Author: Steve Mintz

In Print: Pinelis Paper Published in the Journal Electronic Communications in Probability

Image if Iosif Pinelis who published in the journal electronic communications
Dr. Iosif Pinelis
Professor, Mathematical Sciences

Congratulations to Iosif Pinelis. Dr. Pinelis is the author of a paper published in the Journal Electronic Communications in Probability. The paper is titled “Asymptotics of the rate function in the large deviation principle for sums of independent identically distributed random variables.”

Dr. Pinelis is a professor of mathematical sciences whose main interests are in exact inequalities and limit theorems and extremal problems in probability theory. Other interests include optimization, evolutionary modeling, and operations research.


About the Mathematical Sciences Department

Mathematicians at Michigan Technological University conduct research and guide students, applying concepts to fields like business, engineering, healthcare, and government. The Mathematical Sciences Department offers undergraduate and graduate programs with degrees in mathematical sciences, applied statistics, and statistics. Students supercharge their math skills at Michigan’s premier technological university. They graduate prepared for successful careers in academia, research, and tomorrow’s high-tech business environment.

Questions? Contact us at mathdept@mtu.edu. Follow us on Facebook or read the Mathematical Sciences news blog for the latest happenings.

Ong Closes Contract from Lawrence Livermore National Laboratory

Benjamin Ong
Associate Professor Benjamin Ong

Benjamin Ong is the principal investigator (PI) on a project that has received a $45,000 research and development contract from the Lawrence Livermore National Laboratory, entitled “Systematic Approaches to Construct Coarse-Grid Operators for Multigrid Reduction in Time.”

Multigrid Reduction in Time (MGRIT) [2] uses multigrid reduction techniques to enable temporal parallelism for solving initial value problems. It is known that the convergence rate of MGRIT [3] depends in part on the choice of time-stepping operators on the fine- and coarse-grid, which we call the fine-grid operator and coarse-grid operator respectively. An “ideal” coarse-grid operator is the fine-grid operator applied to approximate the solution on the coarse time interval.

In practice, the ideal coarse-grid operator is never used as the computational cost destroys any parallel speed-up that could be obtained using MGRIT. Instead, a common choice for a coarse-grid operator is a simple re-discretization of the fine-grid operator, i.e., if a single-step method is used on the fine-grid with time-step size h, then the same single-step method is used on the coarse-grid with time-step size m h, where m is a specified coarsening factor.

Numerical simulations are increasingly important in the study of complex systems in engineering, life sciences, medicine, chemistry, physics, and even non-traditional fields such as social sciences. Dr. Ong is working to solve these large-scale evolution problems on modern supercomputing architectures by using a hierarchy of space-time grids to accelerate the solution on the finest time grid.

References

Time permitting, Dr. Ong will explore the connection between the proposed sequences of generated coarse-grid operators to those recently proposed by Vargas et al. [4].

[1] Daniel Crane. The Singular Value Expansion for Compact and Non-Compact Operators. PhD thesis, Michigan Technological University, 2020.

[2] R. D. Falgout, S. Friedhoff, Tz. V. Kolev, S. P. MacLachlan, and J. B. Schroder. Parallel time integration with multigrid. SIAM Journal on Scientific Computing, 36(6):C635–C661, 2014.

[3] Andreas Hessenthaler, Ben S. Southworth, David Nordsletten, Oliver RÅNohrle, Robert D. Falgout, and Jacob B. Schroder. Multilevel convergence analysis of multigrid-reduction-in-time. SIAM Journal on Scientific Computing, 42(2):A771–A796, 2020.

[4] David. A. Vargas. A general framework for deriving coarse grid operators for multigrid reduction in time. Technical report, Lawrence Livermore National Laboratory, 2023.

About the Mathematical Sciences Department

Mathematicians at Michigan Technological University conduct research and guide students, applying concepts to fields like business, engineering, healthcare, and government. The Mathematical Sciences Department offers undergraduate and graduate programs with degrees in mathematical sciences, applied statistics, and statistics. Students supercharge their math skills at Michigan’s premier technological university. They graduate prepared for successful careers in academia, research, and tomorrow’s high-tech business environment.

