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


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.


Chalk Radio Is Here!

Professor Gilbert Strang and Dr. Sarah Hansen, sitting in chais in front of a blackboard

Professor Gilbert Strang in conversation with Chalk Radio host, Dr. Sarah Hansen.

MIT OpenCourseWare is proud to announce the premiere of a new podcast series.

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

Chalk Radio is a podcast about inspired teaching at MIT, hosted by Dr. Sarah Hansen. The show takes listeners behind the scenes of some of the most interesting courses on campus to talk with the professors who make those courses possible. The guests on Chalk Radio open up to us about the passions that drive their cutting-edge research and innovative teaching, sharing stories that are candid, funny, serious, personal, and full of insights. Listening in on these conversations is like being present in person under the MIT dome, talking with your favorite professors.

About the Guests

In the first episodes, we talk with a nuclear science professor who finds surprisingly entertaining educational uses for MIT’s fission reactor, and with an African studies professor who asks her students to attend theatrical performances out in the “real world.” In subsequent episodes, we meet a math professor who champions the value of getting stuck, the instructors of a popular three-day intensive course on piloting small planes, and a literature professor who wants to teach students to love the movies. And that’s just the first half of the first season!

About the Host

Professor M. Amah Edoh and Dr. Sarah Hansen, sitting in front of microphones in a recording studio

Professor M. Amah Edoh and Dr. Sarah Hansen recording the second episode of Chalk Radio.

Sarah Hansen connects educators around the world to openly licensed MIT teaching materials and approaches through the MIT OpenCourseWare Educator Initiative. Before working at MIT, she was a faculty member in the Education Department at St. Catherine University, and before that she was an elementary school teacher. She holds a Ph.D. in Curriculum & Instruction from the University of Minnesota, where her scholarship focused on equity issues in education.

How to Listen

Chalk Radio album artA new episode of Chalk Radio will appear every other Wednesday, starting February 19, 2020. All episodes will be accessible through the podcast’s website, which also includes links to Apple Podcasts and other popular platforms where you can find the latest episodes or subscribe to the whole series.

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


How to Speak, How to Live

Photo of Patrick Winston, with chalkboard highlights of the talk in the background.

Professor Patrick Winston and some highlights of his How to Speak talk. (Image by Brett Paci. Photo by Azeddine Tahiri. Used with permission.)

Watch this one-hour master class on effective presentations by the late Patrick Winston.

By Curt Newton, OCW Director

“Your success in life will be determined largely by your ability to speak, your ability to write, and the quality of your ideas, in that order.” — Patrick Winston

MIT Professor Patrick Winston (1943-2019) was a pioneer in the field of artificial intelligence (AI). He literally wrote the book on AI, and his AI course on OCW has been one of our most popular courses since it was published.

Beyond the considerable quality of his ideas, he’s been celebrated at least as much for how he went about it all. The website A Memorial to Patrick H. Winston includes rich history, fabulous stories, and a gallery of photos. The tributes offered there show clearly his positive impact on the thousands of lives he touched.

One striking way Professor Winston expanded his circle of impact beyond the AI field was through an hour-long talk he gave annually at MIT, called How To Speak. For over 40 years, every January during the MIT Independent Activities Period, people flocked to hear it. Word spread year by year, and the room was frequently overflowing.

Now on OCW, you can join the audience at one of his last How to Speak talks, given in January 2018. How to Speak is full of insights and tips for job interviews, lectures, persuasive talks, and even getting famous. Professor Winston also follows his own advice here: How to Speak demonstrates everything he says we should know and do, a classic embodiment of the principle “show, don’t tell.” It’s a master class in engaging an audience with essential information, at once expansive and crystal-clear, delivered through a rich and deeply human tapestry of stories.

“I believe that we are storytelling animals. We start developing our story understanding and manipulating skills with fairy tales in childhood and continue on through professional schools like law, business, medicine, everything. And we continue doing that throughout life.”

Professor Winston lived this belief, continuing to develop and refine his storytelling skills, and kept sharing what he was learning, throughout his life. OCW is deeply honored to share the How To Speak tradition with you.

Discovering math and physics through MIT OpenCourseWare

Photo of Kyle with his parents, outdoors on a grassy hillside.

Now a PhD student in physics at SUNY Stony Brook, Kyle Lee’s journey began online with MIT OpenCourseWare

By Duyen Nguyen | MIT Open Learning

Within two weeks of taking his first college-level physics course, Kyle Lee knew that he wanted to be a physicist.

Now a PhD candidate at SUNY Stony Brook, Kyle says that the way physicists think, combining physical intuition and mathematics to find creative solutions to problems, is what drew him to the field. He would quickly learn to problem-solve like a physicist. While he enjoyed his first physics course, Kyle found the classes at his community college to be insufficient and began looking online for other resources. That’s when he came across MIT OpenCourseWare, and his newfound dream started to become a reality.

“OCW and MIT’s digital resources have definitely changed the way I learn and my educational experience,” he says.

After graduating from high school, he wasn’t sure about what he wanted to study — or even if college was the right path for him. His family came to the United States from South Korea when he was young so that he could have better opportunities. But despite doing well in school, Kyle received little guidance. He owned a telescope and would drive to the California deserts to look at the stars, but his interests in exploration hadn’t yet taken shape. He took a semester off before enrolling in a nearby community college.

