Academic Catalog

2023-2024 Edition

Mathematics PhD

Degree requirements.

The following requirements are in addition to, or further elaborate upon, those requirements outlined in  The Graduate School Policy Guide .

Total Units Required: 21

  • A student who has passed the qualifying exam may register for TGS 500-0 Funded Doctoral Study beginning in the third year.

Other PhD Degree Requirements

  • Examinations:  three written preliminary examination in the core courses of Analysis, Geometry/Topology, and Algebra; oral qualifying examination
  • Research/Projects:  see PhD Dissertation below
  • PhD Dissertation:  original, independent research
  • Final Evaluations:  defense of dissertation

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DEPARTMENT OF STATISTICS AND DATA SCIENCE

Phd program, phd program overview.

The doctoral program in Statistics and Data Science is designed to provide students with comprehensive training in theory and methodology in statistics and data science, and their applications to problems in a wide range of fields. The program is flexible and may be arranged to reflect students' interests and career goals. Cross-disciplinary work is encouraged. The PhD program prepares students for careers as university teachers and researchers and as research statisticians or data scientists in industry, government and the non-profit sector.

Requirements

Students are required to fulfill the Department requirements in addition to those specified by The Graduate School (TGS).

From the Graduate School’s webpage outlining the general requirements for a PhD :

In order to receive a doctoral degree, students must:

  • Complete all required coursework. .
  • Gain admittance to candidacy.
  • Submit a prospectus to be approved by a faculty committee.
  • Present a dissertation with original research. Review the Dissertation Publication page for more information.
  • Complete the necessary teaching requirement
  • Submit necessary forms to file for graduation
  • Complete degree requirements within the approved timeline

PhD degrees must be approved by the student's academic program. Consult with your program directly regarding specific degree requirements.

The Department requires that students in the Statistics and Data Science PhD program:

  • Meet the department minimum residency requirement of 2 years
  • STAT 344-0 Statistical Computing
  • STAT 350-0 Regression Analysis
  • STAT 353-0 Advanced Regression (new 2021-22)
  • STAT 415-0 I ntroduction to Machine Learning
  • STAT 420-1,2,3 Introduction to Statistical Theory and Methodology 1, 2, 3
  • STAT 430-1, STAT 430-2, STAT 440 (new courses in 2022-23 on probability and stochastic processes for statistics students)
  • STAT 457-0 Applied Bayesian Inference

Students generally complete the required coursework during their first two years in the PhD program. *note that required courses changed in the 2021-22 academic year, previous required courses can be found at the end of this page.

  • Pass the Qualifying Exam. This comprehensive examination covers basic topics in statistics and is typically taken in fall quarter of the second year.

Pass the Prospectus presentation/examination and be admitted for PhD candidacy by the end of year 3 . The statistics department requires that students must complete their Prospectus (proposal of dissertation topic) before the end of year 3, which is earlier than The Graduate School deadline of the end of year 4. The prospectus must be approved by a faculty committee comprised of a committee chair and a minimum of 2 other faculty members. Students usually first find an adviser through independent studies who will then typically serve as the committee chair. When necessary, exceptions may be made upon the approval of the committee chair and the director of graduate studies, to extend the due date of the prospectus exam until the end of year 4.

  • Successfully complete and defend a doctoral dissertation. After the prospectus is approved, students begin work on the doctoral dissertation, which must demonstrate an original contribution to a chosen area of specialization. A final examination (thesis defense) is given based on the dissertation. Students typically complete the PhD program in 5 years.
  • Attend all seminars in the department and participate in other research activities . In addition to these academic requirements, students are expected to participate in other research activities and attend all department seminars every year they are in the program.

Optional MS degree en route to PhD

Students admitted to the Statistics and Data Science PhD program can obtain an optional MS (Master of Science) degree en route to their PhD. The MS degree requires 12 courses: STAT 350-0 Regression Analysis, STAT 353 Advanced Regression, STAT 420-1,2,3 Introduction to Statistical Theory and Methodology 1, 2, 3, STAT 415-0 I ntroduction to Machine Learning , and at least 6 more courses approved by the department of which two must be 400 level STAT elective courses, no more than 3 can be non-STAT courses. For the optional MS degree, students must also pass the qualifying exam offered at the beginning of the second year at the MS level.

*Prior to 2021-2022, the course requirements for the PhD were:

  • STAT 351-0 Design and Analysis of Experiments
  • STAT 425 Sampling Theory and Applications
  • MATH 450-1,2 Probability 1, 2 or MATH 450-1 Probability 1 and IEMS 460-1,2 Stochastic Processes 1, 2
  • Six additional 300/400 graduate-level Statistics courses, at least two must be 400 -level
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Since 1977, the Department of Engineering Sciences and Applied Mathematics has been one of the leading applied mathematics programs in the world.

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Driving Innovations in Biostatistics with Denise Scholtens, PhD

“I'm continually surprised by new data types. I think that we will see the emergence of a whole new kind of technology that we probably can't even envision five years from now…When I think about where the field has come over the past 20 years, it's just phenomenal.”  —  Denise Scholtens, PhD  

  • Director, Northwestern University Data Analysis and Coordinating Center (NUDACC)  
  • Chief of Biostatistics in the Department of Preventive Medicine  
  • Professor of Preventive Medicine in the Division of Biostatistics and of Neurological Surgery  
  • Member of Northwestern University Clinical and Translational Sciences Institute (NUCATS)  
  • Member of the Robert H. Lurie Comprehensive Cancer Center  

Episode Notes 

Since arriving at Feinberg in 2004, Scholtens has played a central role in the dramatic expansion of biostatistics at the medical school. Now the Director of NUDACC, Scholtens brings her expertise and leadership to large-scale, multicenter studies that can lead to clinical and public health practice decision-making.    

  • After discovering her love of statistics as a high school math teacher, Scholtens studied bioinformatics in a PhD program before arriving at Feinberg in 2004.  
  • Feinberg’s commitment to biostatistics has grown substantially in recent decades. Scholtens was only one of five biostatisticians when she arrived. Now she is part of a division with almost 50 people.  
  • She says being a good biostatistician requires curiosity about other people’s work, knowing what questions to ask and tenacity to understand subtitles of so much data.   
  • At NUDACC, Scholtens and her colleagues specialize in large-scale, multicenter prospective studies and clinical trials that lead to clinical or public health practice decision-making. They operate at the executive level and oversee all aspects of the study design.  
  • Currently, Scholtens is involved with the launch of a large study, along with The Ohio State University, that received a $14 million grant to look at the effectiveness of aspirin in the prevention of hypertensive disorders in pregnancy.  
  • Scholtens first started her work in data coordinating through the Hyperglycemia Adverse Pregnancy Outcome (HAPO) study, which looked at 25,000 pregnant individuals. This led to a continued interest in fetal and maternal health.   
  • When it comes to supportive working environments, Scholtens celebrates the culture at Feinberg, and especially her division in biostatistics, for being collaborative as well as genuinely supportive of each other’s projects. She attributes this to strong leadership which established a culture with these guiding principles.   

Additional Reading  

  • Read more about the ASPIRIN trial and other projects taking place at NUDACC   
  • Discover a study linking mothers’ obesity-related genes to babies’ birth weight, which Scholtens worked in through the HAPO study   
  • Browse all of Scholtens recent publications 

Recorded on February 21, 2024.

Continuing Medical Education Credit

Physicians who listen to this podcast may claim continuing medical education credit after listening to an episode of this program..

Target Audience

Academic/Research, Multiple specialties

Learning Objectives

At the conclusion of this activity, participants will be able to:

  • Identify the research interests and initiatives of Feinberg faculty.
  • Discuss new updates in clinical and translational research.

Accreditation Statement

The Northwestern University Feinberg School of Medicine is accredited by the Accreditation Council for Continuing Medical Education (ACCME) to provide continuing medical education for physicians.

Credit Designation Statement

The Northwestern University Feinberg School of Medicine designates this Enduring Material for a maximum of 0.50  AMA PRA Category 1 Credit(s)™.  Physicians should claim only the credit commensurate with the extent of their participation in the activity.

American Board of Surgery Continuous Certification Program

Successful completion of this CME activity enables the learner to earn credit toward the CME requirement(s) of the American Board of Surgery’s Continuous Certification program. It is the CME activity provider's responsibility to submit learner completion information to ACCME for the purpose of granting ABS credit.

All the relevant financial relationships for these individuals have been mitigated.

Disclosure Statement

Denise Scholtens, PhD, has nothing to disclose.  Course director, Robert Rosa, MD, has nothing to disclose. Planning committee member, Erin Spain, has nothing to disclose.  FSM’s CME Leadership, Review Committee, and Staff have no relevant financial relationships with ineligible companies to disclose.

Read the Full Transcript

[00:00:00] Erin Spain, MS: This is Breakthroughs, a podcast from Northwestern University Feinberg School of Medicine. I'm Erin Spain, host of the show. Northwestern University Feinberg School of Medicine is home to a team of premier faculty and staff biostatisticians, who are the driving force of data analytic innovation and excellence here. Today, we are talking with Dr. Denise Scholtens, a leader in biostatistics at Northwestern, about the growing importance of the field, and how she leverages her skills to collaborate on several projects in Maternal and Fetal Health. She is the Director of the Northwestern University Data Analysis and Coordinating Center, NUDACC, and Chief of Biostatistics in the Department of Preventive Medicine, as well as Professor of Preventive Medicine and Neurological Surgery. Welcome to the show.  

[00:01:02] Denise Scholtens, PhD: Thank you so much.  

[00:01:02] Erin Spain, MS: So you have said in the past that you were drawn to this field of biostatistics because you're interested in both math and medicine, but not interested in becoming a clinician. Tell me about your path into the field and to Northwestern.  

[00:01:17] Denise Scholtens, PhD: You're right. I have always been interested in both math and medicine. I knew I did not want to be involved in clinical care. Originally, fresh out of college, I was a math major and I taught high school math for a couple of years. I really enjoyed that, loved the kids, loved the teaching parts of things. Interestingly enough, my department chair at the time assigned me to teach probability and statistics to high school seniors. I had never taken a statistics course before, so I was about a week ahead of them in our classes and found that I just really enjoyed the discipline. So as much as I loved teaching, I did decide to go ahead and invest in this particular new area that I had found and I really enjoyed. So I wanted to figure out how I could engage in the field of statistics. Decided to see, you know, exactly how studying statistics could be applied to medicine. At the time, Google was brand new. So I literally typed in the two words math and medicine to see what would come up. And the discipline of biostatistics is what Google generated. And so here I am, I applied to grad school and it's been a great fit for me.  

[00:02:23] Erin Spain, MS: Oh, that's fantastic. So you went on to get a PhD, and then you came to Northwestern in 2004. And so tell me a little bit about the field then and how it's changed so dramatically since.  

