Making the Difference in Differential Equations

A colorful sphere in graphed in 3 dimensions.

A graphic from the video Tumbling Box. (Image by The MathWorks.)

By Joe Pickett, OCW Publication Director

Among OCW’s most popular courses are 18.06SC Linear Algebra and 18.03SC Differential Equations. They are regulars on OCW’s most visited courses list.

OCW has just published a new video series designed to give math learners a more in-depth exploration of these subjects: Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler.

MIT Professor Gilbert Strang needs no introduction to people familiar with OCW’s math offerings. His videos have received scores of thousands of viewings over the years and have made him a kind of mathematical phenomenon. His Highlights of Calculus videos, for instance, are favored feature of OCW’s Highlights for High School site.

Cleve Moler has been a professor of mathematics at University of Michigan, Stanford University, and the University of New Mexico, although these days he wears the hat of chief mathematician and cofounder of The MathWorks®. He is the creator of the software program MATLAB®, which is widely used in science and engineering.

Screenshot of the course introductory video, with Cleve Moler and Gilbert Strang.

You can meet both of these math makers by watching the course introductory video.

The 68 videos in this new series are all fairly short (usually around 15 minutes, sometimes much shorter) and targeted at specific topics like vector spaces and eigenvalues. Gilbert Strang’s videos are designed to supplement his 2014 textbook Differential Equations and Linear Algebra. In his own videos, Cleve Moler introduces computation for differential equations, explains the MATLAB® ODE (Ordinary Differential Equations) suite, and takes learners through hands-on MATLAB exercises.

Viewers are already raving about this new video series. It is but another of OCW’s many Supplemental Resources.

Confused, Yes. Dazed, No.

In the midst of other marchers, a black women holds a sign reading "March to End Racial Profiling."

On June 17, 2012, thousands participated in a silent march to end racial profiling in New York City. (Image courtesy of longislandwins on Flickr. License CC BY.)

By Joe Pickett, OCW Publication Director

We all make decisions and hold attitudes in our everyday lives that reflect our ethical frameworks. How we value personal freedom in relation to our sense of social justice says much about who we are and what kind of society we want to live in. But our ethical frameworks are often deeply rooted and difficult to articulate, and they can be especially challenging to discuss with people who hold opposing views.

OCW has just published 24.191 Ethics in Your Life: Being, Thinking, and Doing (or Not?), in which this problem is confronted head on. The instructors of the course are Professor Sally Haslanger, Patricia-Maria Weinmann, and Brendan de Kenessey. These last two share the teaching team’s strategies for fostering lively and constructive student discussions about controversial topics on the course site’s This Course at MIT page.

Using Philosophical Tools to Guide Discussion

The subjects that students wrestle with in this class are difficult, to say the least: racial profiling, imprisonment in the US, video games and sexism, military funded research at universities, and more. The instructors use approaches from the discipline of philosophy to help students listen openly and respond respectfully to arguments that challenge their own ethical frameworks:

“Before entering the class, students tend to say, ‘I feel this way, but I’m not really sure why, and I can’t articulate why I think a particular stance is wrong or why I think it’s right,’” the instructors say. “But once we provide them with philosophical tools, they begin to articulate why they feel the way they do. They also begin to use logic to frame discussions about topics that can often spark heated responses…They learn to respond to the arguments of people holding opposing views and to engage these people in conversations, as opposed to dismissing them.”

So the course is “about taking the kinds of skills philosophers use to engage in dispassionate, careful discussions and applying them to cases where people tend to be anything but dispassionate.”

But for all this to happen, students first need to feel comfortable about openly sharing their views.

Getting Students to Make the Rules

Rather than dictating rules for how discussions will take place, Professor Haslanger “asks students to generate the guidelines for classroom discussions. Students talk about the importance of respect and of listening to others. The process of having students create conversation guidelines communicates, right from the start, that the classroom culture is collaborative and focused on respect.”

Knowing Each Other by Name

Some techniques for setting the stage for comfortable discussions about uncomfortable topics are surprisingly simple: arranging the chairs in a circle so students can see one another, and giving students name cards so they address one another using their names. On the first day, students are assigned to pairs, interview one another, and then introduce their partners to the group. “There’s laughter in the room as they interview each other. It’s a great time of sharing and of introducing everyone to each other without stressing students. This practice sets the tone for a comfortable classroom culture.”

Adjusting the Volume of Student Voices

The instructors intervene when discussions get dominated by the more extroverted personalities (as they inevitably do in discussion-based classes) to encourage contributions from the less readily vocal. When the class approaches consensus on one side of an issue, the instructors shake things up by summarizing the discussion with particular support for the other side. But why shatter this social harmony? Isn’t that what the course is trying to achieve?

“It’s only after going through an intermediate stage of feeling confused by understanding both sides of an argument that [the students] can get to a more grounded conviction as opposed to just a knee jerk reaction to an issue. We feel we’ve succeeded as teachers when students come out of the class more confused than when they started! It means they’re considering all sides of an argument and realizing there’s so much more to know about an issue than what they initially thought.”

