MIT Sloan Executive Education Logo

Learn on demand with our NEW Business Sprints .

MIT Logo

System Dynamics and Systems Thinking Courses

Several of our courses introduce participants to System Dynamics and systems thinking—powerful analytic and problem-solving tools that are applicable in any in industry and at any level of an organization.

What is System Dynamics?

System Dynamics is a framework and set of tools for understanding, modeling, and analyzing the change and complexity of a dynamic system—any system—over time. System Dynamics was born at MIT Sloan in the 1950s and developed by Prof. Emeritus Jay W. Forrester.

The system dynamics approach led to the creation of “management flight simulators” that enable managers to do a number of things, including:

  • Quantify the impact of interactions between parts and systems.
  • Experience the long-term side effects of decisions.
  • Design strategies for greater success.

Today, System Dynamics is taught around the world and used by corporations, nonprofit organizations, schools, and governments to manage complex challenges in domains from organizational change to supply chains to climate change.

What is Systems Thinking?

Systems thinking is a process of understanding how things influence one another within a whole.

Originating within Forrester’s Systems Dynamic Group at MIT Sloan, it is a holistic approach to analysis and problem solving that views "problems" as parts of an overall system, rather than in isolation. Systems thinking focuses on cyclical rather than linear cause and effect and on how small catalytic events can cause large changes in complex systems.

Because an improvement in one area of a system can adversely affect another area of that system, this practice promotes organizational communication at all levels.

The Beer Game

Participants in several of our system dynamics courses get to experience the Beer Game, a table game, developed by Jay Forrester.

Played with pen, paper, printed plastic tablecloths, and poker chips, it simulates the supply chain of the beer industry. In so doing, it:

  • Illuminates aspects of system dynamic.
  • Illustrates the nonlinear complexities of supply chains.
  • Explains the way individuals are circumscribed by the systems in which they act.

Learn More:

mit problem solving seminar

Building Organizational Resilience: A System Approach to Mitigating Risk and Uncertainty

Our organizations – designed for optimal performance — work well under normal conditions, but are vulnerable to failure when the unexpected occurs. How do we design systems that work efficiently under typical conditions, yet respond resiliently to “unknown unknowns”? This new course provides business leaders with a practical approach to assess and build organizational resiliency. Learn how systems thinking and continuous improvement can help your team identify problems before they occur and fundamentally alter your organization’s ability to effectively respond when they do. Understand the role hidden factories and irregular operations play in contributing to catastrophic events, and how this knowledge can be leveraged to reverse their effects. Leave with a playbook for improving the resilience of your company.

mit problem solving seminar

Business Dynamics: MIT's Approach to Diagnosing and Solving Complex Business Problems

This 7-day course provides an intensive, hands-on introduction to System Dynamics, a unique framework for understanding and managing complex businesses and organizations. Participants are introduced to a variety of tools, including mapping techniques, simulation models, and MIT’s “management flight simulators” to help them understand the sources of persistent problems and how business decisions may result in complicated cause-and-effect loops.

mit problem solving seminar

Understanding and Solving Complex Business Problems

This 2-day program introduces participants to MIT's unique, powerful, and integrative System Dynamics approach to assess problems that will not go away and to produce the results they want. Through exercises and simulation models participants experience the long-term side effects and impacts of decisions and understand the ways in which performance is tied to structures and policies. 

mit problem solving seminar

Strategies for Sustainable Business

This innovative program applies a System Dynamics framework to the topic of environmental and socio-economic sustainability and uses an engaging mix of interactive lectures, simulation games and action learning. Participants leave with practical and impactful strategies for building consensus and making change, and are empowered to take action on sustainability from the personal through enterprise level.

View All Courses In Our Portfolio

mit problem solving seminar

John Sterman on System Dynamics

System Dynamics is a concept invented at MIT Sloan and used worldwide by companies and governments. John Sterman discusses how our open enrollment courses teach participants the tools they need to solve complex problems.

Sign Up for Email Updates on Executive Education Programs

Review our Privacy Policy.

Suggestions or feedback?

MIT News | Massachusetts Institute of Technology

  • Machine learning
  • Social justice
  • Black holes
  • Classes and programs

Departments

  • Aeronautics and Astronautics
  • Brain and Cognitive Sciences
  • Architecture
  • Political Science
  • Mechanical Engineering

Centers, Labs, & Programs

  • Abdul Latif Jameel Poverty Action Lab (J-PAL)
  • Picower Institute for Learning and Memory
  • Lincoln Laboratory
  • School of Architecture + Planning
  • School of Engineering
  • School of Humanities, Arts, and Social Sciences
  • Sloan School of Management
  • School of Science
  • MIT Schwarzman College of Computing

Making math fun by prepping for friendly competition

Press contact :.

Photo of Yufei Zhao, Tomasz Ślusarczyk, and Dain Kim standing in front of a blackboard.

Previous image Next image

Mark Saengrungkongka, a first-year MIT undergraduate student, stood at the blackboard and explained his solution to a math problem similar to the ones that might appear on the William Lowell Putnam Mathematics Competition , a prestigious annual math competition for college students in the United States and Canada administered by the Mathematical Association of America (MAA). After he finished presenting his proof, the class gave a round of applause. “That was a very nice solution,” math professor Yufei Zhao told the class.

It was a few weeks into the semester, and while there were a few latecomers, students in Class 18.A34 (Mathematical Problem Solving) paid close attention to the intricate proofs presented by their fellow students on the blackboard. The audience asked probing questions and pointed out gaps in the arguments.

This undergraduate seminar, better known as the Putnam Seminar, brings together first-year students who are interested in the annual competition. In recent years, MIT has finished first in the December exam, and all five top-scoring students, known as Putnam Fellows, were from MIT the past two years.

But the Putnam exam is also designed to just instill a love of math to all who attempt the insanely hard problem sets. One of the goals of Zhao’s class is to make solving these problems more like participating in a fun group puzzle rather than a stressful competition. For many first-year students, it’s also a nice way to ease into MIT life.

“The students in the seminar usually come in with a strong preparation from math competitions,” says Zhao. “But college is rather different from high school math Olympiads. A goal of the seminar is to help them transition from a high school math Olympian to a successful college student and beyond.”

Each week, Zhao starts his seminar gently, with a casual discussion. He asks the classes how they are feeling about the semester and talks about life as a college math student. Discussions include class selections, dealing with setbacks, and career paths. One student asks about how to find research opportunities; another student asks about recommendation letters.

Zhao knows that his students are already thinking ahead about upper-level math classes, but he hopes to slow them down a little so that they can take their time to really understand and appreciate what they are learning. “There’s a tendency for these students to do too much,” he says.

About 10 minutes after the start of the class, Zhao wraps up the discussion and starts the student presentations.

Mohit Hulse presented a solution to a combinatorics problem from the 2018 Putnam Competition. When he realized that he made a small mistake in the middle of his presentation, there was some supportive laughter, and he confidently continued on. The audience was respectful, and his classmates often helped with an idea.   

When he was finished, Zhao added compliments and tips. “I suggest looking up the proof of the Chernoff bound, which is quite similar,” he says. “That was a nice solution.” He then pointed to the board and gave some suggestions. “I thought this step could be omitted.”

In addition to discussions and student presentations, the seminar also features weekly lectures by upper-year students, including veterans of the Putnam Seminar. The lectures highlight math problem-solving techniques useful for the Putnam Competition as well as provide a lens into advanced mathematics. 

This year, roughly 60 incoming first-year students applied to the Putnam Seminar, among which 21 were selected. The seminar is internationally diverse, with students from 10 countries outside the United States: Australia, Armenia, Canada, China, Georgia, India, Korea, Portugal, Singapore, and Thailand.

“This class builds connections,” says Zhao. “All of them are new to MIT, and many are arriving in the U.S. for their first time. They are all interested in mathematics. I hope that the seminar will help them meet other students and form a supportive community.”

Any MIT student is welcome to attend the lectures, although the presentation sessions are restricted to the seminar students. These problem sets are also made available through MIT OpenCourseWare for other interested students and teachers.

Practicing presentations

The seminar is designed to provide a rare chance for first-years to develop their mathematical communication skills, including blackboard presentation and proof writing. Zhao says he has been innovating on the format of the seminar in recent years, with ever-increasing emphasis on oral presentation practice and feedback. 