[00:02:36] Denise Scholtens, PhD: So yes, I started here at Northwestern in 2004, just a few months after I had defended my thesis. At the time there was really an emerging field of study called bioinformatics. So I wrote my thesis in the space of genomics data analysis with what at the time was a brand new technology, microarrays. This was the first way we could measure gene transcription at a high throughput level. So I did my thesis work in that space. I studied at an institution with a lot of strengths and very classical statistics. So things that we think of in biostatistics like clinical trial design, observational study analysis, things like that. So I had really classic biostatistics training and then complimented that with sort of these emerging methods with these high dimensional data types. So I came to Northwestern here and I sort of felt like I lived in two worlds. I had sort of classic biostat clinical trials, which were certainly, you know, happening here. And, that work was thriving here at Northwestern, but I had this kind of new skillset, and I just didn't quite know how to bring the two together. That was obviously a long time ago, 20 years ago. Now we think of personalized medicine and genomic indicators for treatment and, you know, there's a whole variety of omics data variations on the theme that are closely integrated with clinical and population level health research. So there's no longer any confusion for me about how those two things come together. You know, they're two disciplines that very nicely complement each other. But yeah, I think that does speak to how the field has changed, you know, these sort of classic biostatistics methods are really nicely blended with a lot of high dimensional data types. And it's been fun to be a part of that.  

[00:04:17] Erin Spain, MS: There were only a handful of folks like you at Northwestern at the time. Tell me about now and the demand for folks with your skill set.  

[00:04:26] Denise Scholtens, PhD: When I came to Northwestern, I was one of a very small handful of biostatistics faculty. There were five of us. We were not even called a division of biostatistics. We were just here as the Department of Preventive Medicine. And a lot of the work we did was really very tightly integrated with the epidemiologists here in our department and we still do a lot of that for sure. There was also some work going on with the Cancer Center here at Northwestern. But yeah, a pretty small group of us, who has sort of a selected set of collaborations. You know, I contrast that now to our current division of biostatistics where we are over 20s, pushing 25, depending on exactly how you want to count. Hoping to bring a couple of new faculty on board this calendar year. We have a staff of about 25 statistical analysts. And database managers and programmers. So you know, when I came there were five faculty members and I think two master's level staff. We are now pushing, you know, pushing 50 people in our division here so it's a really thriving group.  

[00:05:26] Erin Spain, MS: in your opinion, what makes a good biostatistician? Do you have to have a little bit of a tough skin to be in this field?  

Denise Scholtens, PhD: I do think it's a unique person who wants to be a biostatistician. There are a variety of traits that can lead to success in this space. First of all, I think it's helpful to be wildly curious about somebody else's work. To be an excellent collaborative biostatistician, you have to be able to learn the language of another discipline. So some other clinical specialty or public health application. Another trait that makes a biostatistician successful is to be able to ask the right questions about data that will be collected or already have been collected. So understanding the subtleties there, the study design components that lead to why we have the data that we have. You know, a lot of our data, you could think of it in a simple flat file, right? Like a Microsoft Excel file with rows and columns. That certainly happens a lot, but there are a lot of incredibly innovative data types out there: wearables technology, imaging data, all kinds of high dimensional data. So I think a tenacity to understand all of the subtleties of those data and to be able to ask the right questions. And then I think for a biostatistician at a medical school like ours, being able to blend those two things, so understanding what the data are and what you have to work with and what you're heading toward, but then also facilitating the translation of those analytic findings for the audience that really wants to understand them. So for the clinicians, for the patients, for participants and the population that the findings would apply to.   

Erin Spain, MS: It must feel good, though, in those situations where you are able to help uncover something to improve a study or a trial.  

[00:07:07] Denise Scholtens, PhD: It really does. This is a job that's easy to get out of bed for in the morning. There's a lot of really good things that happen here. It's exciting to know that the work we do could impact clinical practice, could impact public health practice. I think in any job, you know, you can sometimes get bogged down by the amount of work or the difficulty of the work or the back and forth with team members. There's just sort of all of the day to day grind, but to be able to take a step back and remember the actual people who are affected by our own little niche in this world. It's an incredibly helpful and motivating practice that I often keep to remember exactly why I'm doing what I'm doing and who I'm doing it for.  

[00:07:50] Erin Spain, MS: Well, and another important part of your work is that you are a leader. You are leading the center, NUDACC, that you mentioned, Northwestern University Data Analysis and Coordinating Center. Now, this has been open for about five years. Tell me about the center and why it's so crucial to the future of the field.  

[00:08:08] Denise Scholtens, PhD: We specialize at NUDACC in large scale, multicenter prospective studies. So these are the clinical trials or the observational studies that often, most conclusively, lead to clinical or public health practice decision making. We focus specifically on multicenter work. Because it requires a lot of central coordination and we've specifically built up our NUDACC capacity to handle these multi center investigations where we have a centralized database, we have centralized and streamlined data quality assurance pipelines. We can help with central team leadership and organization for large scale networks. So we have specifically focused on those areas. There's a whole lot of project management and regulatory expertise that we have to complement our data analytics strengths as well. I think my favorite part of participating in these studies is we get involved at the very beginning. We are involved in executive level planning of these studies. We oversee all components of study design. We are intimately involved in the development of the data capture systems. And in the QA of it. We do all of this work on the front end so that we get all of the fun at the end with the statistics and can analyze data that we know are scientifically sound, are well collected, and can lead to, you know, really helpful scientific conclusions.  

[00:09:33] Erin Spain, MS: Tell me about that synergy between the clinicians and the other investigators that you're working with on these projects.  