Confusion as a goal! It’s a philosophy class, after all!

Nine new courses bloomed in April

Multicolored smaller circles of various sizes, packed into a circular shape.

From 18.177 Universal Structures in 2D: Circle packing of the corresponding triangulation. The colors indicate the order in which the green, space-filling path visits the edges of the triangulation. (Image courtesy of Jason Miller. Used with permission.)

During April, OCW published nine new courses. Six are brand-new subjects on OCW, while three are updates to previously published courses.

New Courses

Updated Courses

OCW courses from MIT’s newest AAAS members

MIT News reports that six MIT faculty members and the chair of the MIT Corporation are among 213 leaders from academia, business, public affairs, the humanities, and the arts elected to the American Academy of Arts and Sciences (AAAS).  AAAS is “one of the nation’s most prestigious honorary societies [and] a leading center for independent policy research. Members contribute to academy publications, as well as studies of science and technology policy, energy and global security, social policy and American institutions, the humanities and culture, and education.”

OCW is pleased to highlight course materials from five of these MIT faculty.

Andrea Louise Campbell, the Arthur and Ruth Sloan Professor of Political Science and head of the Department of Political Science.

Victor Chernozhukov, professor of economics.

Pavel Etingof, professor of mathematics.

John Gabrieli, the Grover M. Hermann Professor in Health Sciences and Technology.

Vann McGee, professor of philosophy.

Also elected to AAAS are Jacqueline Hewitt, professor of physics and director of the Kavli Institute for Astrophysics and Space Research; and Robert Brian Millard ’73, chair of the MIT Corporation. Congratulations to all!

A Closer Look at The Film Experience

Actor Buster Keaton, crouched and leaning forward on the cowcatcher of a steam locomotive.

Buster Keaton in The General (1926). (Public domain image.)

Movies are great entertainment, high art, and a cultural force. And at MIT, a bastion of STEM learning, they’re worthy of serious exploration.

As Deborah Fitzgerald, prior Dean of MIT’s School of Humanities, Arts and Social Sciences has written, “the challenges of our age are unwaveringly human in nature and scale; and engineering and science issues are always embedded in broader human realities, from deeply-felt cultural traditions to building codes to political tensions.” What more direct way to illuminate human realities than through film?

Professor David Thorburn teaches 21L.011 The Film Experience with that universality in mind. It’s been one of MIT’s, and OCW’s, most popular humanities subjects. On the new OCW site for the course, he explains:

One of the ways that the study of literature and the study of film differs from the study of technical things, and the reason I teach it, is that it belongs to everyone, that it’s valuable for everyone. Not everyone needs to know about quantum mechanics. But I believe everyone should know how to read a good story, enjoy plays, know how to enjoy the movies.

New Video Lectures

Professor speaking, gesturing with hand, and an inset still image from film of a man in suit floating on his back in a river.

David Thorburn explains the aesthetic power of Jean Renoir’s Boudu Saved from Drowning. (Film still image © Les Établissements Jacques Haïk.)

The OCW course has just been upgraded with a complete set of 23 video lectures. Topics include the early silent period, classic Hollywood genres including musicals, thrillers and westerns, European and Japanese art cinema, and film through the emergence and cultural dominance of television.

Of course, you’ll learn about different historical eras, essential films, key actors and directors, and technical innovations. But Professor Thorburn approaches film as literature, and also with a keen media scholar’s eye on surrounding cultural forces.  Some of the deeper “thematic spines” of the course include

  • The cultural power of movies to “promulgate, dramatize, rehearse, and in some ways, alter and change” a society’s values and belief systems
  • The role of genre, e.g. the musical or the western, in reflecting important social and historical realities
  • Key artistic qualities of film that distinguish it from mere entertainment, and ways for you to make your own critical judgements.

You know all those great movies you keep telling yourself you’ll see someday? Let these lectures start you on that journey, as Professor Thorburn has done so effectively and enthusiastically for so many hundreds of MIT students.

Insights from 30 Years of Teaching Film

Screenshot of male professor speaking, hands raised in emphasis.

David Thorburn shares his teaching insights in a series of short videos.

Complementing the lectures are a rich collection of instructor insights videos, part of the OCW Educator initiative. Recorded one afternoon in his office, Professor Thorburn speaks directly and honestly about his teaching approaches and the evolution of the course over its three decade history.

For instance, he advocates for the value of the well-crafted lecture:

There’s been a kind of growing negative feeling about lectures as if they’re [giving] students a herd experience, and [not giving] them hands-on experience. I think, intellectually, that’s a foolish perspective…I want [students] to watch the movie as the primary text. And I see myself in the role of a synthesizer [giving] a concise summary of the best that has been said about a particular film, or about the historical processes that lead up to the making of the film…I don’t expect my students to become film scholars or literary scholars. The kind of student I want to reach is that of a literate citizen…I could have the students read five scholarly books and synthesize them, but I do that for them so that they have the time to look at the film and think about it seriously.

