Solid, Cellular, and Surrounding Us

Hands holding a cross-section scale model of  an elephant skull.

A model of an elephant’s skull made with a 3-D printer by students in Professor Lorna Gibson’s 3.054 Cellular Solids: Structure, Properties and Applications.

By Joe Pickett, OCW Publication Director

Pop quiz!

  1. What does a polystyrene coffee cup have in common with a slice of bread?
  2. How is a woodpecker skull like an iris leaf?
  3. How is a porcupine quill like a milkweed stem? *

On the face of it, these questions might seem like set-up lines for jokes, but they evoke serious science for anyone taking 3.054 Cellular Solids: Structure, Properties and Applications, a course just published on OCW with lecture notes, lecture slides, and more.

The course investigates porous cellular materials, which occur abundantly in nature and have synthetic counterparts with myriad applications in engineering. Having the structures of honeycombs and foams, the materials range over an astonishing variety of things, from wood, bone, and leaves to the padding in football helmets and the scaffolds used in tissue engineering.

The course is taught by Professor Lorna Gibson, who was recently named a MacVicar fellow for her distinguished ability as a teacher. She places special emphasis on student projects, where students can apply what they have learned to create models of different kinds of materials. Her students see at firsthand what gives these materials their characteristic properties: their ability to undergo large strains, their light weight, their flexibility, their ability to provide thermal insulation, their large surface area. The students also discover under what conditions the materials fail or break, what purpose suits the use of one material over another, and how synthetic materials can be refined for superior performance.

So, as Professor Gibson observes on her This Course at MIT page, students learn both how the natural world can be seen through the eyes of an engineer and how engineers can design materials inspired by the natural world.

* Quiz answers: 1. Both are foams. 2. Both are sandwich structures. 3. Both have a cylindrical shell and compliant core.

Celebrate Earth Day with some learning

Photo of students and teacher in the woods, in discussion near a stream.

Students in 12.001 Introduction to Geology on a field trip. (Image courtesy of Taylor Perron. Used with permission.)

Tomorrow (April 22) is Earth Day.  We’ve added several more Earth-focused courses in the past year, since Earth Day 2014, that may help you appreciate the marvels of our planet.  Check out:

Also worth noting: last fall MIT kicked off a campus-wide Climate Change Conversation project, and we’ve been maintaining a list of about 40 climate change courses on OCW in support of that effort.

Mind you, as fascinating as our course materials are, we also hope you’ll get outside and connect with nature for a while.  OCW will still be here when you come back inside.

Mathematics as Literature

Three students sitting at a table; female student looks toward speaker at front of room; male student leans forward, holds pen, and looks toward speaker; another male student looks down at paper.

Students listen as their colleague presents a lecture on rational homotopy.

By Joe Pickett, OCW Publication Director

Normally when you think of a literature seminar, you think of a bunch of students sitting around a table talking about Kafka or George Eliot.

OCW has just published a literature seminar of a different stripe—in mathematics. The course is 18.915 Graduate Topology Seminar: Kan Seminar. It is named after its founder, Daniel Kan, an MIT Professor known for his unconventional, conversational style of teaching. Lectures simply did not suit him. He developed an alternative style of instruction more reminiscent of the humanities than the traditional chalkboard session in mathematics. Professor Kan passed away in 2013, but his legacy has been carried on at MIT, most recently by Professor Haynes Miller, who led the published version.

The course serves as a sequel to a first year graduate course in algebraic topology. It introduces graduate students and occasional undergraduates to a broad range of more advanced algebraic topology by requiring them to read some of the classic papers in the field. The idea is “to push students through the transition from someone who takes courses to someone who thinks more actively about mathematics,” as 18.915 alumnus (and Kan PhD student) Philip Hirschhorn puts it.

It’s a process: Students give practice talks to their classmates (no instructor present). These are typically “fractious,” full of interruptions, questions, and criticism. After that, it’s on to formal presentations, with the instructor attending and attentive. In his office after delivery, Professor Miller then “debriefs” students individually on the effectiveness of their presentations and on the mathematics involved.