[00:09:41] Denise Scholtens, PhD: It is always exciting, often entertaining. Huge range of scientific opinion and expertise and points of view, all of which are very valid and very well informed. All of the discussion that could go into designing and launching a study, it's just phenomenally interesting and trying to navigate all of that and help bring teams to consensus in terms of what is scientifically most relevant, what's going to be most impactful, what is possible given the logistical strengths. Taking all of these well informed, valid, scientific points of view and being a part of the team that helps integrate them all toward a cohesive study design and a well executed study. That's a unique part of the challenge that we face here at NUDACC, but an incredibly rewarding one. It's also such an honor and a gift to be able to work with such a uniformly gifted set of individuals. Just the clinical researchers who devote themselves to these kinds of studies are incredibly generous, incredibly thoughtful and have such care for their patients and the individuals that they serve, that to be able to sit with them and think about the next steps for a great study is a really unique privilege.  

[00:10:51] Erin Spain, MS: How unique is a center like this at a medical school?  

[00:10:55] Denise Scholtens, PhD: It's fairly unique to have a center like this at a medical school. Most of the premier medical research institutions do have some level of data coordinating center capacity. We're certainly working toward trying to be one of the nation's best, absolutely, and build up our capacity for doing so. I'm actually currently a part of a group of data coordinating centers where it's sort of a grassroots effort right now to organize ourselves and come up with, you know, some unified statements around the gaps that we see in our work, the challenges that we face strategizing together to improve our own work and to potentially contribute to each other's work. I think maybe the early beginnings of a new professional organization for data coordinating centers. We have a meeting coming up of about, I think it's 12 to 15 different institutions, academic research institutions, specifically medical schools that have centers like ours to try to talk through our common pain points and also celebrate our common victories.  

[00:11:51] Erin Spain, MS: I want to shift gears a little bit to talk about some of your research collaborations, many of which focus on maternal and fetal health and pregnancy. You're now involved with a study with folks at the Ohio State University that received a 14 million grant looking at the effectiveness of aspirin in the prevention of hypertensive disorders in pregnancy. Tell me about this work.  

[00:12:14] Denise Scholtens, PhD: Yes, this is called the aspirin study. I suppose not a very creative name, but a very appropriate one. What we'll be doing in this study is looking at two different doses of aspirin for trying to prevent maternal hypertensive disorders of pregnancy in women who are considered at high risk for these disorders. This is a huge study. Our goal is to enroll 10,742 participants. This will take place at 11 different centers across the nation. And yes, we at NUDACC will serve as the data coordinating center here, and we are partnering with the Ohio State University who will house the clinical coordinating center. So this study is designed to look at two different doses to see which is more effective at preventing hypertensive disorders of pregnancy. So that would include gestational hypertension and preeclampsia. What's really unique about this study and the reason that it is so large is that it is specifically funded to look at what's called a heterogeneity of treatment effect. What that is is a difference in the effectiveness of aspirin in preventing maternal hypertensive disorders, according to different subgroups of women. We'll specifically have sufficient statistical power to test for differences in treatment effectiveness. And we have some high priority subgroups that we'll be looking at. One is a self-identified race. There's been a noted disparity in maternal hypertensive disorders, for individuals who self identify according to different races. And so we will be powered to see if aspirin has comparable effectiveness and hopefully even better effectiveness for the groups who really need it, to bring those rates closer to equity which is, you know, certainly something we would very strongly desire to see. We'll also be able to look at subgroups of women according to obesity, according to maternal age at pregnancy, according to the start time of aspirin when aspirin use is initiated during pregnancy. So that's why the trial is so huge. For a statistician, the statisticians out there who might be listening, this is powered on a statistical interaction term, which doesn't happen very often. So it's exciting that the trial is funded in that way.  

[00:14:27] Erin Spain, MS: Tell me a little bit more about this and how your specific skills are going to be utilized in this study.  

[00:14:32] Denise Scholtens, PhD: Well, there are three biostatistics faculty here at Northwestern involved in this. So we're definitely dividing and conquering. Right now, we're planning this study and starting to stand it up. So we're developing our statistical analysis plans. We're developing the database. We are developing our randomization modules. So this is the piece of the study where participants are randomized to which dose of aspirin they're going to receive. Because of all of the subgroups that we're planning to study, we need to make especially sure that the assignments of which dose of aspirin are balanced within and across all of those subgroups. So we're going to be using some adaptive randomization techniques to ensure that that balance is there. So there's some fun statistical and computer programming innovation that will be applied to accomplish those things. So right now, there are usually two phases of a study that are really busy for us. That's starting to study up and that's where we are. And so yes, it is very busy for us right now. And then at the end, you know, in five years or so, once recruitment is over, then we analyze all the data,  

[00:15:36] Erin Spain, MS: Are there any guidelines out there right now about the use of aspirin in pregnancy. What do you hope that this could accomplish?  

 Prescribing aspirin use for the prevention of hypertension during pregnancy is not uncommon at all. That is actually fairly routinely done, but that it's not outcomes based in terms of which dosage is most effective. So 81 milligrams versus 162 milligrams. That's what we will be evaluating. And my understanding is that clinicians prescribe whatever they think is better, and I'm sure those opinions are very well informed but there is very little outcome based evidence for this in this particular population that we'll be studying. So that would be the goal here, would be to hopefully very conclusively say, depending on the rates of the hypertensive disorders that we see in our study, which of the two doses of aspirin is more effective. Importantly, we will also be tracking any side effects of taking aspirin. And so that's also very much often a part of the evaluation of You know, taking a, taking a drug, right, is how safe is it? So we'll be tracking that very closely as well. Another unique part of this study is that we will be looking at factors that help explain aspirin adherence. So we are going to recommend that participants take their dose of aspirin daily. We don't necessarily expect that's always going to happen, so we are going to measure how much of their prescribed dose they are actually taking and then look at, you know, factors that contribute to that. So be they, you know, social determinants of health or a variety of other things that we'll investigate to try to understand aspirin adherence, and then also model the way in which that adherence could have affected outcomes.  