“Undergraduates don’t get a lot of presentation opportunities, especially blackboard presentations,” says Zhao. “We hear a lot from MIT alumni that they wish they had received more training in communication skills at MIT.”

Two previous seminar students, senior Dain Kim and sophomore Tomasz Ślusarczyk, help the class as undergraduate assistants. Last year, Kim ranked sixth place in the competition, and was awarded the Elizabeth Lowell Putnam Prize for being the top female scorer, and Ślusarczyk earned an honorable mention. As undergraduate assistants, Kim and Ślusarczyk hold regular office hours where students come to practice presentations to a small audience of a few other students, without the professor present. These office hours started last year in response to students seeking more presentation opportunities outside classroom hours.

Kim says that she benefited a lot from taking the seminar as a first-year student. 

“Especially in math classes at MIT, it is hard to get a chance of giving a presentation to other students, unless it is a CI-M [Communication Intensive in the Major] class, because most classes are lecture-based,” Kim says. “I could hear from other students how they approached the problems that I could not solve, and I could also practice math presentations.” 

Ślusarczyk, who took the seminar last year, credited the class with transitioning some of his math contest approaches and mindset to research-oriented mathematics. “Combining the problem-solving focus with a higher level of mathematical maturity was definitely a great educational experience and improved my Putnam skills a lot,” he says. “The skills developed in the seminar were invaluable during problem-set sessions, office hours, or research meetings. The class definitely helped me a lot with my career plans — I learned a lot about research-oriented math and decided that I want to pursue research in a math PhD program after graduation.”

The competition

The Putnam exam was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, and has been offered annually since 1938, administered by the Mathematical Association of America.

Last year’s grueling six-hour exam featured 12 proof-based math problems, each worth 10 points, drawn from calculus, algebra, geometry, combinatorics, number theory, and more. The 2021 exam was taken by 2,975 undergraduates from 427 institutions, 150 of them from MIT.  

The top score was 119 out of 120 points, with the median score a mere four — which meant that most students did not fully solve a single problem. But of the top 105 scorers who finished with honorable mention rankings or higher, 63 were MIT students. 

The top five scorers receive the prestigious title of Putnam Fellow. For the second time in the competition’s history, all five Putnam Fellows came from MIT, and they were all Putnam Seminar alumni. In the more than 80 years of the Putnam Competition, only eight competitors achieved the rarified four-time Putnam Fellow status, including three from MIT. MIT math professor (and former MIT Putnam coach) Bjorn Poonen was one such four-time Putnam Fellow when he was an undergraduate at Harvard University.  

Back in 1973, when MIT math professor Richard Stanley started teaching at MIT, he noticed that MIT had a large number of students taking the Putnam. He had taken the exam three times during his Caltech years. 

“My best result was ninth overall,” he recalls. “At that time, Caltech was the dominant Putnam school. I can remember my freshman year one of the persons in my student house complaining that although he was seventh in the country, he was only fourth at Caltech and second in his hallway!” 

When he looked at how MIT students fared on the exam, he thought that there was room for improvement. 

“I thought that a seminar on problem-solving might stir up some interest and benefit the students,” he recalls.

Stanley’s undergraduate seminar on mathematical problem-solving featured his weekly lecture devoted to a Putnam-related topic such as number theory, linear algebra, generating functions, or inequalities. “These are huge subjects, but the lectures were very narrowly focused on providing background and examples for doing well on the Putnam,” says Stanley. 

He would then assign two problem sets each week, one based on the lecture, and another dedicated to “fun” problems. The second class that week had students discuss their solutions.  

“The class’s second focus was just the enjoyment of problems,” he says. “Many math students enjoy problem-solving and the opportunity to learn interesting tidbits from all areas of math that are not likely to be found in standard classes. They also like the camaraderie of friendly competition.”

Stanley was also the Putnam coach for about 35 years, later joined by Professor Hartley Rogers . The Putnam class seemed to pull MIT students into many first-place team victories. Eight alumni from that seminar eventually became Stanley’s PhD students, and he wrote a book, “ Conversational Problem Solving ,” based on his seminar.

Above all, Stanley emphasizes putting the fun in Putnam. Besides, he says, there’s a downside to all the winning.

“It is as if the Red Sox dominated all other teams every year and won every World Series in four games,” says Stanley. “Great for Boston fans, but not for baseball in general.”

As a first-year student in 2006, Zhao attended the Putnam seminar taught by Stanley and Rogers and went on to earn three Putnam Fellow spots; he missed the fourth by a single point. When he returned to MIT in 2017 to join the faculty, he began teaching the Putnam Seminar. 

Zhao credits Stanley for creating high-quality problem sets, which are still being used in the seminar. And Zhao is also continuing Stanley’s goal to steer students away from seeing the seminar as simply training for Putnam.  

“The class helped me to take the Putnam exam as a by-product,” says Kim. “Every week I solved a problem set, and I enjoyed trying some hard problems. It helped me to get used to Putnam-type problems. But this is not just a ‘Putnam preparation class.’ Although we are talking about Putnam problems and some concepts appear there, the goal of the class is not ‘raising the scores of participants.’” 

At the beginning of a late-November seminar, Zhao asked his students how they felt about the upcoming exam in less than two weeks, and a few mentioned the word “stressed.” But others said how much they just enjoyed working on the problems. “I want to take it without much pressure,” said one student. Added another, “What works for me is that I’m competing with myself, and not others.” 

Zhao then gave the class his most valuable advice: “Make sure you get lots of sleep the days leading up to the exam.”

Share this news article on:

Related links.

  • Course 18.A34 (Mathematical Problem Solving)
  • William Lowell Putnam Mathematical Competition
  • Department of Mathematics

Related Topics

  • Contests and academic competitions
  • Mathematics
  • OpenCourseWare
  • STEM education
  • Undergraduate
  • Education, teaching, academics

Related Articles

Photo of six students standing in Department of Math hallway.

MIT students take first place in the 82nd Putnam Mathematical Competition

A drawing of an icosahedron, a figure with 20 triangular faces, in purple. Red lines are seen drawn from various angles to other angles within the icosahedron. Outside the whole figure are many small yellow lines, as "rays" coming off of a star

Mathematicians solve an old geometry problem on equiangular lines

MIT students set records at this year’s Putnam Competition: (left to right) Shengtong Zhang, Yuan Yao, Kevin Sun, Daniel Zhu, Qi Qi, and Dain Kim. Not pictured: Ashwin Sah.

MIT students dominate annual Putnam Mathematical Competition

Previous item Next item

More MIT News

William Deringer smiles and stands next to an ornate wooden door.

Exploring the history of data-driven arguments in public life

Read full story →

Photos of Roger Levy, Tracy Slatyer, and Martin Wainwright

Three from MIT awarded 2024 Guggenheim Fellowships

Carlos Prieto sits, playing cello, in a well-lit room

A musical life: Carlos Prieto ’59 in conversation and concert

Side-by-side headshots of Riyam Al-Msari and Francisca Vasconcelos

Two from MIT awarded 2024 Paul and Daisy Soros Fellowships for New Americans

Cartoon images of people connected by networks, depicts a team working remotely on a project.

MIT Emerging Talent opens pathways for underserved global learners

Two students push the tubular steel Motorsports car into Lobby 13 while a third sits in the car and steers

The MIT Edgerton Center’s third annual showcase dazzles onlookers

  • More news on MIT News homepage →

Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, MA, USA

  • Map (opens in new window)
  • Events (opens in new window)
  • People (opens in new window)
  • Careers (opens in new window)
  • Accessibility
  • Social Media Hub
  • MIT on Facebook
  • MIT on YouTube
  • MIT on Instagram

mit problem solving seminar

Solve at MIT 2022

Flagship event.

Solve at MIT 2022 is an engaging, three-day event open to the MIT Solve Community on Thursday, May 5 through Saturday, May 7. Solve at MIT brings together these global innovators to build partnerships and tackle global challenges in real-time alongside the Solve community. If you have a registration code and need to submit a late registration, please contact [email protected].

Re-Live Highlights from Solve at MIT

Opening Plenary - Ethical and Inclusive Innovation

Investing in Community-Led Solutions in the U.S.

