Mathematics 21B (fall)
Linear Algebra and Differential Equations (110989)
Roderic Guigo Corominas2026 Fall (4 Credits)
Schedule: TBD
Instructor Permissions: None
Enrollment Cap: n/a
Linear algebra is one of the most widely used areas of mathematics; it has applications in fields as varied as computer science, economics, engineering, epidemiology, ecology, physics, psychology, archaeology and statistics. In linear algebra, we study linear transformations, an important group of functions that play a role in the various applications mentioned above. We’ll start from a very concrete perspective, that of solving linear systems, but we’ll quickly see that we can also adopt a more geometric perspective, which is often useful. Linear transformations enable us to deal with higher-dimensional phenomena as well as vast amounts of data. As we progress through the course, the level of abstraction will increase. This is key, because it allows us to generalize our knowledge to broader and broader contexts. We’ll see how linear algebra can be applied to dynamical systems and differential equations, which model processes throughout the natural and social sciences, and to Fourier series, which are used in engineering and the sciences to analyze waves, signals, and other periodic phenomena.
- Recommended Prep:
- Mathematics 1b or an equivalent background in mathematics. Mathematics 21a is commonly taken before Mathematics 21b, but is not a prerequisite, although familiarity with partial derivatives is useful. If you plan on taking both Math 21a and Math 21b, we highly recommend taking Math 21a first.
- Requirements:
- Anti-requisite: Cannot be taken for credit if you have passed MATH 22A or AM 22A
- Course Notes:
- The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499
- Course Notes:
- Math 21B is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). You will not register for Math 21B directly. Instead, please: Enroll in Math PL. Once you are enrolled, complete the Math Sectioning Form (available on my.harvard) to indicate your course preferences and time preferences. Take the Math Placement Verification Exam during your assigned time slot. For information about how to register for this course and to rank your time preferences, please see the Canvas site.
- Course Notes:
- Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.
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