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 112, 115 or 120 should take the Placement Exam, and pre-register at the appropriate time to guarantee their place in a section. Placement in the higher level courses depends on AP scores and other prior experience, and the permission of the instructor.

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 pages.

  • Math 112a and b Differential Calculus. Prerequisite: A score of 650 or above on the Level I or Level II Mathematics Achievement Test, or an AP score of under 4 (AB) or under 3 (BC).
  • Math 115a and b Integral Calculus. Prerequisite: 112 or an AP score of 4 or 5 (AB) or 3 or better (BC). The fall term begins with a rapid review of differential calculus.
  • Math 116a Mathematics for Biosciences: Calculus techniques. Prerequisite: Math 112 or an AP acore of 4 or 5 (AB) or 3 or better (BC). Discrete and continuous models of population, neural and cardiac dynamics. Stability of fixed points and  limit cycles of differential equations. Applications include Norton's chemotherapy scheduling and stochastic models of tumore suppressor gene networks.
  • 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.
  • 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: 115 or an AP score of 5 (AB) or 4 or 5 (BC).
  • Math 121b Mathematics for Biosciences: Advanced techiques. Prerequisite: Math 116. A continuation of Math 116 focusing on Markov models of ion channel dynamics and applications to find the genetic basis of cardiac arrhythmias, epidemiological models, virus dynamics, quasispecies and anti-viral therapies, and evolutionary aspects of disease.
  • Math 222a and b Linear Algebra with Applications. Prerequisite: Math 120, or an AP score of 4 or 5.
  • Math 225a and b Linear Algebra and Matrix Theory. Prerequisite: same as Math 222. This course is more focused on theory than 222.
  • Math 250a and b Vector Analysis. This course generalizes the material in 120 to arbitrary dimensions, and explores the underlying mathematics more deeply, using the tools of linear algebra. Prerequisite: 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. Prerequisite: AP score of 5 or a grade of A in Math 115.