Promoting Our Care Providers

Young Leaders on the Horizon

About the Event

Every year, MIT Solve hosts open innovation Challenges to source tech-based solutions to urgent global problems. The most promising social entrepreneurs from across the world are chosen to join our Solver class in the areas of Economic Prosperity, Sustainability, Learning, and Health. 

Solve at MIT brings together these global innovators to build partnerships and tackle global challenges in real-time alongside the Solve community–Solver teams, MIT faculty, and social impact leaders from Solve Member organizations, such as General Motors, The Nature Conservatory, HP, The Bill & Melinda Gates Foundation, and many more.

Join the Solve Community

Interested in future MIT Solve events? Learn more about membership  here  or reach out to [email protected]

Featured Speakers

Noubar afeyan, co-founder and chairman, moderna, azra akšamija, director, art, culture and technology program, the future heritage lab, david alabo, multi-disciplinary artist, benjamin alexander, jamaica's first olympic alpine ski racer, (virtual), sabrina asturias, chief of trauma and emergency surgery at roosevelt hospital and professor of trauma simulation, francisco marroquin school of medicine, lynette bell, president, truist foundation, cynthia breazeal, dean for digital learning, mit, michael christian, board president, someone else’s child and managing partner, community impact ventures, l.p., melissa corto, ceo & co-founder, education modified, united states, jeffrey cyr, ceo, raven indigenous impact foundation, president & trustee, patrick j. mcgovern foundation, thanasios dilos, co-founder and cgo, civics unplugged, dr. shirin ebadi, nobel peace prize winner; founder, defenders of human rights center (virtual), omolara fatiregun, founder & ceo, thrive industries incorporated (thrive), professor yuval noah harari, historian, bestselling author, and co-founder, sapienship (pre-recorded), linda henry, ceo, boston globe media, editor in chief, mit technology review, dr. angela jackson, chief ecosystem investment officer, kapor enterprises, geci karuri-sebina, organizer, african civic tech innovation network, utsav kheria, co-founder, rocket learning, gideon lichfield, global editorial director, wired, latanya mapp frett, president and ceo, global fund for women, ceasar l. mcdowell, professor of the practice, civic design; associate department head, department of urban studies and planning, mit associate director, center for constructive communication, mit, catherine mohr, president , the intuitive foundation, eyitayo ogunmola, serhii plokhy, director and professor of ukrainian history, ukrainian research institute at harvard university (pre-recorded), l. rafael reif, president, massachusetts institute of technology, helena samsioe, founder & ceo, globhe, sanjay sarma, vice president for open learning, mit, social innovations director, national domestic workers alliance, janti soeripto, president & chief executive officer, save the children, june sugiyama, director, vodafone americas foundation || judge for the innovation for women prize, gita syahrani, chief of partnership, alam siak lestari, javier van cauwelaert, ceo, smartfish, value rescue for sustainable seafood, kristin welch, founder and executive director, waking women healing institute, anne wojcicki, co-founder & ceo, 23andme (virtual), dr. sakena yacoobi, president & executive director, the afghan institute of learning (ail), related articles, tackling systemic racism with antiracist technology, solve at mit 2022: demystifying world issues one connection at a time, ethical innovation: a conversation between yuval noah harari and serhii plokhy.

General Motors

We Use Cookies

We use cookies and other tracking technologies to improve your browsing experience on our website and to understand where our visitors are coming from. By browsing our website, you consent to our use of cookies and other tracking technologies.

Browse Course Material

Course info.

  • Prof. Yufei Zhao

Departments

  • Mathematics

As Taught In

Learning resource types, mathematical problem solving (putnam seminar), 18.a34 mathematical problem solving (putnam seminar): supp_ps 7.

facebook

You are leaving MIT OpenCourseWare

Past Seminars:

Mit probability seminar, current organizers.

  • Tomas Berggren
  • Alexei Borodin
  • Konstantinos Kavvadias
  • Elchanan Mossel
  • Scott Sheffield
  • Dan Mikulincer

Subscription to a mailing list

Spring 2024

Monday 4.15 - 5.15 pm

Scheduled virtual talks will be held on Zoom, Monday 4:15-5:15 pm. Zoom Link

Matan Harel (Northeastern University)

The loop O(n) model and the XOR trick

Abstract: The loop O(n) model is a model for random configurations of non-overlapping loops on the hexagonal lattice, which contains many models of interest (such as the Ising model, self-avoiding walks, and random Lipshitz functions) as special cases. Its conjectured phase diagram is very rich, and the model is believed to undergo several different phase transitions. Over the last decade, several features of the phase diagram have been proven rigorously, mostly through the use of particular bijections or observables at critical values. We use an expansion around critical percolation to prove that, near the values that correspond to critical Bernoulli percolation, the loop O(n) model has long , infinitely-nested loops, without relying on exact solvability. This is joint work with Nick Crawford, Alexander Glazman, and Ron Peled.

February 12

Scaling limits for random growth driven by reflecting Brownian motion

Abstract: We discuss long-time asymptotics for a continuum version of origin-excited random walk. It is a growing submanifold in Euclidean space that is pushed outward from within by the boundary trace of a reflecting Brownian motion. We show that the leading-order behavior of the submanifold process is described by a flow-type PDE whose blow-ups correspond to changes in diffeomorphism class of the growth process. We then show that if we simultaneously smooth the submanifold as it grows, fluctuations of an associated height function are described by a regularized KPZ equation with noise modulated by a Dirichlet-to-Neumann operator. If the dimension of the manifold is 2, we show well-posedness of the singular limit of this regularized KPZ-type equation. Based on joint work with Amir Dembo.

February 19

Presidents Day

February 26

Tomas Berggren (MIT)

Geometry of the doubly periodic Aztec dimer model

Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions -- known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

Jiaming Xu (Duke)

Recent advances on random graph matching

Abstract: Random graph matching aims to recover the hidden vertex correspondence between two random graphs from correlated edge connections. This is a ubiquitous problem arising in a variety of applications across diverse fields such as network privacy, computational biology, computer vision, and natural language processing. The problem is also deep and rich in theory, involving the delicate interplay of algorithms, complexity, and information limits. Recently, extensive efforts have been devoted to the study of matching two correlated Erdős–Rényi graphs and exciting progress have been made, thanks to collective efforts from a wide research community. The speaker in his talk will present an overview, recent results, and important future directions on this topic. Based on joint work with Cheng Mao (Georgia Tech), Yihong Wu (Yale), and Sophie H. Yu (Stanford).

Sky Cao (MIT)

Random surfaces and lattice Yang-Mills

Abstract: I will talk about recent work which studies Wilson loop expectations in lattice Yang-Mills models. In particular, I will give a representation of these expectations as sums over embedded maps. Time permitting, I will also discuss alternate derivations, interpretations, and generalizations of several recent theorems about Brownian motion limits (Dahlqvist), lattice string trajectories (Chatterjee and Jafarov) and surface sums (Magee and Puder).

This is joint work with Minjae Park and Scott Sheffield.

Spring Break

Guillaume Baverez (Humboldt University of Berlin)

Quantisation of the Segal's semigroup from Liouville theory

Abstract: In Segal's definition of conformal field theory (CFT), one key ingredient is to construct a representation of the semigroup of complex annuli with parametrised boundaries. In the first part of the talk, I will explain how this statement can be understood as a generalisation of the Hille-Yosida theorem, using only an analytic language. In particular, the (infinite dimensional) family of generators form a representation of the Virasoro algebra and encode the conformal symmetry of the theory. In the second part, I will give an example of this construction using the Gaussian free field, and show how it can be extended to treat the Liouville CFT. Based on joint works with Guillarmou, Kupiainen, Rhodes, Vargas.

Shalin Parekh (University of Maryland)

Extreme value theory for random walks in random media

Abstract: The KPZ equation is a singular stochastic PDE arising as a scaling limit of various physically and probabilistically interesting models. Often this equation describes the “crossover” between Gaussian and non-Gaussian fluctuation behavior in models of interacting particles, directed polymers, or interface growth models. In this talk, I will discuss recent progress we have made in understanding the KPZ crossover for models of random walks in dynamical random media. This talk includes joint work with Sayan Das and Hindy Drillick.

