Mathematics 1A (fall)

Introduction to Calculus (123680)

Hannah Constantin

2026 Fall (4 Credits)

Schedule: TBD

Instructor Permissions: None

Enrollment Cap: n/a

Calculus stands as one of the great intellectual achievements of the last millennium, developed by Newton and Leibniz to understand motion, growth, and change. This single-variable course introduces you to that achievement by focusing on these central ideas: how differential calculus describes rates of change, how integral calculus describes accumulation, and how the Fundamental Theorem of Calculus connects them. Throughout, you will see these ideas at work in concrete problems drawn from the physical sciences, life sciences, economics, and everyday contexts. A central theme of the course is understanding, describing, and calculating rates of change. You will learn to interpret derivatives graphically and numerically, connect derivatives to the shape and behavior of graphs, and use derivative techniques—including product, quotient, and chain rules, implicit and logarithmic differentiation—to solve optimization and related rates problems in context. In the second part of the course, attention shifts from rates to accumulation. You will be introduced to the definite integral as a precise way to describe accumulated change over time—mathematically, a way of “adding up pieces” such as small changes, areas, or contributions to a total. Throughout the semester, you will use algebraic reasoning—together with graphical, numerical, and symbolic representations of functions—to justify your conclusions, interpret situations, test ideas, and make sense of unfamiliar problems.

Recommended Prep:

Strong precalculus skills are essential for success in this course. If you are advised to take Math Ma, that recommendation indicates that your precalculus foundation needs strengthening, and you should take the recommendation seriously.

Requirements:

Anti-requisite: cannot be taken for credit if MATH S-1AB already completed.

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 1A 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 1A 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.

: