Faculty Profile: Gilbert Strang

“My life is in teaching,” says one of MIT’s most revered professors. “To have a chance to do that with a world audience is just wonderful.”

By MIT OpenCourseWare

Portrait of Gilbert Strang

MIT mathematics professor Gilbert Strang was among the first MIT faculty members to publish a course on OpenCourseWare. He has continued to contribute content through the years: to date, his contributions have included six full courses, two video resources, and an online textbook on the OCW website.

He has also shared his knowledge and passion for mathematics in person, traveling extensively around the world. Open thinking has played a major role in his professional career. “A big part of my life is to open mathematics to students everywhere,” says Strang. “I’m very supportive of the whole idea of making these courses available to people around the world. Everyone has the capacity to learn mathematics, and if you can offer a little bit of guidance, the process of discovery is so valuable.”

Linear Algebra

The concepts in Strang’s foundational Linear Algebra course are useful in physics, economics and social sciences, natural sciences, computer sciences, and engineering. Due to its broad range of applications, it has long been one of the most popular courses on OCW. The 18.06 site has received more than 10 million visits since its first publication in 2002. Professor Strang has a website dedicated to his linear algebra teaching.

A new version was released in 2011, in the innovative OCW Scholar format designed for independent learners. The OCW Scholar version of Linear Algebra includes 35 lecture videos and 36 short (and highly-praised) problem-solving help videos by teaching assistants.

Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

In 2017, Professor Strang launched a new undergraduate course at MIT: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Published on the OCW site in 2019, the course uses linear algebra concepts for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization—and above all a full explanation of deep learning.

MIT News Article: Gil Strang is Still Going Strong, Online and in Print

Calculus

Professor Strang has also published a collection of other materials on the OCW site including his Calculus textbook. First released in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and independent learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. The book has an online instructor’s manual and a student study guide.

When OCW approached Professor Strang about contributing to Highlights for High School, he offered his support immediately. “I’ve always wanted to contribute to K-12. I think high school students taking Algebra or Calculus would find some of the study materials useful.”

The result is Highlights of Calculus—a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The videos are garnering praise and thanks from viewers around the world. To quote one OCW user, “This series is fabulous! It summarizes the important points of calculus and gives me confidence to learn calculus without being so fearful about it.”

Differential Equations and Linear Algebra Textbook & Videos

Professor Strang has continued to offer new insights into key mathematics subjects. In 2014, he published Differential Equations and Linear Algebra. In 2016, that textbook was developed into a series of 55 short videos supported by MathWorks—with parallel videos about numerical solutions by Dr. Cleve Moler, the creator of MATLAB®. The textbook and video lectures help students in a basic Ordinary Differential Equations (ODE) course. This new series, Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, is also available on the MathWorks website.

Higher-Level Mathematics

Computational Science and Engineering

Professor Strang also teaches two graduate-level courses on Computational Science and Engineering, a discipline that deals with the development and application of computational models and simulations. Both courses are on OCW and have full sets of lecture videos:

Wavelets, Filter Banks, and Applications

Another graduate-level course that Professor Strang has published on OCW is Wavelets, Filter Banks, and Applications, a subject with broad applications, including audio and image compression, digital communication, medical imaging, and scientific visualization.

OCW Publications by Prof. Gilbert Strang

All of Professor Strang’s books are available through Wellesley-Cambridge Press.

Professor Strang on Chalk Radio

Interested in learning about Professor Strang’s approach to teaching at MIT? Click to listen to his conversation with Dr. Sarah Hansen on Chalk Radio, the new podcast from OCW’s Educator initiative.

 

Faculty Profile: Hazel Sive

How do cells organize themselves into a heart or a brain?

Portrait of Hazel Sive

By MIT OpenCourseWare

Ask MIT’s Hazel Sive, an expert in developmental biology, about her work in embryonic development, and her love for teaching immediately shines through. She’s just as likely to start talking to you about music. “Embryonic development has its own tempo—from the thumping rock beat of early cell division to something more like modern minimalism, where you have cells working together while still doing their own thing, making the music more melodious and complex. Finally, as nerves start working and sending impulses, it moves to something more syncopated and rhythmic.”

Sive has been teaching at MIT since 1991 and is currently Associate Dean of the School of Science and Member of the Whitehead Institute, where she runs her own lab. Her multidisciplinary work, combining genetics, molecular biology, and brain imaging, is highly regarded worldwide for opening exciting new pathways in biomedical research. She has been a pioneer in the study of the vertebrate embryo, with a focus on the various signaling systems that determine how cells differentiate into specific organs.