Patriots' Day

Pierre Patie (Cornell)

A spectral and algebraic algorithm: the centralizer and the fixed points, scaling and universality classes

Abstract: Over the last few decades, the exploration of scaling limits and universality classes has unveiled a spectrum of intriguing results, alongside complex and fascinating challenges. In this talk, we present a comprehensive framework designed to address these challenges in a constructive and solvable manner. It is based on an appropriate combination of group representation theory, group actions, spectral theory and operator algebras. Relying on the Stone-von Neumann Theorem, we identify a canonical setting for this framework, the so-called canonical G-module, and design a constructive algorithm. This formalism not only highlights the fundamental role played by the choice of the representation of mathematical objects but also offers constructive perspectives and connections into classical mathematical topics such as the spectral theory of self-adjoint operators, Lie point symmetry, von Neumann algebras, and the fundamental Stone-von Neumann theorem. We will illustrate this framework by describing the universality classes of the LUE ensemble, emphasizing the canonical role of its limit to the Bessel ensemble in the comprehensive framework. Finally, we shall discuss the role played by the Fourier transform, the Laplacian, and Brownian motion in this formalism.

Jinwoo Sung (University of Chicago)

Supercritical LQG conditioned to be finite

Abstract: Liouville quantum gravity (LQG) in the subcritical and critical phases, corresponding to 𝛾 ≤ 2 or central charge c ≤ 1, has been extensively studied as a theory of random metric measure space and conformal field theory. On the other hand, few rigorous results about LQG with parameters outside these ranges are known, mainly for the supercritical LQG metric constructed by Ding and Gwynne. In this talk, I will discuss other properties of supercritical LQG that can be investigated from its branching structure, which is due to the coupling of supercritical LQG disk with nested CLE4 by Ang and Gwynne. There are two main results: (1) the supercritical LQG area measure, which we define as a random Borel measure locally determined by a GFF and satisfying the LQG coordinate change rule, does not exist, and (2) a natural discretization of the CLE-decorated supercritical LQG disk has the continuum random tree as its scaling limit if we condition it to have a finite number of vertices. The latter behavior was predicted by Gwynne, Holden, Pfeffer, and Remy in a pioneering paper on supercritical LQG. This is joint work with Manan Bhatia and Ewain Gwynne.

Brice Huang

Current Term Accessibility

MIT

Serving technical professionals globally for over 75 years. Learn more about us.

MIT Professional Education 700 Technology Square Building NE48-200 Cambridge, MA 02139 USA

Accessibility

MIT

MIT Professional Education Launches New MicroCourse: Effective Problem Solving for Teams

Digital plus programs microcourse teaches mit’s unique framework for problem-solving and brainstorming to help organizations grow creative cultures and drive innovation.

Cambridge, Mass. , September 20, 2018 – MIT Professional Education, a gateway to renowned MIT research, knowledge and expertise through advanced education programs, today announced the launch of a new Digital Plus Programs MicroCourse titled,  Effective Problem Solving for Teams. The debut MicroCourse runs twice this Fall on October 22, 2018 and November 5, 2018. It is designed for professionals at all levels across any industry, especially those in the engineering and technology fields who are looking to grow their capacity for problem-solving in a way that promotes creativity and innovation. “Businesses today face more problems than they have time to solve. As a result, people admit how they tend jump too quickly to solutions — which is often ineffective,” said instructor Dr. David Niño, Senior Lecturer at MIT.  “ This MicroCourse helps people see problems more clearly, prioritize them, and define them in actionable ways. In addition, it helps leaders understand how problems present a unique opportunity — an opportunity for leading innovation.” Participants will learn MIT’s unique methodology for problem solving and brainstorming, as well as:

  • Techniques for identifying and defining problems
  • Ways to frame and communicate a compelling vision
  • Practices that enable more creative brainstorming
  • Strategies for evaluating and choosing a game-changing solution

Each MicroCourse session is available online for one week and can be completed in approximately 4 hours. It is offered through a well-designed, intuitive virtual campus that offers leaders and managers the opportunity collaborate with peers from across the globe. Those who complete the MicroCourse earn a certificate as well as CEUs, which may be applied toward a professional certification, licensing requirements, or other required training or continuing education hours. In addition, the $195 fee for the MicroCourse will be credited toward enrollment in MIT Professional Education's January 7, 2019 session of the complimentary course,  Leadership & Innovation for Technology Professionals . “Everything we do at MIT Professional Education boils down to helping people become better problem solvers. So, it's fitting that this is the first in a series of MicroCourses we plan to offer through our Digital Plus Program,” said Bhaskar Pant, Executive Director at MIT Professional Education. “Our goal is to make critical knowledge more accessible to professionals around the globe through multiple teaching modalities, so they can use that knowledge to drive innovation and help organization's solve the complex challenges we face in today's fast-paced business world.” For more information or to register visit: Digital Plus Programs ABOUT MIT PROFESSIONAL EDUCATION For more than 65 years, MIT Professional Education has been providing technical professionals worldwide a gateway to renowned MIT research, knowledge and expertise, through advanced education programs designed specifically for them. In addition to industry-focused, two-to-five-day courses on campus through Short Programs, MIT Professional Education offers professionals the opportunity to take blended learning courses through Digital Plus Programs, attend courses abroad through International Programs, enroll in regular MIT academic courses through the Advanced Study Program, or attend Custom Programs designed specifically for their companies. For more information, please visit: professional.mit.edu Media Contact: Andrea LePain eMedia Junction Phone: 617-894-1153 Email:  [email protected]

  • Who’s Teaching What
  • Subject Updates
  • MEng program
  • Opportunities
  • Minor in Computer Science
  • Resources for Current Students
  • Program objectives and accreditation
  • Graduate program requirements
  • Admission process
  • Degree programs
  • Graduate research
  • EECS Graduate Funding
  • Resources for current students
  • Student profiles
  • Instructors
  • DEI data and documents
  • Recruitment and outreach
  • Community and resources
  • Get involved / self-education
  • Rising Stars in EECS
  • Graduate Application Assistance Program (GAAP)
  • MIT Summer Research Program (MSRP)
  • Sloan-MIT University Center for Exemplary Mentoring (UCEM)
  • Electrical Engineering
  • Computer Science
  • Artificial Intelligence + Decision-making
  • AI and Society
  • AI for Healthcare and Life Sciences
  • Artificial Intelligence and Machine Learning
  • Biological and Medical Devices and Systems
  • Communications Systems
  • Computational Biology
  • Computational Fabrication and Manufacturing
  • Computer Architecture
  • Educational Technology
  • Electronic, Magnetic, Optical and Quantum Materials and Devices
  • Graphics and Vision
  • Human-Computer Interaction
  • Information Science and Systems
  • Integrated Circuits and Systems
  • Nanoscale Materials, Devices, and Systems
  • Natural Language and Speech Processing
  • Optics + Photonics
  • Optimization and Game Theory
  • Programming Languages and Software Engineering
  • Quantum Computing, Communication, and Sensing
  • Security and Cryptography
  • Signal Processing
  • Systems and Networking
  • Systems Theory, Control, and Autonomy
  • Theory of Computation
  • Departmental History
  • Departmental Organization
  • Visiting Committee
  • IAP offerings
  • Subject numbering
  • FAQ about Fall 2024 Changes
  • 2022 Curriculum Transition
  • 6-1: Electrical Science and Engineering
  • 6-2: Electrical Engineering and Computer Science
  • 6-3: Computer Science and Engineering
  • 6-4: Artificial Intelligence and Decision Making
  • 6-5: Electrical Engineering with Computing
  • 6-7: Computer Science and Molecular Biology
  • 6-9: Computation and Cognition
  • 11-6: Urban Science and Planning with Computer Science
  • 6-14: Computer Science, Economics, and Data Science
  • Requirements
  • Application, Acceptance, and Deferral
  • Thesis Proposal
  • MEng Thesis
  • UROP and SuperUROP
  • Study Abroad
  • USAGE Members, 2023-24
  • 6-A Industrial Program
  • Degree Audits and Departmental Petitions
  • Space on Campus
  • Resources for International Students
  • Resources for Incoming Double Majors
  • Resources for Advisors
  • Graduate Admissions FAQs
  • Graduate Admissions Information Letter
  • What faculty members are looking for in a grad school application essay.
  • Conditions of Appointment as a Teaching Assistant or Fellow
  • RA Appointments
  • Fellowship Appointments
  • Materials and Forms for Graduate Students
  • Subject Updates Fall 2024
  • Subject Updates Spring 2024
  • Subject Updates Fall 2023
  • Subject Updates Spring 2023
  • Subject Updates Fall 2022
  • Subject Updates Spring 2022
  • Subject Updates Fall 2021

mit problem solving seminar

Here are the course offerings available through EECS during IAP 2023 for credit (non-credit activities are further down).