Questions? Contact us at mathdept@mtu.edu. Follow us on Facebook or read the Mathematical Sciences news blog for the latest happenings.

Math’s McFall Makes Deans’ Teaching Showcase Finals

Patrick McFall
When he’s not in the classroom in Fisher, you can find McFall canoeing on Portage Lake

College of Sciences and Arts Dean Ravindra Pandey has selected Patrick McFall as this week’s featured instructor in the Deans’ Teaching Showcase.

McFall, assistant teaching professor in the department of mathematical sciences, will be recognized at an end-of-term event with other showcase members. Recognition qualifies him as a candidate for the CTL Instructional Award Series.

McFall served as the Director of the Math Learning Center from 2020-2023. He co-directed the center in 2023. McFall teaches many large sections of fundamental math courses for the department, going back to spring 2021. He’s appeared in the top 10% of Michigan Tech instructors based on the “Average of 7 Dimensions” for student evaluation scores in three different semesters.

McFall’s Teaching Experience Helps Reduce DFW Rate

In the spring of 2023, McFall took on the coordinator role for MA 1160/1161 Calculus 1. He co-developed the department’s proposal to address the DFW rate for this class. McFall was instrumental in implementing the project. He piloted weekly algebra reviews, and developed pre-class videos and quizzes for a blended learning structure. McFall provided handouts for all instructors to increase student engagement. McFall met weekly with the instructors to ensure consistency in instruction. As a result, the Spring 2023 DFW rate for MA 1160/1161 showed a significant decrease from previous spring semesters. The rate for Spring 2023 declined 25-30 percentage points lower than Spring 2022 and Spring 2021. McFall’s work continued this fall, with similar results.

McFall’s Teaching Garners Praise in the College

Jiguang Sun, Chair of the Mathematical Sciences department, praised McFall. “He is enthusiastic about teaching and promotes a positive and engaging environment in the classroom. Dr. McFall cares for his students, and provides motivation for learning.”

Maria Bergstrom, Associate Dean for Undergraduate Education in the College of Sciences and Arts highlighted the significance of McFall’s contributions as an outstanding instructor. “Patrick McFall’s work to reduce DFW rates in Calculus I through innovations in pedagogy and curriculum has had a tremendous impact,” she said. “The impact is not just in his department but also for undergraduate education as a whole at Michigan Tech. A solid understanding of calculus is fundamental to most of the science and engineering programs on campus. And thus student success efforts in these key courses have a ripple effect across campus. We are pleased to showcase his instructional achievements.”

About the Mathematical Sciences Department

Mathematicians at Michigan Technological University conduct research and guide students, applying concepts to fields like business, engineering, healthcare, and government. The Mathematical Sciences Department offers undergraduate and graduate programs with degrees in mathematical sciences, applied statistics, and statistics. Students supercharge their math skills at Michigan’s premier technological university. They graduate prepared for successful careers in academia, research, and tomorrow’s high-tech business environment.

Questions? Contact us at mathdept@mtu.edu. Follow us on Facebook or read the Mathematical Sciences news blog for the latest happenings.

In Print: Iosif Pinelis Published in The American Mathematical Monthly

Iosif Pinelis article cover page
Iosif Pinelis article as it appears in The American Mathematical Monthly

Iosif Pinelis authored a paper accepted for publication in The American Mathematical Monthly. The paper is titled “An exact bound for the inner product of vectors in C^n”. View a preprint version of the paper and/or download it online.

About the Mathematical Sciences Department

Mathematicians at Michigan Technological University conduct research and guide students, applying concepts to fields like business, engineering, healthcare, and government. The Mathematical Sciences Department offers undergraduate and graduate programs with degrees in mathematical sciences, applied statistics, and statistics. Students supercharge their math skills at Michigan’s premier technological university. They graduate prepared for successful careers in academia, research, and tomorrow’s high-tech business environment.

Questions? Contact us at mathdept@mtu.edu. Follow us on Facebook or read the Mathematical Sciences news blog for the latest happenings.

Michigan Tech Hosts Copper Country Workshop on Applied Mathematics, Statistics, and Data Sciences

CAMS and the Department of Mathematics successfully organized the Copper Country Workshop on Applied Mathematics, Statistics, and Data Sciences, July 5-7, 2022 at Michigan Technological University. The goal of the workshop is to bring leading researchers to discuss the recent developments in applied mathematics, statistics, and data science, and build collaborations among the participants from different areas.