“I became desperate to find something to be passionate about,” he says. “I didn’t think about grades and just took classes I thought I would enjoy.”

An aptitude test pointing him to electrical engineering — a career he’d never even heard of — landed him in the physics class where he’d find his calling.

“I knew I had to distinguish myself if I wanted to be a physicist,” he recalls.

Through OCW, Kyle discovered not only MIT’s physics and math courses, but the world of free and open digital educational resources. With the advanced knowledge he gained from the lectures and other course materials on OCW and similar platforms — and the confidence that this gave him — Kyle knocked on the door of a physics professor at UC Irvine to ask for a research position.

After that, the doors continued to open for Kyle. He was accepted to Chapman University’s newly established physics program, where his excellent grades and the research he was doing at UC Irvine earned him a full scholarship. For Kyle, coming from a working-class immigrant background, this was the only path to affording an education at a four-year institution. It’s a path that he’s worked hard to pave.

But along the way, OCW has been there to help. Today, Kyle still consults OCW resources to remind himself of certain concepts. “During my PhD, I took Effective Field Theory,” a graduate-level course available on both OCW and MITx, “which has had a huge impact on my work,” he says. And recently, the MIT department of physics invited Kyle to speak at the Theoretical Physics Seminar on campus, where he shared his work on quantum chromodynamics, a theory of the strong nuclear force. There, he met many of the leading physicists whom he’d admired for years.

As he prepares to complete his PhD, Kyle reflects, “I strongly believe in OCW’s mission to make this sophisticated knowledge available globally. It really has changed the entire path of my educational career.”

Explore the New MIT Open Learning Library

Now even more opportunities to learn from MIT at your own pace.

Screenshot of Open Learning Library webpage.

MIT Open Learning Library (OLL) is a new home to selected educational content from MIT OpenCourseWare and MITx on edX courses, available for free to anyone in the world at any time. We’re glad to share this prototype, combining some of the most important characteristics of the OCW and MITx experiences.

Interactive Assessments and Progress Tracking

One advantage to using the MIT Open Learning Library is that, by creating a free account, you will be able to keep track of your progress as you work your way through a course and to see the answers you’ve submitted to problems within the course – just as you can with MITx on edX courses. However, Open Learning Library does not include discussion forums, certificates, or the ability to transfer your progress to MITx on edX. 

How OLL Compares to OCW and MITx

You can think of OCW, MITx, and OLL along a spectrum of learning scenarios, in which MIT content is presented in different formats to meet different user needs. 

  • MITx courses on edX are end-to-end course experiences with optional certificates available for you to earn, live teaching support and interaction with other learners in discussion forums, and start and end dates.
  • MIT OpenCourseWare offers a completely self-guided experience with published content from MIT courses that is open all of the time and licensed for download, remix, and reuse, but does not offer certificates nor interaction with teachers and learners. 
  • MIT Open Learning Library sits in between MITx on edX and OCW. As in many MITx courses, OLL provides interactive course experiences that include auto-graded assessments that give you instant feedback and allow you to track your progress as you work your way through the subject matter. Like OCW, this content is always open and self-guided and includes no live support, discussion forum, or certificates.

Open Learning Library resources designated as OCW content are free to download, remix, and reuse for non-commercial purposes.  Resources designated as MITx content have varying licenses: some are All Rights Reserved, others Creative Commons, and some have mixed licenses. You will see the license type indicated on the About Pages.

Take a Closer Look

6.042J Mathematics for Computer Science is an example of an OCW course on OLL. As taught at MIT, Professor Albert Meyer used MIT’s residential version of the edX platform to deliver short videos interspersed with interactive concept questions that checked and effectively reinforced student learning — in other words, a structure very similar to MITx courses. This structure was reflected in the the openly licensed OCW version of this course, although OCW’s current platform is not able to track a learner’s progress through the course. Now with the new OLL version of the course, learners have a “best of both worlds” experience where the platform keeps track of their progress, while preserving OCW’s always-available openness.  

This version of Open Learning Library is an evolving prototype. Watch for new content, new site features, and an enhanced user experience. We welcome your feedback on the site, including your thoughts on areas for improvement.

Webinar on OCW Recent Highlights and Future Direction

Headshot photo of Curt Newton.Please join OCW Director Curt Newton on a free webinar, Monday March 4, 12:30-1:30 ET, for a tour through some recent highlights on MIT OpenCourseWare, and thoughts on its bright future.

Register here.

This webinar is presented by the Abdul Latif Jameel World Education Lab (J-WEL). A program of MIT Open Learning, J-WEL at MIT seeks to promote excellence and transformation in education globally. As an incubator for change in education at MIT and around the world, J-WEL provides a platform that engages educators, technologists, policymakers, and societal leaders in addressing global opportunities for education through online and in-person collaborations, workshops, and information sharing events.

The webinar is a contribution to Open Education Week, a global event to raise awareness of free and open sharing in education and the benefits they bring to teachers and learners. Coordinated by the Open Education Consortium, Open Education Week showcases projects, resources, and ideas from around the world that demonstrate open education in practice.