In another segment, he explains why film should be seen in context with television and literature:

One of the central arguments of my film course…is that it sees the advent of television as a critical factor in the history of the movies, much more central and critical than most contemporary histories acknowledge. Because what I try to show is that the function that the movies had in American society before the advent of television was the function that the novel had in the 19th Century in Europe, and the function that Shakespeare’s public theater had in Shakespeare’s day, a form of popular narrative that’s articulated a kind of assumed or imagined consensus of values for the whole of the society. That made it a culturally, and anthropologically, and socially much more important medium then a mere artistic medium, even though it’s artistic quality remains very important.

With such heartfelt perspectives, David Thorburn makes his signature course come to life for film buffs and educators alike.

Digital Humanities at MIT—Seeing Data in New Light

Image of world map with "push-pin" icons in various locations, connected together by colored lines.

The interface for the app NewsConnect, that aims to visually represent national connections presented in world news articles. (Image from student project in CMS.633 Digital Humanities, courtesy of Meghana Bhat and Karleigh Moore. Used with permission.)

By Joe Pickett, OCW Publication Director

The application of computers to the Humanities has spawned many sophisticated tools that have advanced understanding in a variety of disciplines and created striking new approaches to visualization using digital media. From analyzing vast libraries of texts to assembling huge collections of images, digital technologies have unearthed discoveries and revealed patterns that were unimaginable in the pre-digital era.

How does MIT factor in all this? The School of Humanities, Arts and Social Sciences has long championed digital initiatives, and its website showcases a gallery of digital humanities that are ongoing under its aegis.

Among these is CMS.633 Digital Humanities. OCW has just published a website showcasing the Spring 2015 iteration of this course, taught by Dr. Kurt Fendt and Andy Kelleher Stuhl, of MIT’S Hyperstudio in the Comparative Media Studies / Writing department. The OCW course site includes readings and assignments, links to a variety of tools and data banks, and design documents and presentations of student projects.

How does the course work?

The instructors share insights about the course’s structure on their This Course at MIT page:

“In the first half of the semester, students read theoretical texts and we discuss core concepts in digital humanities, such as data representation, digital archives, information visualization, and user interaction . . . During the second half of the semester, students apply the concepts they’ve learned in real-world contexts through the development of digital humanities projects that meet scholarly, educational, or public needs. In developing their projects, we ask students to follow a process based in design thinking.”

Fendt and Stuhl require students to work on their projects in groups “because [group work] mirrors how digital humanists typically work in the field: collaboratively.”

Unique connections

Perhaps not surprisingly, most students taking CMS.633 are science or engineering majors, not humanities majors, but this is in many ways a blessing, says Fendt, as it opens a two-way street between disciplines:

“MIT students tend to focus on how they can use tools from the digital humanities to visualize data in their own fields in innovative ways. Additionally, they often contribute approaches and tools from their different fields that influence how we think about data in the humanities. This kind of knowledge sharing and adaptation is very exciting and is part of what makes digital humanities at MIT unique.”

Fine Tuning                               

Fendt cites the example of two astrophysics students who used a technique normally used to spot pulsars and applied it to data from the Comédie-Française Registers Project, which makes available over a century of daily records of this theater troupe.

“They overlaid two periods of data from the Comédie-Française Registers Project to see spikes that would be unnoticeable if you just examined the data in traditional ways. We thought it was a brilliant approach. It really captures what Digital Humanities is all about: taking approaches from other fields, and tuning them to make them appropriate for humanities data.”

Interpreted Data

And what about the other way around? In what ways do Digital Humanities affect the thinking of science and engineering majors?

“Typically, when students work with data in technical fields they often take the data as given items that need to be processed. We’re trying to help students think more critically about those data. When they encounter a data set, we want them to ask questions such as: What has been eliminated from the original data set? Is this data set therefore already an interpretation of the original data?  . . .  How do visual representations impact my interpretation of the data? In short, we help students realize that data are not neutral or objective. They are always filtered through an interpretive lens.”

The stars, as we imagine them, must be beaming.

2001 was a banner year

Image of New York Times headline about OCW announcement, alongside Wikipedia logo and an image of DNA sequences on a computer screen.

OCW launched in 2001, alongside the creation of Wikipedia and the first publication of the Human Genome sequence.

This week, as we celebrate the 15 year anniversary of  MIT OpenCourseWare’s unveiling, we’re reflecting on other great strides taken in 2001 and in the years since. It wasn’t so long ago, but it can be hard to remember life before these other prominent “firsts.”

January 2001Wikipedia launched with the crowdsourcing concept that no central authority should control editing.

February 2001: the Human Genome Project published its draft sequence and analysis in Nature.

October 2001: Apple released the first iPod, putting “1,000 songs in your pocket.”

2001 was a time of tremendous energy, and also great uncertainty, about the growth and impact of the Internet. The dot-com investment bubble had burst in the previous year, and many early Internet high-fliers were crashing back to Earth.

The MIT faculty and administration were asking, “What impact will the Internet have on education, and what should MIT do about it?” Their answer, in the form of OCW, was a bold bet on the power of openly shared knowledge. Fifteen years later, the 200 million learners and educators around the world who have used OCW are grateful for their foresight and generosity.