6.9300/6.9302 StartMIT: Workshop for Entrepreneurs and Innovators

Description

Designed for students who are interested in entrepreneurship and want to explore the potential commercialization of their research project. Introduces practices for building a successful company, such as idea creation and validation, defining a value proposition, building a team, marketing, customer traction, and possible funding models. Students taking graduate version complete different assignments.

Students should apply at https://orbit.mit.edu/applications/startmit23

6.9600 Mobile Autonomous Systems Laboratory: MASLAB

  • Units: 2-2-2
  • Prereqs: none
  • Instructor: John Zhang ( [email protected] )
  • Faculty Advisor: Professor Russ Tedrake ( [email protected] )
  • Schedule: Monday-Friday, 10a-12, January 9-13, room TBD

Autonomous robotics contest emphasizing technical AI, vision, mapping and navigation from a robot-mounted camera. Few restrictions are placed on materials, sensors, and/or actuators enabling teams to build robots very creatively. Teams should have members with varying engineering, programming and mechanical backgrounds. Culminates with a robot competition at the end of IAP. Enrollment limited.

6.9610 The Battlecode Programming Competition

Artificial Intelligence programming contest in Java. Student teams program virtual robots to play Battlecode, a real-time strategy game. Competition culminates in a live BattleCode tournament. Assumes basic knowledge of programming.

6.9620 Web Lab: A Programming Class and Competition

  • Units: 1-0-5
  • Instructor: Nicholas Tsao ( [email protected] )
  • Faculty Advisor: Professor Arvind Satyanarayan ( [email protected] )
  • Schedule:  Monday-Friday, 11-3, January 9 – February 3, room 26-100

Students form teams of 1-3 people and learn how to build a functional and user-friendly website. Lectures and workshops teach everything you need to make a complete web application. Topics include version control, HTML, CSS, JavaScript, ReactJS, and nodejs. All teams are eligible to enter a competition where sites will be judged by industry experts. Beginners and experienced web programmers welcome, but some previous programming experience is recommended.  Students must register at https://portal.weblab.is . Registering via WebSIS does NOT automatically put you on the official class mailing list.

6.9630 Pokerbots Competition

Build autonomous poker players and acquire the knowledge of the game of poker. Showcase decision making skills, apply concepts in mathematics, computer science and economics. Provides instruction in programming, game theory, probability and statistics and machine learning. Concludes with a final competition and prizes. Enrollment limited.

6.S086 Transcribing Prosodic Structure of Spoken Utterances with ToBI

  • Prereqs: linguistics, acoustic or psycho linguistics or speech science background suggested Pass/Fail
  • Instructor: Dr. Stefanie Shattuck-Hufnagel ( [email protected] ), Drs. Alenja Brugos and Nanette Veilleux, Simmons University, Boston
  • Schedule: Tuesdays & Thursdays, 11-1, January 10 – February 2, room 36-112

Sign up using this form https://forms.gle/X879LkKMMGacR1726 in advance by January 7th, and preregister on WebSIS , listeners accepted. Description:

This course presents a tutorial on the ToBI (Tones and Break Indices) system, for labelling certain aspects of prosody in Mainstream American English (MAE-ToBI). The course is appropriate for undergrad or grad students with background in linguistics (phonology or phonetics), cognitive psychology (psycholinguistics), speech acoustics or music, who wish to learn about the prosody of speech, i.e. the intonation, rhythm, grouping and prominence patterns of spoken utterances, prosodic differences that signal meaning and phonetic implementation.

Contact Stefanie Shattuck-Hufnagel,  [email protected] .

6.S088 Modern Machine Learning: Simple Methods that Work

  • Prereqs: see below
  • Instructor: Adityanarayanan Radhakrishnan ( [email protected] )
  • Faculty Advisor: Professor Caroline Uhler ( [email protected] )
  • Schedule:  MWF, 1-2:30, January 9 – February 3, room 32-141

Over the past decade, interest in machine learning research has spiked drastically, with advancements in deep learning being a significant driving force. Indeed, deep learning has transformed many areas in computer science including computer vision, natural language processing, and reinforcement learning. Unfortunately, given the rapid pace of progress in deep learning, a newcomer looking for a simple set of guiding principles for building machine learning applications can be easily overwhelmed by the nuances of training deep networks. Thus, motivated by recent developments in machine learning, we present a simple class of machine learning methods that are easy to implement and which achieve competitive performance in practice. In particular, our methods rely on the recently established equivalence between kernel regression and infinite width neural networks given by the neural tangent kernel (NTK). In addition to being a theoretical tool for understanding neural networks, we demonstrate that the NTK is a simple method for achieving competitive results in a variety of machine learning applications including regression, classification, image completion, and drug screening. We provide problem sets containing both theoretical and coding exercises with the aim of (1) providing newcomers, a simple toolkit for building effective machine learning models in practice and (2) preparing interested students for research in the area.

Recommended Pre-requisites

Knowledge of linear algebra (level of 18.06 or 18.700) and probability (level of 6.041 or 18.600) is generally assumed. Familiarity with Python (in particular, NumPy) is also assumed. While not necessary for the course, knowledge of Fourier analysis (18.103), functional analysis (18.102), random matrix theory (18.338), and complex analysis (18.112) is suggested for students who want to pursue research in this area.

6.S089 Introduction to Quantum Computing

  • Instructors:  Amir Karamlou, ( [email protected] ) and Agnes Villanyi ( [email protected] )
  • Faculty Advisor:  Professor William Oliver
  • Schedule: MWF, 3-5pm, January 9 – February 3, room 32-155

Quantum computation is a growing field at the intersection of physics, computer science, electrical engineering and applied math. This course introduces the basics of quantum computation. Specifically, we will cover some fundamental quantum mechanics, survey quantum circuits, and introduce the most significant quantum algorithms. Furthermore, we will survey advanced topics towards the end of the course. In the past these topics have included quantum error correction, quantum communication and applications to fields ranging from machine learning to chemistry. This course is self-contained and does not require any prior knowledge of quantum mechanics.

6.S090 nanoStories – Workshop on Science Communication at the Nanoscale

  • Instructors:  Professor Vladimir Bulovic ( [email protected] ) and Dr. Annie I. Wang ( [email protected] )
  • Schedule:  Tuesdays, Thursdays, Fridays, 2-4pm, January 10 – January 20, room 12-3005 also hybrid option

Designed for students with an interest in science communication and STEAM outreach. Guided by instructors, in each two-hour class students will explore a new topic, jointly developing an instructional narrative to be told in text, video, and/or interactive multimedia. Outside of MIT labs, nanoscience and nanotechnology appear mysterious. Help us demystify them! The content of the classes will reflect research/exploratory interests of participants.

6.S091 Causality: Policy Evaluation, Structure Learning, and Representation Learning

  • Instructor: Chandler Squires ( [email protected] )
  • Schedule: Tuesdays & Thursdays, 1-3pm, January 10 – February 2, room 4-231

Covers introductory material from three active research areas related to causality and machine learning. In the first third of the course, we will discuss the fundamentals of policy evaluation, where a known causal structure is used to estimate causal quantities such as (conditional) average treatment effects. In this section, we will cover algorithms for identification of causal estimands, as well the principles behind state-of-the-art estimation methods based on double/de-biased machine learning. In the second third of the course, we will consider causal structure learning, i.e., the estimation of an unknown causal structure from data. We will cover classical algorithms such as the PC algorithm, as well as newer methods which incorporate interventional data and allow for unobserved confounding. We will also cover experimental design techniques for causal structure learning. In the final third of the course, we will discuss the emerging field of causal representation learning, highlighting recent papers which connect machine learning with more traditional causal principles.

Recommended Prerequisites: Knowledge of probability (level of 6.3700) and statistics (level of 18.650) is generally assumed. Familiarity with Python is also assumed.

