Yale University

Calculus and Linear Algebra

Calculus and linear algebra are fundamental to virtually all of higher mathematics and its applications in the natural, social and management sciences. These topics therefore form the core of the basic requirements in mathematics, both for Mathematics majors, and for students in science and engineering.

Students who plan to take Math 110, 112, 115, 116, 118, or 120 must take the Placement Exam, and students who plan to take Math 112, 115, or 120 must pre-register at the appropriate time to guarantee their place in a section.

Each Mathematics Major must complete one of the following alternatives: either Math 222 or 225 plus Math 250; or Math 230 and 231, described below. Click on the links, where available, for current or recent web page.

  • Math 110a  Integrated Precalculus and Differential Calculus.  Comprehensive review of precalculus, limits, differentiation and the evaluation of definite integrals, with applications.  Precalculus and calculus topics are integrated. Emphasis on conceptual understanding and problem solving.  Successful completion of Math 110 and 111 is equivalent to Math 112 in that it satisfies the same major and professional-school (e.g. pre-med) requirements; however a student completing Math 110 and 111 receives two course credits and two QR credits.  Only students who complete Math 110 will be allowed to enroll in Math 111.  No prior acquaintance with calculus is assumed; some knowledge of algebra and precalculus mathematics is helpful.  Prerequisite: A result of "Math 110" on the math placement exam.
  • Math 112a and b Differential Calculus.  Limits and their properties.  Definitions and some techniques of differentiation and the evaluation of definite integrals, with applications.  Prerequisite: A result of "Math 112" on the math placement exam.
  • Math 115a and b Integral Calculus. Applications of integration, with some formal techniques and numerical methods. Improper integrals, approximation of functions by polynomials, infinite series. Prerequisite: Passing Math 111 or 112 at Yale, or a result of "Math 115 or 116" on the math placement exam.
  • Math 116a Mathematical Models in the Biosciences.  Integration techniques and applications to differential equations.  Solving linear systems of differential equations.  Stability of fixed points and limit cycles of non-linear systems.  Power series solutions.  Assignments include readings from life-science journals.  Prerequisite:  Passing Math 111 or 112 at Yale, or a result of "Math 115 or 116" on the math placement exam.
  • Math 118a and b Introduction to functions of several variables. Calculus of several variables and some linear algebra. This course contains parts of 222 and 120 and is intended for students in the social and life sciences. Students intending to take further courses in mathematics should take 222 and 120 instead. Math 118 is a prerequisite for Stat 238, Introduction to Statistics. It cannot be used as a prerequisite for upper division mathematics courses. Prequisite: Passing Math 111 or 112 at Yale, or a result of "Math 115 or 116" on the math placement exam.
  • Math 120a and b Multi-variable calculus. Vector functions, mostly in three dimensions; gradient, curl, and divergence; line and surface integrals; the theorems of Gauss, Greeen, and Stokes. Prerequisites: Passing Math 115 or 116 at Yale, or a result of "Math 120" on the math placement exam.
  • Math 222a and b Linear Algebra with Applications. Prerequisite: Math 115.
  • Math 225a and b Linear Algebra and Matrix Theory. This course is more focused on theory than Math 222. Prerequisite: After or concurrently with Math 120.
  • Math 250a and b Vector Analysis. This course generalizes the material in Math 120 to arbitrary dimensions, and explores the underlying mathematics more deeply, using the tools of linear algebra. Prerequisite: Math 120 and Math 222 or 225.
  • Math 230a and 231b Vector Calculus and Linear Algebra. A two-term course covering roughly the material in Math 120, 222, and 250, but with a greater emphasis on proof and logical structure. A demanding, but rewarding, course for well-motivated students with a strong background. Permission of the instructor is required.