The workshop attracted 47 participants including faculty and students. There were 30 speakers from 19 universities including:

  • Auburn University
  • Brown University
  • Columbia University
  • The George Washington University
  • Iowa State University
  • Kansas State University
  • Michigan State University
  • Michigan Technological University
  • Missouri University of Science and Technology
  • Purdue University
  • Stevens Institute of Technology
  • University of Florida
  • University of Georgia
  • University of Michigan
  • University of Minnesota
  • University of Notre Dame
  • University of South Carolina
  • The University of Texas at San Antonio
  • York University

Sessions of note included:

  • High-Performance Spectral Methods for Scalable Graph Embedding and Robust Machine Learning by Zhuo Feng of Stevens Institute of Technology
  • Coupling Learning With Classical Computational Inversion by Kui Ren of Columbia University
  • Deterministic-Statistical Approach for Moving Sources With Sparse Partial Data by Yanfang Liu of The George Washington University
  • Learning Dirichlet-to-Neumann Maps From Randomly Sampled Points: A Consistency Result by Yang Yang of Michigan Technological University
  • Bayesian Hierarchical Modelling for Process Optimization by Min Wang of the University of Texas at San Antonio
  • Visualization of Mixed-featured Datasets by Fan Dai of Michigan Technological University

Visit the workshop website to see a list of all the session titles and speakers. To learn more about the Copper Country Workshop, please contact Michigan Tech’s Mathematical Sciences department chairperson Jiguang Sun.

Parallel Time Integration Workshop to be Hosted by Michigan Tech

Michigan Tech’s Department of Mathematical Sciences will host the NSF-CBMS Summer Workshop on Parallel Time Integration from August 1 – 5th, 2022. The free workshop will feature ten lectures by Martin J. Gander, Université de Genève, an expert in parallel time integration. The primary focus of the proposed parallel-in-time workshop is to educate and inspire researchers and students in new and innovative numerical techniques for the parallel-in-time solution of large-scale evolution problems on modern supercomputing architectures, and to stimulate further studies in their analysis and applications. This workshop aligns with the National Strategic Computing Initiative (NSCI) objective: “increase coherence between technology for modeling/simulation and data analytics.”

Image of Professor Gander
Professor Martin J. Gander, Université de Genève

Register for the workshop today. Registration closes on July 1, 2022.

More on the parallel-in-time workshop.

Computational simulations are a key part of scientific research for government, industry, and academia, complementing laboratory experimentation and theory.  However, changes in computer architectures are leading to future supercomputers that will have billions of processors, as opposed to millions today. Further, each individual processor will be no faster than individual processors today.  Thus, these next-generation machines will no longer automatically provide a speedup to existing computational simulations. New mathematical algorithms must be developed and deployed that can utilize this unprecedented number of processors.

One such class of mathematical algorithms, parallel-in-time methods, is the subject of this workshop.  In particular, parallel-in-time methods add a new dimension (time) of parallelism and thus allow existing computer models to be extended to next-generation supercomputers. The range of potential applications for parallel-in-time to dramatically speed up is vast, e.g., computational molecular dynamics (e.g., protein and DNA folding), computational biology (e.g., heart modeling), computational fluid dynamics (e.g., combustion, climate, and weather), and machine learning.

Using appropriate mathematical methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretizations, integration techniques, and convergence analyses of these iterative methods, conference participants will be exposed to the numerical analysis of parallel-in-time methodologies and their implementations. The proposed topics include multiple shooting type methods, waveform relaxation methods, time-multigrid methods, and direct time-parallel methods. These lectures will be accessible to a wide audience from various disciplines, including mathematics, computer science and engineering.

About your lecturer, Professor Martin J. Gander

Professor Martin J. Gander is a Professor of Mathematics at the University of Geneva, Switzerland. He is an internationally recognized expert in the area of Domain Decomposition Methods (DDM) and time-parallel integrators, among many other research interests. Professor Gander has published over 200 manuscripts and serves on the editorial boards of various journals, including SIAM Review, Computers and Mathematics with Applications, and the Electronic Transactions in Numerical Analysis. Professor Gander has also published two textbooks, Scientific Computing: an Introduction using Maple and MATLAB and Numerical Analysis of Partial Differential Equations using Maple and MATLAB.