6.S092 The Art and Science of PCB Design

Description 

This class is project-focused, and you will build a PCB of your own design in this class. This includes schematic capture, board layout, assembly, and debugging to get it working. We’ll pay for your PCBs and the components on them – there’s no cost to you. We’ll do this by teaching you each step of the process in lecture, letting you try your hand at it, and then following up on your work with a design review (DR). DRs are 20-minute chunks where we sit with you and go over your design, and provide feedback before moving onto the next step. You’ll have three of these – one after you make your schematic, one after you make your board layout, and one before you send them to the fab house for fabrication. This class is open to all skill levels, and you don’t need previous electrical design experience! We’ve got a few different ways to progress through the class, and your background will probably dictate which one you choose.

   

6.S094 Introduction to Quantum Network

After 20th century, Quantum innovations has brought us to a new dimension of information. Quantum network plays an important role for the physical implementation of quantum computing, quantum communication and sensing. In this course, aims to give you a concrete glance of state-of-art quantum technologies, covering the fundamental concepts of quantum network protocols, measurements, device physics and using analytical simulation tools, with guest lectures from frontier researchers covering different topics.

6.S095 Intermediate Probability Problem Solving

6.S095 is a survey of advanced problem solving techniques in probability, random variables, and stochastic processes. It picks off from a standard introduction to the subject and goes towards more advanced techniques. The first half of 6.S095 reviews standard concepts in probability while introducing much more involved applications of these topics, while the second half will introduce adjacent areas of exploration. The aim of this class is to develop problem solving ability and mathematical maturity that will enable students to succeed in advanced and graduate-level EECS classes that involve probability, such as 6.046, 6.262, 6.265, 6.437, 6.438, and 6.856.

6.S096 Introduction to the C Programming Language CANCELLED.

6.S097 Ultrafast Photonics

  • Instructor: Donnie Keathley, Principal Research Scientist, RLE, ( [email protected] ), Prof. William Putnam, UC Davis
  • Schedule: Tuesdays & Thursdays, 11-12:30, January 10 – February 2, room 34-304

Knowledge of the fundamentals of ultrafast photonics is becoming increasingly valuable as ultrafast optical sources become more ubiquitous with an ever-growing number of applications. Relatively compact ultrafast optical sources with pulse durations ranging from nanoseconds down to femtoseconds are now commercially available across a broad range of wavelengths. Current applications are wide-ranging and include biological imaging, quantum optical technologies, chemical sensing, and precision measurements of time and distance among many others. During this IAP course, we will cover the essentials of ultrafast photonics. Topics will include: (1) the science of ultrafast laser pulses and their interaction with matter; (2) the technology to generate and manipulate ultrafast pulses of light; and (3) an overview of select applications of ultrafast photonics systems. This course will serve as a foundation for those interested in experimental and/or theoretical work involving ultrafast optical systems. Some basic knowledge of Fourier analysis, differential equations, and electromagnetic waves is assumed. Note that this course is designed to overlap and coordinate with an ultrafast photonics course taught by Prof. William Putnam at U.C. Davis. Dr. Keathley will lead the lectures and course at MIT, with online material, such as lecture recordings and notes, being shared between MIT and UC Davis.

6.S098 Introduction to Applied Convex Optimization

  • Prereqs: multivariable calculus (18.02), linear algebra (18.06 or 18.061), basic probability, programming, mathematical maturity (e.g., 6.042)
  • Instructor: Theo Diamandis ( [email protected] )
  • Faculty Advisor:  Professor Pablo Parrilo ( [email protected] )
  • Schedule: Tuesdays & Thursdays, 1-2:30, room 32-124

More information can be found at [email protected]

Convex optimization problems appear in a huge number of applications and can be solved very efficiently, even for problems with millions of variables. However, recognizing what can be transformed into a convex optimization problem can be challenging. This course will teach you how to recognize, formulate, and solve these problems. We will briefly survey theoretical results in convex analysis, but the majority of the course will focus on formulating and solving problems that come up in practice. Applications will include signal processing, statistics & machine learning, finance, circuit design, mechanical structure design, control, power systems, and other areas based on student interest. This course is designed for advanced undergraduates and beginning graduate students.

6.S099 Machine Learning Single-Cell Cancer Immunotherapy Competition

  • Instructor: Professor Caroline Uhler ([email protected])
  • Schedule: Tuesdays & Thursdays, 11:30-1, January 10-February 2, room 26-168

Machine learning contest to predict the effect of genetic perturbations on T cells in the context of cancer. The goal is to identify genetic perturbations that make T cells more effective at killing cancer cells. All participants enter a competition with prizes. The top scoring submissions based on the prediction tasks will be validated experimentally. Assumes basic knowledge of programming, but no biological background.

Recommended prereqs:

We expect students to be familiar with at least one programming language (e.g. Python) at the level of 6.1010. In addition, it is recommended that students have taken a course in data science and/or machine learning such as 6.3720 (Introduction to Statistical Data Analysis), 6.3900 (Introduction to Machine learning) or 6.3730/IDS.012 (Statistics, Computation and Applications). No background in biology is required for this course.

6.S187 Code for Good

Apply at http://codeforgood.mit.edu/apply

For this class, students have the opportunity to work on software-related projects with local nonprofit organizations. Teams of 3-4 students choose a project that is of interest to the group, or suggest their own project ideas. Students are mentored by a representative from the nonprofit organization as well as subject instructors. During the entirety of the course, students have access to mentors and other resources. At the conclusion of the course, students will deliver their project to their nonprofit organization, and they’ll also have the opportunity to show off their projects at an exposition that is open to representatives of the nonprofit organizations, mentors, and the general MIT community.

Project listings and detailed information are available on the website: http://codeforgood.mit.edu/programs/iap-class/

6.S190 Concepts in Embedded Machine Learning

  • Units: 3 units
  • Prereqs: Permission of Instructor (see below)
  • Instructors: Professor Steven Leeb ( [email protected] ), Greg Landry, Ali Atti, and Patrick Kane (Infineon)
  • Schedule: Tuesday, Wednesday, Thursday, 9-5pm, January 17-19, room, 34-501

Enrollment Limited to 30: Advance sign up required

Sign up by: January 3, 2023

A 3-day in-depth course focused on exploring ML concepts such as voice and gesture recognition. We will be using Infineon PSoC 6 development kits and shields (provided by Infineon). The first two days will focus on lectures and instructor led labs. The last day will consist of student teams creating ML projects. Infineon  ModusToolbox™ IDE and its features will be explored and explained. Students will receive in-depth instruction and will complete exercises related to:

Some programming experience is required. Experience with C programming is helpful but not required.

  • Voice Recognition
  • Gesture recognition
  • The Infineon CY8CKIT-062S2-43012 Architecture and development environment
  • The CY8CKIT-028 TFT shield (TFT, audio, and multiple sensors)
  • ModusToolbox IDE

PERMISSION OF INSTRUCTOR IS REQUIRED TO REGISTER . Email [email protected] for permission before registering. Registering for this course is a FIRM commitment to attend; others will be turned away to make room for you.

6.S197 Tube Electronics

  • Prereqs: 6.2000 (6.002)
  • Instructor: Joseph Steinmeyer ( [email protected] ) , Senior Lecturer, EECS
  • Schedule: Tuesdays & Thursdays, 2:30-4, January 10 – February 2, room 34-304

This class will study vacuum tubes and build some simple circuits using them. We will focus on using a subset of tubes developed in the late 1950’s for 12V car circuits and this will keep us at a safe voltage relative to other tube circuit voltages. We’ll have a series of lectures and we’ll build towards a functioning AM regenerative receiver with some lab sessions, While the class will study tubes, it will also be a very basic and simple introduction to RF. Prerequisite will be 6.2000 (6.002).

IAP 2023 Activities

Here are the activities available sponsored by EECS during I AP 2023.

Introduction to the D Programming Language

Instructor: Michael Coulombe ([email protected])

Schedule: Thursday, January 26, 3-5pm, room 32-141

Join this interactive session on D to learn the basics and unique features behind this powerful and expressive general-purpose programming language. You will also hear from two active members of the D community to share their experience using D in industry, academia, and beyond. Open to new and advanced programmers, but some background in another language (such as Python, C/C++, Java, etc…) will be expected. Check out the D homepage to learn more in advance at https://dlang.org/

Bring your laptop to participate in the live coding!

