Fall 2020 Math 605 Probability Theory I
Fall 2020 Math 611 Algebra I
Fall 2020 Math 623 Real Analysis I
Fall 2020 Math 645 ODE and Dynamical Systems
Fall 2020 Math 651 Numerical Analysis I
Fall 2020 Math 671 Topology I
Fall 2020 Math 691T S-Teaching in Univ C
Fall 2020 Math 691Y Applied Math Project Seminar
Fall 2020 Math 697B Introduction to Riemann Surfaces
Fall 2020 Math 697PA* Math Foundations/ProbabilistAI
Fall 2020 Math 703 Topics in Geometry I
Fall 2020 Math 731 Partial Differential Equations I
Fall 2020 Math 797EC* Elliptic Curves
Fall 2020 Math 797RT* Intro/Representation Theory
Spring 2020 Math 534H Intro to Partial Differential Equations
Spring 2020 Math 612 Algebra ll
Spring 2020 Math 624 Real Analysis ll
Spring 2020 Math 646 Applied Math & Math Modeling
Spring 2020 Math 652 Numerical Analysis ll
Spring 2020 Math 672 Algebraic Topology
Spring 2020 Math 691Y Applied Math Project Seminar
Spring 2020 Math 697SS* Sums of Squares
Spring 2020 Math 697U Stochastic Processes & Applications
Spring 2020 Math 705 Symplectic Topology
Spring 2020 Math 708 Complex Algebraic Geometry
Spring 2020 Math 725 Functional Analysis
Spring 2020 Math 797D* Topology & Geometry of Singular Spaces
Spring 2020 Math 797DS* Infinite Dimensional Integral Systems
Spring 2020 Math 797P Stochastic Calculus
Fall 2019 Math 532H Nonlinear Dynamics & Chaos w/ Applications
Fall 2019 Math 611 Algebra l
Fall 2019 Math 621 Complex Analysis
Fall 2019 Math 623 Real Analysis l
Fall 2019 Math 645 ODE & Dynamical Systems
Fall 2019 Math 651 Numerical Analysis l
Fall 2019 Math 671 Topology l
Fall 2019 Math 691T Teaching in University
Fall 2019 Math 691Y Applied Math Project Seminar
Fall 2019 Math 697SG* Symmetric functions and representation theory of the symmetric group
Fall 2019 Math 703 Topics in Geometry l
Fall 2019 Math 718 Lie Algebras
Fall 2019 Math 731 Partial Differential Equations l
Spring 2019 Math 534H Intro to Partial Differential Equations
Spring 2019 Math 612 Algebra ll
Spring 2019 Math 624 Real Analysis ll
Spring 2019 Math 672 Algebraic Topology
Spring 2019 Math 691Y Applied Math Project Seminar
Spring 2019 Math 697AM (now Math 646) Applied Mathematics & Math Modeling
Spring 2019 Math 697CM* Combinatorial Optimization
Spring 2019 Math 697U Stochastic Processes & Applications
Spring 2019 Math 704 Tpcs In Geometry II
Spring 2019 Math 725 Functional Analysis
Spring 2019 Math 797AS* Algebraic Surfaces
Spring 2019 Math 797CV* Calculus of Variations
Spring 2019 Math 797P* Stochastic Calculus
Spring 2019 Math 797W Algebraic Geometry
Fall 2018 Math 532H Nonlinear Dynamics & Chaos w/ Applications
Fall 2018 Math 611 Algebra l
Fall 2018 Math 621 Complex Analysis
Fall 2018 Math 623 Real Analysis l
Fall 2018 Math 645 ODE & Dynamical Systems
Fall 2018 Math 651 Numerical Analysis l
Fall 2018 Math 671 Topology l
Fall 2018 Math 691Y Applied Math Project Seminar
Fall 2018 Math 697CP* Convex Polytopes
Fall 2018 Math 703 Topics in Geometry l
Fall 2018 Math 731 Partial Differential Equations l
Fall 2018 Math 797DE* Dynamical Systems and Ergodic Theory
Fall 2018 Math 797EC* Elliptic Curves
Fall 2018 Math 797RT* Representation Theory
Spring 2018 Math 534H Intro to Partial Differential Equations
Spring 2018 Math 612 Algebra ll
Spring 2018 Math 621 Complex Analysis
Spring 2018 Math 624 Real Analysis ll
Spring 2018 Math 672 Algebraic Topology
Spring 2018 Math 691Y Applied Math Project Seminar
Spring 2018 Math 697AM (now Math 646) Applied Mathematics & Math Modeling
Spring 2018 Math 697U Stochastic Processes & Applications
Spring 2018 Math 697WA* Nonlinear Waves & Applications in Continua and Lattices
Spring 2018 Math 705 Symplectic Topology
Spring 2018 Math 708 Complex Algebraic Geometry
Spring 2018 Math 797DC* Derived Categories
Fall 2017 Math 532H Nonlinear Dynamics & Chaos w/ Applications
Fall 2017 Math 611 Algebra l
Fall 2017 Math 623 Real Analysis l
Fall 2017 Math 645 ODE & Dynamical Systems
Fall 2017 Math 651 Numerical Analysis l
Fall 2017 Math 671 Topology l
Fall 2017 Math 691Y Applied Math Project Seminar
Fall 2017 Math 697AM* Foundations/Analysis Machine Learning
Fall 2017 Math 703 Topics in Geometry l
Fall 2017 Math 713 Intro Algebraic Number Theory
Fall 2017 Math 731 Partial Differential Equations l
Fall 2017 Math 797RE* Modeling, Simulation and Uncertainty Quantification of Rare Events
Fall 2017 Math 797U (now 718) Lie Algebras