Professor Gander is a highly accomplished and engaging lecturer, winning several teaching awards over his career. Professor Gander recently conducted a short course on Schwarz methods in August 2015, a short course on Time Parallel integration at the CEMRACS Summer School 2016: Numerical challenges in parallel scientific computing, and has given over 120 plenary lectures over his career. “In addition to being a leading researcher in the area of parallel time integrators, Professor Gander has influenced many lives through his commitment to training the next generation of scientists and engineers. We are so grateful that Professor Gander will be the principal lecturer at our NSF-CBMS summer school,” says Benjamin Ong, conference organizer and associate professor of mathematical sciences.

Thank you to our sponsors

The conference organizers, Professor Benjamin Ong (Michigan Technological University) and Professor Jacob Schroder (University of New Mexico) thank the sponsors for making this free conference with travel support possible: the National Science Foundation (NSF), Conference Board of the Mathematical Sciences, Michigan Technological University, Igor Kliakhandler, and the Time-X H2020 project.

Applied and Computational Mathematics Major Anthony Palmer Wins Best Poster at Computing [MTU] Showcase

Michigan Tech double major in applied and computational mathematics and physics, Anthony Palmer, along with computer science PhD candidate Elijah Cobb, won the best poster recently in the Computing [MTU] Showcase for “Universal Sensor Description Schema: An extensible metalanguage to support heterogenous, evolving sensor data.”

Learn more about their accomplishment.

Image of Anthony Palmer and Elijah Cobb with their poster at Michigan Tech’s Computing Showcase
Anthony Palmer (left) and Elijah Cobb present their poster at Michigan Tech’s Computing [MTU] Showcase

Applied Mathematics + Computer Engineering = 2x Experiences

Image of Drew Rosales, applied mathematics major at Michigan Tech
Drew Rosales

What to do if you’re a computer engineering major and have plenty of math credits from high school?

If you’re Drew Rosales, you add an applied mathematics major, Blue Marble Enterprise, use your love of coding to help a PhD student conduct his research, and co-op for 10 to 15 hours a week. This Husky knows all about personal and professional exponential growth!
Drew is from Ann Arbor. He chose Michigan Tech because he relished the chance to try something different, get away from his hometown with a few friends, and be more independent. Experience a different part of the world. Drew likes the personable campus and class sizes. “I love the level of bonding here,” he says. “It’s not cutthroat.”

Drew has always enjoyed the engineering process. He’s been competing in Vex Robotics
since middle school, programming and building robots to perform tasks. He’s always been interested in mathematics. Coursework in linear algebra and differential equations helped him to better understand how space and time functions worked and how they relate to the world around us. He found he could use math to describe how objects move through the air and how different variables like drag and torque impact the robots he worked with. The robot improved through increased knowledge of how to manipulate sensor data and control algorithms — a great intersection between math, computer science, and physics. Applied math seemed like a perfect addition to computer engineering. Looking at the influence of mathematical techniques on computer algorithms added excitement to Drew’s studies.

One of his favorite courses is numerical partial differential equations (NPDE). He worked with a group to make a finite element analysis (FEA) tool to create a virtual mesh around a real-world product. The mesh allows the group to use math to show how different forces might impact the product. For example, think about a bridge subject to stressors like winds, tides, and weight-bearing. The tool makes it possible to select the optimal designs and materials for essential project specifications and conditions well before production.

“In NPDE I gained insight into how to use the tool and work with group members. It really was a point at which my two worlds of coding and mathematics (came together).”

Drew Rosales, 2022, double major in applied and computational mathematics and computer engineering

“Research is fun,” says Drew, who’s grateful he’s been able to acquire valuable research experience as an undergrad. He enjoys writing code to support PhD student Praveen Hettige and Professor Ben Ong’s research to find structure in data using Geometric Multi-Resolution Analysis (GMRA). Drew reads academic papers — an art in itself — on GMRA, which is an approach for taking large amounts of high dimensional data and approximating it using affine hyperplanes (think line segments used to approximate a curve) enabling the data to be more easily stored and accessed. He grapples with challenges like creating data representations that can be easily interpreted as well as streamable and applicable to different scientific and engineering domains.