Guest Speakers include:

Steven Schveighoffer started using D in 2007. He is one of the core developers of the standard library, having written the array runtime, and various other pieces, mainly focusing on memory safety and performance. He has been working in software for over 24 years, most recently as a software consultant for several clients using D. He maintains several D projects, including mysql-native (a fully-D msyql client), raylib-d (D bindings for raylib), and iopipe (a high performace i/o library).

Mike Shah is currently an Associate Teaching Professor at Northeastern University in the Khoury College of Computer Sciences. Mike’s primary teaching interests are in computer systems, computer graphics, and software engineering. Mike’s research experience is in the areas related to performance engineering (dynamic analysis), software visualization, and computer graphics. Along with teaching and research work, Mike has occasionally done consulting work as a 3D Senior Graphics Engineer using OpenGL. More recently, Mike has been working on personal and professional projects in the DLang, and spending time building training materials available on YouTube.

High-performance computing basics

Instructors: Guillaume Leclerc ([email protected]) EECS Grad Student and Djuna von Maydell ([email protected]) BCS Grad Student

Schedule: Monday-Friday, January 9-13, 2-4pm, room 36-112

Most research projects involve auxiliary computing tasks: preparing / processing data, solving optimization problems etc… A popular approach is to focus on simply getting code that works. In this class we introduce a panel of simple strategies to improve the performance of research code by orders of magnitude with minimal additional work, enabling you to solve bigger problems. The class will use Python (and sometimes Julia) for illustration but the takeaways will be programming language agnostic.\

Noise, Perception and Learning: Applications in AI art

Instructor: Sarah Muschinske ([email protected]) EECS Grad Student, Aspen Hopkins, PhD student in EECS, CSAIL; Mikey Fernandez, PhD student in MechE, Media Lab; Logan Engstrom, PhD student in EECS, CSAIL; Andrew Ilyas, PhD student in EECS, CSAIL; Chandler Squires, PhD student in EECS, LIDS; John Simonaitis, PhD student in EECS, RLE

Schedule: Tuesdays & Thursdays, January 10 – February 2; Wednesday, January 25; 5-7pm, room 36-112

more information can be found at: https://sarahmuschinske.github.io/gen_art_mit/

This seminar-style course will cover fundamental physical, chemical and biological origins of noise & how it affects perception for both natural and artificial neural networks. This will be applied to generation of AI art.

Future of AI: Self-Supervised Learning and World Models

Instructor: Rickard Brüel Gabrielsson ([email protected]) EECS Grad Student

Schedule: Thursdays January 12 – February 2, 2-3pm, room 24-121

ChatGPT, Code Pilot, CLIP, Dall-e, Stable Diffusion, AlphaFold, Self-driving cars – is now the time that AI lives up to all its hype? What’s the secret sauce behind these recent breakthroughs within AI? It’s called self-supervised learning and it is changing everything. With the help of it, Facebook’s Yann LeCun now believes he sees a way to Artificial General Intelligence (AGI) in the form of foundation models. In this non-technical series of lectures, we will start with the history of AI, then with what supervised learning and reinforcement learning is missing, and conclude with the deep practical and foundational implications of self-supervised learning. We cover applications in both science and business. Lectures (Thursdays at 2-3pm, room 24-121) will be recorded and all backgrounds are welcome. Website at  https://futureofai.mit.edu/ ​

Building skills for a successful PhD

Instructor: David Nino ([email protected]), Senior Program Manager and Senior Lecturer Graduate Program in Engineering Leadership, and Prof. Vivienne Sze, EECS ([email protected])

Schedule: Tuesday, January 31, 1-4pm, room 32-144

Please note that you need to register in advance using  this form .  Attendance will cap at 50 participants.

In this workshop, we will discuss non-technical skills that are critical for a successful PhD journey and professional career. Topics will focus on personal and interpersonal skills, including developing self-confidence, giving/receiving feedback, and managing conflict and stress. We will showcase how these skills can be used to address real scenarios/challenges encountered during the PhD journey (e.g., managing relationships with your advisor or other students). In addition to providing resources and guidance and how to use these skills, the workshop will also contain a skills development component, where students will have an opportunity to practice the skill.

This is an archived course. A more recent version may be available at ocw.mit.edu .

MIT OpenCourseWare, Massachusetts Institute of Technology

Assignments

Problems based on class lectures, as well as supplementary problems, are handed out during the week of the lecture. You are expected to solve on your own problems which you hand in. Some collaboration with other students in the seminar is o.k. as long as you don't simply copy someone else's work.

You should also not hand in any problems whose solution you are already familiar with. If you get completely stuck you can hand in solutions from another source, provided: (1) the solution is written up in your own words, (2) you understand the solution, and (3) you indicate on your paper the source of the solution. You should hand in six problems each week, at least four from the problem set based on the lecture. Do not hand in supplementary problems rated less than [2]; these are too easy.

Solutions to all of the problems are not provided, but a selection of hints and answers to supplementary problems are available.

Solutions to all of the problems are not provided, but a selection of hints and answers to the Supplementary Problems are available.

Some Hints and Answers to Supplementary Problems ( PDF )

More Hints and Answers to Supplementary Problems ( PDF )

  • Courses for Individuals

Unlocking the Power of Perspectives: Problem Solving with Clarity, Creativity, and Collaboration

Silhouette of two heads facing each other with light bulb lit up in between them. image number null

Management and Leadership

Certificate Credits

- Negotiation & Communication

- Organizations & Leadership

  • Participants

Course Highlights

  • Immerse yourself in a learning experience that has the potential to substantially alter how you lead, listen, collaborate, negotiate, and connect with others
  • Work individually and in groups to better understand the value of different perspectives and how to incorporate those perspectives into your management and leadership styles
  • Take inspiration from the work of jazz musicians to understand how to organize, communicate, and connect with others while engaging in change
  • Learn visual thinking strategies that can help you elicit and harness perspectives in ways that cultivate adaptability, creativity, and innovation
  • Earn a certificate of course completion from the MIT Sloan School of Management

Featured content

Why attend Unlocking the Power of Perspectives?

The ability to work with multiple and diverse perspectives is a valuable skill set that enables creative problem-solving, fosters greater interpersonal connection, increases clarity and collaboration, and motivates groups. This highly interactive problem-solving course focuses on advanced leadership skills for holding and managing multiple perspectives simultaneously to leverage and unleash the creative potential of divergence in and across business to generate richer outcomes.

In the context of great change and uncertainty, we must show up differently as leaders. We must be great problem solvers. Creativity is a necessity. We must put ourselves in a position of constant learning. And we must be able to change and flex our point of view: not necessarily the way we see the world, but certainly the way we see ourselves.

This problem-solving course is taught by Aithan Shapira, an internationally acclaimed artist and MIT Sloan lecturer, and Wanda Orlikowski, Professor of Information Technologies and Organization Studies at MIT Sloan.  Unlocking the Power of Perspectives is an immersive learning experience with the potential to substantially alter how you lead, listen, collaborate, negotiate, and connect with others.

Course experience

This critical thinking and problem-solving course is highly interactive—be prepared to participate and engage. You will work individually and in groups to better understand the value of different perspectives and how to incorporate those perspectives into your management and leadership styles. As you build rapport with your peers, you’ll complete challenges related to the tension of holding conflicting perspectives, starting at different reference points, and tracking and learning from healthy differentiation. Stepping outside the conventional business context, you will take inspiration from the work of jazz musicians to understand how to organize, communicate, and connect with others while engaging in change.

Faculty will share examples of highly successful leaders who changed and evolved their own leadership styles to enable their companies to survive disruption and thrive. You’ll learn how executives have transformed company culture and increased revenue simply by changing the way they listen and solve problems. 

The course also covers skills for visualizing and working in opposing perspectives. You will learn visual thinking strategies that can help you elicit and harness perspectives in ways that cultivate adaptability, creativity, and innovation. Because the better you are at shifting your mindset and approach and concentrating on relationships in the moment, without losing sight of your motivation, the more likely you are to steer your team toward success.

Learn more about the live online experience .    

Learn more about the in-person experience .

Applying to the course

We accept enrollments until the offering reaches capacity, at which point we will maintain a waitlist. Many of the courses fill up several weeks in advance, so we advise that you enroll as early as possible to secure your seat.

You can begin the application process by using the red 'Enroll Now' bar at the bottom of the screen.