According to Professor Miller, a second course objective is to help students learn “to scan an article quickly, to glean the essential points and relate them to the rest of their evolving intellectual infrastructures, and to express this understanding.” So seminar participants must write “reading responses” to all of the papers they are not presenting. Professor Miller responds to the responses. The course site has a full list of readings and some sample student reading responses, along with Professor Miller’s replies.

There must be something contagious about this approach to teaching mathematics, because the OCW site has links to Kan seminars taught at other institutions. As Professor Miller sees it, instructors shouldn’t be put off by the list of long and difficult papers that have been used in the course. “You’re not there to teach the material to the students; you’re there to help students learn the material.”

18.915 is the second project-based course by Professor Miller published as part of OCW’s Educator initiative. The first was 18.821 Project Laboratory in Mathematics, in which students acquire a taste of what it’s like to do mathematical research.

Adding up to a big win: MIT dominates at annual Putnam Math Competition (MIT News)

A cylinder shape cut into eight equal-sized wedge-shaped pieces, with four vertical cuts through the center.

It’s easy to see that a cylinder of cheese can be cut into eight identical pieces with four straight cuts. Can this be done with only three straight cuts? For the answer, see OCW’s 18.S34 Problem Solving Seminar.

As reported last week, some MIT math students recently racked up a big honor.

MIT swept the board at this year’s prestigious William Lowell Putnam Mathematical Competition, winning the team award and placing five students among the top six individual spots, an achievement that earns each the title of “Putnam Fellow.”

The Putnam competition, the premier undergraduate mathematics contest in the U.S. and Canada, is notoriously tough: The median score for the latest exam, held last Dec. 6, was just three points out of a possible 120; more than half of the participants did not solve a single problem fully.

Read the full story >

With OCW, you can try some of the same training methods as these stellar mathletes. The course 18.S34 Problem Solving Seminar is geared to “students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.” In fact, students that take this course are expected to compete in the Putnam competition.

Congratulations to the MIT Putnam Fellows — senior Zipei Nie, sophomore Mark Sellke, sophomore Bobby Shen, sophomore David H. Yang, and sophomore Lingfu Zhang — and the entire MIT team!

What Two Years of MOOCs Can Tell Us

Diagram of many interconnected circles, each representing one MOOC.

This visualization of MOOCs from HarvardX (blue nodes) and MITx (red nodes) highlights how over 300,000 unique registrants participated in sequences of multiple courses.

By Joe Pickett, OCW Publication Director

Researchers at Harvard and MIT have just published a study of user behavior in 68 MOOCs offered by HarvardX and MITx on the edX platform from Fall 2012 through Summer 2014.

HarvardX and MITx: Two Years of Open Online Courses runs to 37 pages and analyzes massive amounts of data: 1.7 million participants, 10 million participant hours, and 1.1 billion participant logged events. But don’t be intimidated. The study opens with a convenient executive summary, and all terms (like participant and logged event) are clearly defined in a brief glossary.

Harvard’s Andrew Ho and MIT’s Isaac Chuang are the lead authors of the report, which identifies trends and patterns in demographics and outcomes, reveals the top five courses in a variety of categories (like female participation and participation by people without Bachelor’s degrees), and visualizes the emerging MOOC curriculum by participation in multiple courses in sequence.

The report reveals a dynamic and subtly changing situation, in which the numbers both of total participants and of unique participants are steadily rising, and the make-up of the population is becoming slightly older and more female.

Perhaps the most interesting finding from surveys of MOOC participants is that as many as 39% are teachers, and some 21% of them are taking courses in their areas of expertise, suggesting that there be a substantial multiplier effect in classrooms around the world.

Happy birthday, “Doc” Edgerton

Photo of two pieces of fruit side-by-side, with a bullet exiting.

In 6.163 Strobe Project Laboratory, students explore the photography techniques of Prof. Harold “Doc” Edgerton. (Image courtesy of Tara Andrews, Ruben Brown, Francisco Delatorre, and Heather Hooper. Used with permission.)