Praveen says Drew is a fast learner who’s up to the task. “In order to complete the coding parts, it’s necessary to have a basic understanding of the theoretical concepts about my research topic,” said the PhD student, who completed his master’s work in statistics at Michigan Tech. “ caught up with those concepts quickly.”

The research is aimed at taking data efficiently in smaller quantities instead of one big dump. Doing so makes it easier to process and analyze the information, reducing computation time and allowing data-based decisions to be made much faster and more efficiently.

Working on Real-World Projects with Michigan Tech Enterprise

Image of Drew Rosales working with the Blue Marble Security Enterprise team
Drew (far left) works with his Blue Marble Security project team


Drew is also a member of Michigan Tech’s Enterprise program, serving as president of Blue Marble Security, a virtual company focused on industry-sponsored R&D and commercial product development including security, the environment, and industrial process control. The team is currently involved in seven multi-disciplinary projects, from smart tow capability for the US Navy to vision sensing for General Motors. In addition to his leadership role, Drew is doing coding and engineering work for the Navy project. Drew’s presidential duties include making sure the teams are progressing in their projects and have the resources they need to be successful. He assists teams in assessing timelines and tasks, is the point person for check-ins with Glen Archer, project sponsors, and keeps the Board informed. “Blue Marble has been instrumental in building my leadership skills. I have to assess how the team is doing and determine how to respond,” Drew says.

Archer goes a bit farther in assessing Drew’s skill. “One of Drew’s strengths that I have come to really appreciate is his calm approach to events around him. He is pretty much imperturbable. Drew is also resolute in his pursuits. He has risen steadily from a project engineer to project manager to the most senior leader in the organization. “

“It’s a pleasure to work with him because I know that if I ask him to do something, he will ask the questions he needs answered in order to do a good job. Once he has the answers, he will not fail to complete the task.”

Glen Archer, Interim Chair, Electrical and Computer Engineering, Blue Marble Security Enterprise Advisor
Image of the Blue Marble Security Enterprise team
Blue Marble Security Enterprise Team, with Drew Rosales standing next to Glen Archer in the lower left.

A Co-op with Caterpillar Builds Skills and Confidence


In addition to classes, research, and Enterprise, Drew works as a co-op student for Caterpillar for 10 to 15 hours per week, a stellar addition to his engineering portfolio. His primary role has been to develop software for engine system sensors and to integrate the sensors into existing software. Drew conducts simulation testing on software for engines, validating that an engine reaches fuel efficiency guidelines and standards. The software allows Caterpillar to validate engine functionality before producing an engine en masse.

The work he’s put into presentation skills during his co-op has built confidence as well as a vision of what a bright future looks like. “I’ve learned more about how a full-time job works, how to work with others in a corporate setting, and what is expected of me on the job,” Drew says. “In addition, I have learned how to prepare myself while in college, building the skill set I need to be successful in my future career.”

Q&A on Drew’s Past, Present, and Future


Q: What have you learned about yourself and what advice would you give your high school self now?

DR: A lot of the time I see myself working on a task that might seem irrelevant or boring and tedious at the time, but it does come together, in the end, to be important. In college, with everything I have done, I’ve gained the ability to think about how to get better. Where are the gaps in knowledge I need to fill in and how do I go about doing it? It goes back to the dualities I’ve encountered between math and engineering, industry, and research. How can I grow and find value out of present and future opportunities? How does this influence what I find interesting and learned thus far?

Before college, I was more shy. Not as well-spoken. I always felt things would come together and fall into my lap. College helped me to see that I needed to be proactive, take initiative and make things happen. That breeds confidence. You would be surprised with the opportunities that you come across through networking, being bold, and sticking to your passions.

Q: Where do you go from here?

DR: I’m switching to a research role this summer doing predictive modeling with autonomous vehicles and possibly putting my GMRA research experience into practice. I plan to continue working at the intersection of math and computer science and putting research into practice. Eventually, I hope to go to graduate school.