Erin Spain, MS: This is not the first study that you've worked on involving maternal and fetal health. Tell me about your interest in this particular area, this particular field, and some of the other work that you've done.  

[00:17:31] Denise Scholtens, PhD: So I actually first got my start in data coordinating work through the HAPO study. HAPO stands for Hyperglycemia Adverse Pregnancy Outcome. That study was started here at Northwestern before I arrived. Actually recruitment to the study occurred between 2000 and 2006. Northwestern served as the central coordinating center for that study. It was an international study of 25,000 pregnant individuals who were recruited and then outcomes were evaluated both in moms and newborns. When I was about mid career here, all the babies that were born as a part of HAPO were early teenagers. And so we conducted a follow up study on the HAPO cohort. So that's really when I got involved. It was my first introduction to being a part of a coordinating center. As I got into it, though, I saw the beauty of digging into all of these details for a huge study like this and then saw these incredible resources that were accumulated through the conduct of such a large study. So the data from the study itself is, was of course, a huge resource. But then also we have all of these different samples that sit in a biorepository, right? So like usually blood sample collection is a big part of a study like this. So all these really fun ancillary studies could spin off of the HAPO study. So we did some genomics work. We did some metabolomics work. We've integrated the two and what's called integrated omics. So, you know, my work in this space really started in the HAPO study. And I have tremendously enjoyed integrating these high dimensional data types that have come from these really rich data resources that have all, you know, resulted because of this huge multicenter longitudinal study. So I kind of accidentally fell into the space of maternal and fetal health, to be honest. But I just became phenomenally interested in it and it's been a great place.  

[00:19:24] Erin Spain, MS: Would you say that this is also a population that hasn't always been studied very much in biomedical science?  

[00:19:32] Denise Scholtens, PhD: I think that that is true, for sure. There are some unique vulnerabilities, right, for a pregnant individual and for the fetus, right, and in that situation. You know, the vast majority of what we do is really only pertaining to the pregnant participant but, you know, there are certainly fetal outcomes, newborn outcomes. And so, I think conducting research in this particular population is a unique opportunity and there are components of it that need to be treated with special care given sort of this unique phase of human development and this unique phase of life.  

[00:20:03] Erin Spain, MS: So, as data generation just really continues to explode, and technology is advancing so fast, faster than ever, where do you see this field evolving, the field of biostatistics, where do you see it going in the next five to ten years?  

[00:20:19] Denise Scholtens, PhD: That's a great question. I think all I can really tell you is that I'm continually surprised by new data types. I think that we will see an emergence of a whole new kind of technology that we probably can't even envision five years from now. And I think that the fun part about being a biostatistician is seeing what's happening and then trying to wrap your mind around the possibilities and the actual nature of the data that are collected. You know, I think back to 2004 and this whole high throughput space just felt so big. You know, we could look at gene transcription across the genome using one technology. And we could only look at one dimension of it. Right now it just seems so basic. When I think about where the field has come over the past 20 years, it's just phenomenal. I think we're seeing a similar emergence of the scale and the type of data in the imaging space and in the wearable space, with EHR data, just. You know, all these different technologies for capturing, capturing things that we just never even conceived of before. I do hope that we continue to emphasize making meaningful and translatable conclusions from these data. So actionable conclusions that can impact the way that we care for others around us. I do hope that remains a guiding principle in all that we do.  

[00:21:39] Erin Spain, MS: Why is Northwestern Medicine and Northwestern Feinberg School of Medicine such a supportive environment to pursue this type of work?  

[00:21:47] Denise Scholtens, PhD: That's a wonderful question and one, honestly, that faculty candidates often ask me. When we bring faculty candidates in to visit here at Northwestern, they immediately pick up on the fact that we are a collaborative group of individuals who are for each other. Who want to see each other succeed, who are happy to share the things that we know and support each other's work, and support each other's research, and help strategize around the things that we want to accomplish. There is a strong culture here, at least in my department and in my division that I've really loved that continues to persist around really genuinely collaborating and genuinely sharing lessons learned and genuinely supporting each other as we move toward common goals. We've had some really strong, generous leadership who has helped us to get there and has helped create a culture where those are the guiding principles. In my leadership role is certainly something that I strive to maintain. Really hope that's true. I'm sure I don't do it perfectly but that's absolutely something I want to see accomplished here in the division and in NUDACC for sure.  

[00:22:50] Erin Spain, MS: Well, thank you so much for coming on the show and telling us about your path here to Northwestern and all of the exciting work that we can look forward to in the coming years.  

[00:22:59] Denise Scholtens, PhD: Thank you so much for having me. I've really enjoyed this.  

[00:23:01] Erin Spain, MS: You can listen to shows from the Northwestern Medicine Podcast Network to hear more about the latest developments in medical research, health care, and medical education. Leaders from across specialties speak to topics ranging from basic science to global health to simulation education. Learn more at feinberg. northwestern.edu/podcasts.  

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Six Northwestern faculty named 2024 Guggenheim Fellows

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Six Northwestern faculty are among the 2024 Guggenheim Fellows  recently named by the John Simon Guggenheim Memorial Foundation. The faculty members are Mike Cloud, Nina Kraus, Chad Mirkin, Teri Odom, Krista Thompson and Petia Vlahovska.