A Teacher Who Can Teach Anyone Anything

As a child growing up in South Africa, Sive showed an early curiosity for the sciences, and credits her father as a major influence: “He was an inventor—an electrical engineer. I remember him working in his shop, designing switching devices or circuits that he would sell to the telephone company,” she recalls. “I was always welcome in his shop. For me, as a child, it was a wonderful place to explore. He allowed me to use absolutely anything, his band saw, his tools, anything,” she jokes.

Yet her love for the lush coastal landscape of South Africa, and “digging in the garden for all sorts of crawly, jumping things,” eventually led Sive into the life sciences. Her high school science teacher noticed Sive’s aptitude for science: “She was a very serious teacher. I think if she saw that you were interested, she paid extra attention to you. I remember how she once took me aside in lab and taught me how to properly use a burette. She said, ‘You’re going to study science in university someday, so you better learn to use this thing properly.’ That really meant a lot to me, that kind of attention.”

Although Sive admits that she had only a vague idea where her studies would actually lead her, she held on to two goals as an undergraduate—either to become a veterinarian and fight for animal rights, or to study ecology and politics and work to preserve the South African environment. Growing political tensions in apartheid South Africa, however, led her to make the difficult decision to leave for England after completing a double major in zoology and chemistry at the University of Witwatersrand in Johannesburg.

At the time, England’s public high schools were short of qualified science teachers: “It meant that as a chemistry-zoology double major, they were ready to let me teach practically anything, even without a teacher’s diploma. But it was trial by fire, and all very challenging. I was only 21 and at one point they had me teaching A-level boys who were sometimes as old as 19.”

“Two weeks later I received a teaching diploma from the government, which meant I could teach anywhere in England. I suppose they felt that someone who could successfully teach 60 kids about fractions could teach anyone anything.”

From those days in England, she recalls one of the proudest moments in her early teaching career. “On one particular day, I had sixty pre-teen boys in my class and my job was to teach them something about fractions—not such an exciting lesson. A gentleman in a suit asked if he could observe, and I told him that if he could find a seat, he was welcome to stay. By the end of the hour, I’d managed to cover my lesson, and the gentleman left without a word. Two weeks later I received a teaching diploma from the government, which meant I could teach anywhere in England. I suppose they felt that someone who could successfully teach 60 kids about fractions could teach anyone anything.”

A Different Style of Thinking

Teaching remains a core focus of Sive’s professional life and a clear source of enjoyment and inspiration to her. She teaches an introductory biology course to incoming first-year students every year, and she loves how the students constantly challenge her with new questions that she’s never considered. She remarks admiringly how, in recent years, students have acquired a more sophisticated molecular vocabulary, thanks to the increased presence of molecular biology in the high school curriculum: “When I ask students how cells know to build a heart, they talk about active and inactive genes, and signaling pathways. It’s a different style of thinking, a different approach. Students use a very different vocabulary than I might have encountered even five years ago.”

It’s a vocabulary that Sive’s research continues to enrich. Her undergraduate studies, doctoral studies at Rockefeller University, and postdoctoral studies at the Fred Hutchinson Cancer Center influenced the three major pursuits of the Sive Lab at the Whitehead Institute. The first is trying to better understand why the brain forms in a tubular shape, and what specific properties and advantages that brings to vertebrates. The second is gaining an understanding of how the various features of a face form and organize themselves at a cellular level. Lastly, she studies the early development of the zebrafish nervous system as a means to better understand how genetic mutations can cause human mental health disorders.

Hazel Sive’s early and ardent support of OCW is a perfect reflection of her firm belief in the importance of science and education in advancing society today.

OCW Courses Taught by Professor Sive

 

M. Amah Edoh on Creating a Supportive Academic Culture

Close up photo of woman in blue shirt standing in Killian Court at MIT

M. Amah Edoh, Assistant Professor of African Studies (Image courtesy of Jonathan Sachs Photography.)

Educators can’t just be providers of information, Professor Edoh argues; they have to be nurturers of their students’ intellectual growth.

By Peter Chipman, OCW Digital Publication Specialist and OCW Educator Assistant

Assistant Professor M. Amah Edoh is a young faculty member, young enough to remember what it felt like to be a student. Her approach to teaching reflects this fact. The Instructor Insights section of the OpenCourseWare site for her course 21G.026 Global Africa: Creative Cultures provides interesting details about how she taught that specific course, but it also offers a generous helping of observations about pedagogy in general and the role faculty members can play in helping students move from mystery to mastery. Here are a few highlights.