Health and Safety

See our on campus healthy and safety policies.  

Have questions?

Contact us if you would like to speak with a program director or visit our Frequently Asked Questions page for answers to common questions about our courses.

Upon successful completion of your course, you will earn a certificate of completion from the MIT Sloan School of Management. This course may also count toward MIT Sloan Executive Certificate requirements.

Participants of this course will acquire

  • Frameworks and methods to improve the quality and effectiveness of collaboration and problem-solving at your organization 
  • A toolkit of corrective and self-reflective practices around listening and perspective taking.
  • A deeper understanding of the thinking process that leads us from a fact to a decision or action
  • Tools to suspend beliefs and judgments that block clear listening and an open mind
  • Visual thinking strategies on how to draw out and harness perspectives to enable innovation and create value
  • A broader set of skills to organize, communicate, and connect with others while engaging in change
  • Clarity around your strengths and challenges as a leader

Sample Schedule—Subject to Change

This innovative and experiential course is designed for

  • Mid- and senior-level executives who are interested in introspection, self-reflection, and transformation and who are willing to engage, share, and collaborate within teams and groups
  • The course content is applicable to professionals in any role and in any industry

Request Course Information

Receive email updates related to this course, including faculty news and additional offering dates.

Review our Privacy Policy.

This course provided more than I ever could have expected or anticipated. I was able to reflect on my own perspective and how that informs the work that I do; I was introduced to frameworks to understand the perspectives of and work effectively with my colleagues; and was exposed to this work through a lens of art and music, which was truly breathtaking (I won't say more as to not spoil the experience for others!). These lessons were so relevant for me and my work that in real-time I was implementing my learning in my work and saw a direct impact. I continue to use all I have learned from this course and could not recommend others to take this course more strongly!

—Julia R.

Enroll Now!

Harnessing choice to thrive as a leader, access your artistic side to lead through uncertainty, train your brain to unlock creativity and innovation, leadership cues to take from performers and artists, course offerings.

IMAGES

  1. What Is Problem-Solving? Steps, Processes, Exercises to do it Right

    mit problem solving seminar

  2. 7 Steps to Improve Your Problem Solving Skills

    mit problem solving seminar

  3. Live Seminar: Problem Solving & Decision Making

    mit problem solving seminar

  4. Solving the world’s great challenges

    mit problem solving seminar

  5. Problem Solving Meeting Agenda: 4 Effective Steps to Conduct a Problem

    mit problem solving seminar

  6. seven steps problem solving

    mit problem solving seminar

VIDEO

  1. AMC 10 and 12 Problem Solving Seminar

  2. AMC 10 and AMC 12 Problem solving seminar

  3. Tumana Seminar: Solving the Problem

  4. Seminar on Problem Solving and Ideation

  5. AMC 8 Problem Solving Seminar # 11

  6. Stanford Lecture: "Aha" Sessions

COMMENTS

  1. Mathematical Problem Solving (Putnam Seminar)

    This course is a seminar intended for undergraduate students who enjoy solving challenging mathematical problems, and to prepare them for the Putnam Competition. All students officially registered in the class are required to participate in the William Lowell Putnam Mathematical Competition. Show more. Course Info.

  2. Solving Complex Problems: Structured Thinking, Design Principles, and AI

    In our new course Solving Complex Problems: Structured Thinking, Design Principles, and AI, you'll acquire core principles that will change the way you approach and solve large-scale challenges—increasing your likelihood of success. Over the course of five days, you will explore proven design principles, heuristic-based insights, and ...

  3. Systems thinking and System Dynamics courses at MIT

    Originating within Forrester's Systems Dynamic Group at MIT Sloan, it is a holistic approach to analysis and problem solving that views "problems" as parts of an overall system, rather than in isolation. ... MIT's Approach to Diagnosing and Solving Complex Business Problems. This 7-day course provides an intensive, hands-on introduction to ...

  4. 18.A34 Mathematical Problem Solving (Putnam Seminar): PS 1

    MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity ... 18.A34 Mathematical Problem Solving (Putnam Seminar): PS 1 Download File DOWNLOAD. Course Info Instructor Prof. Yufei Zhao; Departments Mathematics; As Taught In Fall 2018 ...

  5. Mathematical Problem Solving (Putnam Seminar)

    MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity ... 18.A34 Mathematical Problem Solving (Putnam Seminar): PS 10. pdf. 126 kB 18.A34 Mathematical Problem Solving (Putnam Seminar): PS 11. pdf.

  6. Making math fun by prepping for friendly competition

    The William Lowell Putnam Mathematics Competition inspires MIT class 18.A34 (Mathematical Problem Solving), which helps students solve proofs for the joy of solving, ... Stanley's undergraduate seminar on mathematical problem-solving featured his weekly lecture devoted to a Putnam-related topic such as number theory, linear algebra ...

  7. MIT Solve

    Solve at MIT: Afternoon Plenary - Promoting Our Care Providers Media Lab. COVID-19 vaccine • Get the latest information from the CDC. Watch on. Solve at MIT: Closing Plenary - Young Leaders on the Horizon. Watch on. Connecting the MIT Solve Community to solve global challenges in realtime.

  8. 18.A34 Mathematical Problem Solving (Putnam Seminar): Supp_PS 7

    MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity 18.A34 Mathematical Problem Solving (Putnam Seminar): Supp_PS 7 | Mathematical Problem Solving (Putnam Seminar) | Mathematics | MIT OpenCourseWare

  9. Complex Problem Solving Through Systems Thinking

    This complex problem-solving course introduces participants to MIT's unique, powerful, and integrative System Dynamics approach to assess problems that will not go away and to produce the results they want. Through exercises and simulation models, participants experience the long-term side effects and impacts of decisions and understand the ...

  10. MIT Mathematics Probability Seminar

    MIT seminar in probability. Past Seminars: ... This is a ubiquitous problem arising in a variety of applications across diverse fields such as network privacy, computational biology, computer vision, and natural language processing. The problem is also deep and rich in theory, involving the delicate interplay of algorithms, complexity, and ...

  11. MIT Professional Education Launches New MicroCourse: Effective Problem

    Digital Plus Programs MicroCourse teaches MIT's unique framework for problem-solving and brainstorming to help organizations grow creative cultures and drive innovation Cambridge, Mass., September 20, 2018 - MIT Professional Education, a gateway to renowned MIT research, knowledge and expertise through advanced education programs, today announced the launch of a new Digital Plus Programs ...

  12. IAP 2022

    The aim of this class is to develop problem solving ability and mathematical maturity that will enable students to succeed in advanced and graduate-level EECS classes that involve probability, such as 6.046, 6.262, 6.265, 6.437, 6.438, and 6.856. *hybrid option available, contact instructors for more information

  13. IAP 2023

    The aim of this class is to develop problem solving ability and mathematical maturity that will enable students to succeed in advanced and graduate-level EECS classes that involve probability, such as 6.046, 6.262, 6.265, 6.437, 6.438, and 6.856.

  14. MIT OpenCourseWare

    This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. ... Your use of the MIT OpenCourseWare site and course materials is subject to the ...

  15. MIT OpenCourseWare

    The seminar will hold two one-hour meetings each week (except for Institute holidays). In general, the second class each week will be devoted to a lecture on a topic useful for mathematical problem-solving. Two sets of problems will be passed out - a set directly related to the lectures, and a set of supplementary problems on a variety of topics.

  16. Assignments

    Assignments. Problems based on class lectures, as well as supplementary problems, are handed out during the week of the lecture. You are expected to solve on your own problems which you hand in. Some collaboration with other students in the seminar is o.k. as long as you don't simply copy someone else's work.

  17. Problem-Solving Techniques From Other Perspectives

    This highly interactive problem-solving course focuses on advanced leadership skills for holding and managing multiple perspectives simultaneously to leverage and unleash the creative potential of divergence in and across business to generate richer outcomes. In the context of great change and uncertainty, we must show up differently as leaders ...

  18. PDF Using Devising Seminars to Advance Collaborative Problem Solving in

    setting. Such an approach is a lot closer to the ongoing problem-solving workshops hosted by Herbert Kelman (see Kelman 1972,1996).In contrast to Kelman's problem-solving workshops, however, devising seminars put more emphasis on bringing the full array of involved or potentially affected stakeholders together in their personal capacities.