This year, the foundation awarded 188 Guggenheim Fellowships to a diverse group of culture-creators working across 52 disciplines. Chosen through a rigorous application and peer review process from a pool of almost 3,000 applicants, the Class of 2024 Guggenheim Fellows was tapped on the basis of prior career achievement and exceptional promise. As established in 1925 by founder U.S. Senator Simon Guggenheim, each fellow receives a monetary stipend to pursue independent work at the highest level under “the freest possible conditions.”

Since its establishment, the foundation has awarded more than $400 million in fellowships to more than 19,000 fellows.

“Humanity faces some profound existential challenges,” said Edward Hirsch, award-winning poet and president of the John Simon Guggenheim Memorial Foundation. “The Guggenheim Fellowship is a life-changing recognition. It’s a celebrated investment into the lives and careers of distinguished artists, scholars, scientists, writers and other cultural visionaries who are meeting these challenges head-on and generating new possibilities and pathways across the broader culture as they do so.”

Mike Cloud is a painter and an associate professor of art, theory and practice in the Weinberg College of Arts and Sciences.

His artistic practice encompasses an expanded field of painting and image-making. He dissects photographic and painterly form, scrambling text and re-aligning content in a way that produces new breaks in legibility and new understandings.

A focus of his work is to examine paintings as objects within a system of objects. He uses marks, symbols, motifs, palettes and forms in an expressive technique that blurs and blends elements together into aesthetic compositions, while also interrogating the politics, contrivances and language of painting to locate his complicity in its system of functions.

His solo exhibitions include “Called Ahead” (2024) at Fahrenheit Madrid, Spain; “Tears in Abstraction” (2019) and “Bad Faith and Universal Technique” (2014) at Thomas Erben Gallery, New York; “The Myth of Education” (2018) at the Logan Center for the Arts in Chicago; and “Special Projects: Mike Cloud” (2005), MoMA PS1, New York.

He will use his Guggenheim Fellowship to develop “Holistic Abstraction,” a new body of research, writing and paintings inspired by ancient, classical and religious diagrams of the universe that present modes of abstraction that take a holistic view of artistic ambition.

Nina Kraus is a professor of neurobiology and otolaryngology and holds the Hugh Knowles Chair of communication sciences and disorders in the School of Communication and is the director of the Auditory Neuroscience Lab “Brainvolts” at Northwestern.

A scientist, inventor and amateur musician, her research is focused on the biology of auditory learning. She was among the first to discover that individual neurons change their firing patterns when sound-to meaning connections are made. Through auditory neuroscience, Kraus shows how our lives in sound impact our neurological health, changing the brain and affecting our interactions with others. 

An author of over 400 scientific publications, she also seeks to engage a broader audience through public lectures and writing. She is the author of the book “Of Sound Mind: How Our Brain Constructs a Meaningful Sonic World” (MIT Press, 2022). Pursuing connections across disciplines in science and the humanities, Kraus’ research is conducted beyond the laboratory and inside schools, community centers, athletic facilities and clinics to advocate for best practices in education, health and social policy. 

Kraus will use her Guggenheim Fellowship to write a book that asks what music can teach us about our biology.

Chad Mirkin

Chad A. Mirkin is the director of the International Institute for Nanotechnology and the George B. Rathmann Professor of Chemistry, Chemical and Biological Engineering, Biomedical Engineering, Materials Science and Engineering, and Medicine at Northwestern. He is a chemist and a world-renowned nanoscience expert, who is known for his discovery and development of spherical nucleic acids (SNAs) and SNA-based biodetection and therapeutic schemes, dip-pen nanolithography (and related cantilever-free nanopatterning and materials discovery methodologies), on-wire lithography and co-axial lithography and high-area rapid printing and contributions to supramolecular chemistry and nanoparticle synthesis.

He has authored over 870 manuscripts and over 1,200 patent applications worldwide (over 430 issued) and founded multiple companies. Mirkin has been recognized with over 250 national and international awards and served for eight years on the President’s Council of Advisors on Science and Technology and is one of a few scientists to be elected to all three U.S. National Academies and the American Academy of Arts and Sciences.

Mirkin will use the award to pursue groundbreaking research that will use nanotechnology to transform how vaccines are developed for treating deadly forms of cancer.

Teri W. Odom

Teri W. Odom is the Joan Husting Madden and William H. Madden, Jr. Professor of Chemistry and the chair of the department of chemistry in Weinberg College. She also is a member of the International Institute for Nanotechnology and Chemistry of Life Processes Institute.

A member of the National Academy of Sciences and the American Academy of Arts and Sciences, Odom is an expert in designing structured nanoscale materials with exceptional optical and physical properties. By controlling materials architectures over multiple length scales, Odom’s research group can transform ordinary materials into extraordinary ones. For example, her team has demonstrated that precious metals can be made even more precious by tuning their size and shape at the nanoscale.

Among her many achievements, Odom has pioneered a suite of multi-scale nanofabrication tools, which have resulted in flat optics capable of manipulating light at the nanoscale and beating the diffraction limit, plasmon-based nanoscale lasers that exhibit tunable color, and hierarchical substrates that show controlled wetting and super-hydrophobicity.

Odom will use her Guggenheim Fellowship in chemistry to design and develop structured color materials that can be used as nanoscale coatings for cooling surfaces, such as those on city buildings.

Krista Thompson

Krista Thompson is an art historian, curator and the Mary Jane Crowe Professor in Art History and director of graduate studies in art history in Weinberg, where she is a faculty affiliate in the department of Black studies . Thompson also is a faculty affiliate in the department of performance studies in the School of Communication.