Course Planning

Every academic course has a central topic or idea, but Professor Edoh emphasizes that the instructor should also consider what the central question is, so that the course can be an exploration rather than a mere transfer of information:

“It’s crucial to be clear on what the core issue is, what the question is that animates this class….As long as the core question is clear, you can tailor the building blocks to your interests.”

Of course, students will bring more energy to the classroom if their work there also draws on their own interests, not just their professor’s. So Professor Edoh used the final project assignment in 21G.026 to draw on the different creative skills–cooking, drawing, horticulture, creative writing, and so on–that each student brought to the course.

“I had no idea how it would turn out, because I didn’t know what they were bringing to the table, what particular creative skills they had. But I want to believe—this is something I try to enact in my own life—that we all have creative skills, and that whatever you have, we can do something with it.”

The Need for Flexibility in Teaching

New faculty members, Edoh suggests, may not immediately realize that successful teaching depends on not always having every moment of every class planned in advance, and that lecturers need to be able to revise their teaching plan constantly in response to the needs of the moment. Doing this effectively doesn’t necessarily come easily, but it’s a core competency for a master teacher:

“When you’re a student, the professors up front seem to know exactly what they’re doing and what they’re talking about; you don’t fully appreciate the fact that it’s a lot of intuitive and improvisational work. You can be surprised at how taxing it is.”

Teaching at MIT

To counteract the tendency of the university to become a closed circle or the proverbial ivory tower, Professor Edoh asks her students to attend cultural performances out in the world to supplement and enrich their in-class learning:

“Even the experience of leaving MIT is really useful. Part of our duty as educators is to help broaden our students’ horizons, not only in the classroom but also by encouraging them to explore beyond campus.”

She also seeks to show students that the humanities have something to say about technology, and that we can fruitfully examine the meanings and cultural implications of technical systems and practices, not just the details of their operation or their practical potentials:

“At MIT in particular, we tend to fetishize technology and consider it as existing in a realm outside of other material practices, other ways of knowing. One of my personal missions is to show that technology is no different from these other practices—they’re all objects, ways of doing, ways of knowing. So whether we’re talking about plant healing or developing the next nano-technology, we can think about these things next to each other, no matter where they’re happening.”

Academic Study and the Wider World

As Professor Edoh sees it, the so-called ivory tower is an illusion; it’s neither possible nor desirable for the academy to remain divorced from the wider world. At its best, she suggests, academic work exists in constant dialogue with real-world experience, with each enriching the other:

“What we do in the classroom is not separate. Academic work isn’t separate from life, and it’s not something that’s only accessible to some people. We’re always theorizing. Making sense of our experience is about theorizing. If we can help students make links between what they’re reading for school and what they’re experiencing in the world around them, we’re in great shape as educators.”

Nurturing Student Growth

Professor Edoh distinctly remembers what it was like to be a student struggling to make sense of the often-obscure writings one encounters in academic life:

“When I was in grad school for my PhD, I was frustrated by the fact that academic texts often feel like they’re written to not be understood. This made me really angry. I thought, ‘OK, I’ve been in school for many years. How is it that this still makes no sense? If it makes no sense to me, what are we doing here? What is the point of the academic enterprise if we produce work that can’t be understood?’…The danger when you’re a student, especially at elite institutions, is that when you don’t understand, you think there’s something wrong with you: you’re not good enough, you’re not smart enough. But it’s actually a structural issue, and it’s the writers’ responsibility to write better work, to write more clearly.”

She feels passionately that it’s a professor’s job to make academic discourse less intimidating, and to encourage students as they take their first tentative steps toward being confident participants in scholarly and intellectual work:

“What made the biggest difference for me in the classroom as a student was instructors who made me feel like I had something to offer. Having instructors who make you feel you have nothing to offer is not just neutral, it’s damaging. It’s really important for me to valorize students’ voices, to show that I’m taking their work seriously.”

“My teaching philosophy stresses the importance of using classroom time to build students’ confidence, to instill in our students a sense that they’re capable of doing this work, to undo some of the damage that academic work has done for so many people—to try to make it less alienating. To say, ‘We can do this. And we know how to do this. It’s OK not to know this particular material, because we’re in school to learn. We’re not supposed to know everything when we come here. But we know how to learn and that’s what we’re here for.'”

Professor Short on Chalk Radio

Interested in learning about Professor Edoh’s approach to teaching at MIT? Click to listen to her conversation with Dr. Sarah Hansen on Chalk Radio, the new podcast from OCW’s Educator initiative.