Recent Statistics Courses

Semester Course Number Course Title
Spring 2022 Stat 608 (offered at both Amherst and Mt. Ida campuses) Mathematical Statistics II
Spring 2022 Stat 697DS (Newton-Mt. Ida) Statistical Methods for Data Science
Spring 2022 Stat 697MV* (Newton-Mt.Ida) Applied Multivariate Statistics
Spring 2022 Stat 697TS* Time Series Analysis
Spring 2022 Stat 697V* (Newton-Mt.Ida) Data Visualization
Fall 2021 Stat 607 (offered at both Amherst and Mt. Ida campuses) Mathematical Statistics I
Fall 2021 Stat 610 Bayesian Statistics
Fall 2021 Stat 625 (offered at both Amherst and Mt. Ida campuses) Regression Modeling
Fall 2021 Stat 691P (Newton-Mt. Ida campus) S-Project Seminar
Fall 2021 Stat 697L (Newton-Mt. Ida campus) ST-Categorical Data Analysis
Fall 2021 Stat 697ML ST-Stat Machine Learning
Fall 2021 Stat 697TS (Newton-Mt. Ida campus) ST-Time Series Analysis and Appl
Fall 2021 Stat 705 Linear Models I
Fall 2021 Stat 797S ST-Estimation/Semi Non Parametric Models
Spring 2021 Stat 608 (offered at Amherst and Mount Ida campuses) Mathematical Statistics II
Spring 2021 Stat 697D* Applied Statistics and Data Analysis
Spring 2021 Stat 697DS* (Mount Ida campus) Statistical Methods for Data Science
Spring 2021 Stat 697MV* (Mount Ida campus) Applied Multivariate Statistics
Spring 2021 Stat 697V* (Mount Ida campus) Data Visualization
Fall 2020 Stat 607 (offered at Amherst and Mount Ida campuses) Mathematical Statistics I
Fall 2020 Stat 610 Bayesian Statistics
Fall 2020 Stat 625 (offered at Amherst and Mount Ida campuses) Regression Modeling
Fall 2020 Stat 691P S-Project Seminar
Fall 2020 Stat 697BD* Biomedical and Health Data Analysis
Fall 2020 Stat 697L* (Mount Ida campus) Categorical Data Analysis
Fall 2020 Stat 697ML* Statistical Machine Learning
Fall 2020 Stat 697TS* (Mount Ida campus) Time Series Analysis and Application
Fall 2020 Stat 725 Estimation Theory and Hypothesis Testing I
Spring 2020 Stat 526 (Mount Ida Campus) Design Of Experiments
Spring 2020 Stat 598C Statistical Consulting Practicum
Spring 2020 Stat 608 (offered at Amherst and Mount Ida Campuses) Mathematical Statistics ll
Spring 2020 Stat 691P Project Seminar
Spring 2020 Stat 697DS* (Mount Ida Campus) Statistical Methods/Data Science
Spring 2020 Stat 697L* Categorical Data Analysis
Spring 2020 Stat 697TS* Time Series Analysis and Appl
Spring 2020 Stat 797S* Estimation/SemiNonParametMD
Fall 2019 Stat 535 (offered at Amherst and Mount Ida Campuses) Statistical Computing
Fall 2019 Stat 598C Statistical Consulting Practicum
Fall 2019 Stat 605 (now Math 605) Probability Theory l
Fall 2019 Stat 607 (offered at Amherst and Mount Ida Campuses) Mathematical Statistics l
Fall 2019 Stat 610 Bayesian Statistics
Fall 2019 Stat 625 (offered at Amherst and Mount Ida Campuses) Regression Modeling
Fall 2019 Stat 697BD* Biomedical and Health Data Analysis
Fall 2019 Stat 697ML* Statistical Machine Learning
Fall 2019 Stat 705 Linear Models 1
Spring 2019 Stat 597G* Intro to Statistical Learning
Spring 2019 Stat 598C Statistical Consulting Practicum
Spring 2019 Stat 608 Mathematical Statistics ll
Spring 2019 Stat 691P Project Seminar
Spring 2019 Stat 697D* Applied Statistics & Data Analysis
Fall 2018 Stat 535 Statistical Computing
Fall 2018 Stat 598C Statistical Consulting Practicum
Fall 2018 Stat 605 (now Math 605) Probability Theory l
Fall 2018 Stat 607 Mathematical Statistics l
Fall 2018 Stat 625 Regression Modeling
Fall 2018 Stat 697S* Statistical Network Inference
Fall 2018 Stat 725 Estimation Theory & Hypothesis Testing
Fall 2018 Stat 797N* Non-parameteric Regression for Data Analysis
Spring 2018 Stat 526 Design of Experiments
Spring 2018 Stat 598C Statistical Consulting Practicum
Spring 2018 Stat 608 Mathematical Statistics ll
Spring 2018 Stat 691P Project Seminar
Spring 2018 Stat 797L* Mixture Models
Fall 2017 Stat 535 Statistical Computing
Fall 2017 Stat 597L* Dynamic Linear Models
Fall 2017 Stat 598C Statistical Consulting Practicum
Fall 2017 Stat 605 (now Math 605) Probability Theory l
Fall 2017 Stat 607 Mathematical Statistics l
Fall 2017 Stat 625 Regression Modeling
Fall 2017 Stat 697B (now Stat 610) Bayesian Statistics
Fall 2017 Stat 697ML* Statistical Machine Learning
Fall 2017 Stat 705 Linear Models l

Sample Qualifying Exams

Basic Exams

Advanced Exams

Advanced Statistics Version II

Applied Mathematics Practice Problems

Stochastics Practice Problems

Topology Practice Problems

Old Exams (no longer offered)