Thompson’s research focuses on modern and contemporary art and visual culture of the African diaspora and Caribbean, with an emphasis on photography, photographic archives and lens-based practices. She is the author of “An Eye for the Tropics” (Duke University Press, 2006) and “Shine: The Visual Economy of Light in African Diasporic Aesthetic Practice” (Duke University Press, 2015).   Thompson is the co-editor (with Claire Tancons) of “En Mas’: Carnival and Performance Art of the Caribbean” (2015) and co-editor ( with Huey Copeland) of a series of articles on afrotropes published by Art Journal.

She will use her Guggenheim Fellowship to complete   a   book on Tom Lloyd, an African American artist who was among a wave of artists working with light and electronic technologies in the 1960s.  

Petia Vlahovska

Petia Vlahovska is a professor of engineering sciences and applied mathematics in the McCormick School of Engineering , where she directs the Complex Fluids and Soft Interfaces Lab.

An expert in fluid dynamics and soft matter, Vlahovska integrates theory and experiments in mathematical modeling of physical and biological systems leading to cutting-edge work on blood flow, biomembrane mechanics, electrohydrodynamics and active matter. In her studies of active fluids, Vlahovska was the first to examine the collective dynamics of “microrotors,” or dense suspensions of self-propelled, tiny rotating spheres.

Vlahovska also is interested in the membranes that encapsulate cells and play a central role in all living systems. Her work examines membranes’ non-equilibrium behavior, an emerging topic at the forefront of biophysics research.

The Guggenheim Fellowship will support Vlahovska’s efforts to harness active fluids for the engineering of micro-robotic systems mimicking the autonomous motility and responsivity of biological cells.

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Six Northwestern faculty elected to American Academy of Arts and Sciences

Two named fellows of the american association for the advancement of science, harry pei wins nsf career award.

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Jillian rastinejad selected for competitive gemini graduate student visitor program.

Posted April 24, 2024

northwestern math phd application

“I’m absolutely thrilled to visit Gemini-North and see the telescope that’s played a huge role in my graduate work in action,” shared Rastinejad. “I study rapidly-evolving explosions that often require a massive, complicated telescope to observe a new target with just a few hours notice, a feat that Gemini and its staff regularly accomplish for us. Since there’s no guarantees that an explosion will happen while we’re there, I’ll be learning about Gemini’s instruments in detail so that I can make better decisions faster when a future explosion happens – but fingers crossed the Universe will send us something good that week!”

Rastinejad is a member of CIERA Professor Wen-fai Fong ‘s group, where she researches astronomical transients and kilonovae. The successful program that secured Rastinejad’s Gemini visit involved her and Professor Fong designing an experiment to uncover the astrophysical origins of the heavy, r-process elements by following a long gamma-ray burst (produced by the collapse of massive stars).

Congratulations, Jillian!

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Image: International Gemini Observatory/NOIRLab/NSF

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  1. Application: Department of Mathematics

    The Department of Mathematics will not consider general or subject GRE scores in applications for September 2024. International students, other than those who have completed or will complete an undergraduate or graduate degree at an academic institution whose language of instruction is English, must submit as part of their application the result of the TOEFL, IELTS or MET exam.

  2. Mathematics : The Graduate School

    The Graduate Program in the Department of Mathematics aims to develop students into productive research mathematicians. The extremely low student-faculty ratio, approximately two-to-one, allows for close relationships between students and faculty. Department research strengths include algebra, algebraic geometry, algebraic topology, classical ...

  3. Admissions

    Admissions to the PhD program is competitive; approximately 10 students enter the PhD program each year. Not all of our applicants have a math undergraduate degree; many have degrees in science, engineering, or other fields, prior to arriving at Northwestern. Learn more about admissions process for the McCormick School of Engineering

  4. PhD

    The PhD program in applied mathematics is designed for students who want to pursue research in applied math at the highest level. The PhD program prepares students for independent research and emphasizes flexibility in adapting research areas to current opportunities. PhD students can obtain a master's degree after successful completion of the ...

  5. Mathematics PhD < Northwestern University

    A student who has passed the qualifying exam may register for TGS 500-0 Funded Doctoral Study beginning in the third year.; Other PhD Degree Requirements. Examinations: three written preliminary examination in the core courses of Analysis, Geometry/Topology, and Algebra; oral qualifying examination Research/Projects: see PhD Dissertation below PhD Dissertation: original, independent research

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    Graduate Study. The Department of Engineering Sciences and Applied Mathematics offers two graduate programs in engineering sciences and applied mathematics: a master of science program and a doctoral program. Qualified students with backgrounds in engineering, mathematics, or science are eligible for admission to either program. Not all of our ...

  8. Admissions

    Admission to the master of science program in engineering sciences and applied mathematics is competitive. Not all of our applicants have a math undergraduate degree; many have degrees in science, engineering, or other fields prior to arriving at Northwestern. Learn more about admissions process for the M c Cormick School of Engineering.

  9. Application Checklist

    Graduate Application Checklist. Please note: The information provided on this page is for applicants applying to programs offered through The Graduate School at Northwestern University. Applicants to the following programs offered directly through the McCormick School of Engineering, should refer to their program's website for application instructions as they vary by program: Master of Science ...

  10. Graduate Program: Welcome: Department of Mathematics

    Our program aims to develop graduate students into productive research mathematicians. We offer the benefits of an internationally-renowned faculty together with the close-knit collegiality of a small department. Our extremely low student-faculty ratio, small class size, and close interactions among students and faculty allow us to give you ...

