Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality.
Course Format

This course has been designed for independent study. It consists of four units, one for each topic. The units can be used individually or in combination. The materials for each unit include:

Lecture Videos by MIT faculty.
Learning activities, including Interactive Concept Quizzes, designed to reinforce main concepts from lectures.
Problem Sets you do on your own and check your answers against the Solutions when you’re done.
Problem Solving Video help sessions taught by experienced MIT Teaching Assistants.
Lists of important Terms and Definitions.
Suggested Topics and Links for further study.
Exams with Solution Keys.

Content Development

Eric Lander
Robert Weinberg
Tyler Jacks
Hazel Sive
Graham Walker
Sallie Chisholm
Dr. Michelle Mischke

Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality.
Course Format

This course has been designed for independent study. It consists of four units, one for each topic. The units can be used individually or in combination. The materials for each unit include:

Lecture Videos by MIT faculty.
Learning activities, including Interactive Concept Quizzes, designed to reinforce main concepts from lectures.
Problem Sets you do on your own and check your answers against the Solutions when you’re done.
Problem Solving Video help sessions taught by experienced MIT Teaching Assistants.
Lists of important Terms and Definitions.
Suggested Topics and Links for further study.
Exams with Solution Keys.

Content Development

Eric Lander
Robert Weinberg
Tyler Jacks
Hazel Sive
Graham Walker
Sallie Chisholm
Dr. Michelle Mischke

This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.

How to solve for the horizontal displacement when the projectile starts with a horizontal initial velocity. We also explain common mistakes people make when doing horizontally launched projectile problems. Created by David SantoPietro.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"The next time you swat away that fly buzzing around your head, consider this: an international team of researchers has shown that common houseflies and blowflies are more than just annoying insects. Covered with hundreds of different bacterial species, they’re also a type of airborne delivery service, transporting pathogens from organic decaying matter right to your countertops, food…and body. Although flies have been long known to spread disease, the researchers show that we’ve previously underestimated both the number and diversity of microbes that each insect can transmit. The team devised a new optimized way to collect flies without cross-contaminating them with other microorganisms and used the method to amass 116 flies from urban, rural, and natural sites on three continents..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

During this lesson, students start to see the data structure they will use to store their images, towards finding a solution to this unit's Grand Challenge. Students are introduced to two-dimensional arrays and vector classes. Then they are guided to see that a vector class is the most efficient way of storing the data for their images. Grand Challenge: To write a program to simulate peripheral vision by merging two images.

In this lesson, students will learn how great navigators of the past stayed on course that is, the historical methods of navigation. The concepts of dead reckoning and celestial navigation are discussed.

Figuring out the acceleration of ice down a plane made of ice. Created by Sal Khan.

Figuring out the components of the force due to gravity that are parallel and perpendicular to the surface of an inclined plane. Created by Sal Khan.

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.

Students learn about video motion capture technology, becoming familiar with concepts such as vector components, magnitudes and directions, position, velocity, and acceleration. They use a (free) classroom data collection and processing tool—the ARK Mirror—to visualize and record 3-D motion. The Augmented Reality Kinematics (ARK) Mirror software collects data via a motion detector. Using an Orbbec Astra Pro 3D camera or Microsoft Kinect (see note below), students can visualize and record a robust set of data and interpret them using statistical and graphical methods. This lesson introduces students to just one possible application of the ARK Mirror software—in the context of a high school physics class. Note: The ARK Mirror is ported to operate on an Orbbec platform. It may also be used with a Microsoft Kinect, although that Microsoft hardware has been discontinued. Refer to the Using ARK Mirror and Microsoft Kinect attachment for how to use the ARK MIrror software with Microsoft Kinect.

The difference between vectors and scalars. ​Introduction to distance, displacement, speed, and velocity. Created by Sal Khan.

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Welcome to this online course on Linear Algebra.

Linear Algebra is a branch of mathematics that plays a fundamental to role in many parts of Science and Engineering, such as Quantum Mechanics, Coding Theory, Signal Processing and Control Theory .

As Linear Algebra is a common component of many university programmes in Science or Engineering, this course can be used as additional study or preparation for on campus courses on Linear Algebra. Please note that we cannot guarantee that this course can replace an on campus course.

The course has no preliminaries other than basic high school mathematics. Furthermore, the course is self contained; it can be studied without extra resources. Nevertheless, for each topic you can find some references to standard literature that you can consult for further reading.

This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

This 25-minute video lesson introduces the idea of an angle between two vectors.

This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]

This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]

This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]