“Work hard. Tell everyone everything you know. Close a deal with a handshake. Have fun!” 

That was the philosophy of Harold “Doc” Edgerton. Born on this day, April 6, in 1903, the late MIT engineering professor, inventor and explorer is best known for his high-speed strobe photographs of milk drops, bullets through fruit and playing cards, flying birds and human gymnasts.

Edgerton’s love of hands-on learning is alive and well throughout MIT, and especially in the courses and projects of the MIT Edgerton Center. OCW has numerous Edgerton Center courses, from re-creations of Galileo’s experiments to several D-Lab courses on how to design appropriate technology for developing countries.

You can also follow MIT students learning about Edgerton’s photography innovations in the OCW course 6.163 Strobe Project Laboratory. Taught by Jim Bales, this course explains how to make your own strobe photographs, and includes image galleries and demonstration videos of student projects.

“Doc” himself demonstrates strobe photography in this 1987 video from Prof. Alan Oppenheim’s course on Signals and Systems.

Screenshot of Harold "Doc" Edgerton demonstrating strobe photography in his lab.

And for the Edgerton aficionado, the MIT Museum’s Edgerton Digital Collections website is a must-see. With hundreds of images and videos, stories from his life, descriptions of his techniques, and even scans of lab notebooks, it’s sure to inspire the inventor and explorer in all of us.

He’s Seen Colder

Photo of professor speaking to class, gesturing with both hands.

Learn about Atomic, Molecular, and Optical physics from Nobel laureate Wolfgang Ketterle.

By Joe Pickett, OCW Publication Director

Imagine you are an undergraduate studying physics, and you dream of doing research making fundamental discoveries about matter and energy. But you have no way of penetrating the mystery of how this research takes places, or what exactly is needed to get to this level of understanding.

You don’t, that is, until now.

OCW has just published two MIT graduate-level courses providing a full academic year’s worth of study in AMO (Atomic, Molecular, and Optical) physics: 8.421 Atomic and Optical Physics I and 8.422 Atomic and Optical Physics II.

Both courses have full video lectures, extensive reading lists, and assignments.

The courses are taught by Professor Wolfgang Ketterle, who, along with other MIT researchers and researchers from Harvard University, is a member of the group known as the Center for Ultracold Atoms.

As Professor Ketterle explains in his introductory lectures, students who take these courses “will be able to talk about atoms and light as experts at the most profound level.”

AMO physics is a fascinating field. Long ago (i.e., in the 1950s and 1960s), research focused on individual particles, especially two-particle collisions. The field was thought to have played itself out, reaching the limits of what was discoverable. But advances in technology and bold new ideas opened the field to undreamed-of possibilities in the decades following.

More powerful lasers, with extremely short pulses (down to the attosecond—one quintillionth of a second) have enabled researchers to control single photons and to cool atoms until their temperature registers in terms of the picokelvin (one trillionth of a Kelvin).

Researchers first explored “few body” physics, entanglement, and quantum information science, then advanced to “many body” physics, quantum gases, and ultracold states, barely above absolute zero.

Breakthrough after breakthrough has arisen, where no one had predicted. As a result, a number of Nobel prizes have been awarded in AMO physics—in 1997, 2001, 2005, 2012—for very recent discoveries, in contrast to the usual gap of decades between discovery and award.

Although he does not mention it in his introductory lectures, Professor Ketterle was one of the Nobel recipients in 2001 for demonstrating the ultracold form of matter known as the Bose-Einstein Condensate, in which atoms condense into a single quantum state.

On his This Course at MIT page, Professor Ketterle discusses how he uses clicker questions, how he’s been thinking about web-based problem sets, why he uses a tablet computer instead of a blackboard when lecturing, and more.

So think of it—the opportunity to learn from a leading researcher of cutting-edge science for an entire academic year, at your leisure and pace—all for free on OCW.

Who would have predicted that?