  11. Graduate Admissions : Northwestern University

    Admissions; Graduate Admissions; Applying is the next step to achieving your professional goals. Get started by learning more about the application process, which can vary by school. Use the links below to access admissions instructions and deadlines. Admissions Websites Find instructions and tips for your application.

  12. Application Requirements

    In general, to apply to The Graduate School (TGS), you will be required to: Submit an application online. Pay an online application fee by credit card. Submit your essays. Upload your transcript (s) or academic record (s). Submit your test scores (international applicants are required to submit English language test scores; programs may also ...

  13. PhD Program : Department of Statistics and Data Science

    PhD Program Overview. The doctoral program in Statistics and Data Science is designed to provide students with comprehensive training in theory and methodology in statistics and data science, and their applications to problems in a wide range of fields. The program is flexible and may be arranged to reflect students' interests and career goals.

  14. Engineering Sciences & Applied Mathematics

    Since 1977, the Department of Engineering Sciences and Applied Mathematics has been one of the leading applied mathematics programs in the world.. Our department is uniquely housed within Northwestern's McCormick School of Engineering. This allows our highly interdisciplinary faculty and students to connect with engineers and scientists across departments, schools, a nd institutions ...

  15. Engineering Sciences and Applied Mathematics PhD Program

    Dive into the research topics where Engineering Sciences and Applied Mathematics PhD Program is active. These topic labels come from the works of this organization's members. ... Engineering Sciences and Applied Mathematics PhD Program; NCWR - Northwestern Center for Water - Member; Northwestern Institute on Complex Systems (NICO) - Co-Director ...

  16. Mathematics PhD Program

    antieau northwestern edu; Mathematics - Professor; Mathematics PhD Program; Person: Academic. 2011 2023. Antonio Auffinger. tuca ... 2009 2023. Nir Avni. nir.avni northwestern edu; Mathematics - Professor; Mathematics PhD Program; Person: Academic. 2005 2023. View all 44 experts Research Output Research Output per year 2016 2016 2020 ...

  17. Graduate Programs : Northwestern University

    Filter graduate and professional programs and certificates by personal interests or Northwestern school. You can dive into a potential program's specifics on its departmental website, linked below. Find what's next. Explore Northwestern University's graduate and professional programs for certificates, master's, and PhD degrees.

  18. Department of Mathematics

    2022-2023 NU Mathematics Department Newsletter. Catch up on NU Mathematics research announcements as well as 2022-2023 highlights on our programs, faculty, conferences, graduate students, and other Math news in our annual newsletter. Thank you to all of our 2022-2023 donors, whose ongoing support ensures our department will continue to thrive ...

  19. Mathematics PhD Program

    Mathematics PhD Program. Graduate Programs; Physical Sciences, Math, and Engineering Graduate Programs; Overview; Fingerprint; Network; Experts (44) Research Output (12) Profiles 44 results Last Name (ascending) Last Name (descending) Search results. Benjamin Antieau. antieau northwestern edu; Mathematics - Professor; Mathematics PhD Program ...

  20. Admissions

    Academics Overview Explore our degrees, programs, courses, and other enrichment opportunities.; All Areas of Study View a chart of all study areas cross-categorized by degree type.; Undergraduate Study Explore majors, minors, student groups, research, enrichment, and support opportunities. Plan your visit to campus and start your application. Graduate Study Explore our full-time and part-time ...

  21. Driving Innovations in Biostatistics with Denise Scholtens, PhD

    After discovering her love of statistics as a high school math teacher, Scholtens studied bioinformatics in a PhD program before arriving at Feinberg in 2004. Feinberg's commitment to biostatistics has grown substantially in recent decades. Scholtens was only one of five biostatisticians when she arrived.

  22. Annual 2024-2025 Class Schedule: Department of Political Science

    Address; Department of Political Science; Scott Hall 2nd Floor, 601 University Place; Evanston, IL 60208; Phone number; Phone: 847.491.7450; Fax number; Fax: 847.467.6601

  23. Engineering Sciences and Applied Mathematics: The Graduate School

    Degree Types: PhD, MS. The program in Engineering Science and Applied Mathematics educates students in mathematical methods and their application to various scientific and engineering fields. Our program emphasizes techniques associated with asymptotic analysis, bifurcation theory, dynamical systems, numerical analysis, ordinary and partial ...

  24. Six Northwestern faculty named 2024 Guggenheim Fellows

    This year, the foundation awarded 188 Guggenheim Fellowships to a diverse group of culture-creators working across 52 disciplines. Chosen through a rigorous application and peer review process from a pool of almost 3,000 applicants, the Class of 2024 Guggenheim Fellows was tapped on the basis of prior career achievement and exceptional promise.

  25. Graduate Study: Department of Mathematics

    Graduate Schools. Below is a list of graduate schools that Northwestern mathematics majors have attended since 2015. Graduate Schools. Arizona State University. Carnegie Mellon University. Carnegie Mellon University, Tepper School Of Business. Columbia University. Depaul University. Fairfield University.

  26. Program Statistics: The Graduate School

    Program Statistics. An important element of promoting master's and doctoral education and postdoctoral training is providing reliable and meaningful data. Use our interactive data visualization tool for PhD and master's students to explore admissions, enrollment, academic outcomes, and career placements. These data can be sorted by academic ...

  27. Jillian Rastinejad selected for competitive Gemini Graduate Student

    In early April 2024, 5 graduate students from across the International Gemini Observatory community were selected to visit the observatory and participate in a night of observing, including CIERA graduate student Jillian Rastinejad.The Gemini Observatory, operated by the National Science Foundation's NOIRLab, consists of twin 8.1-meter optical/infrared telescopes - Gemini-North (Hawai'i ...