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, 120, or 121 must take the calculus placement exam, and students who plan to take Math 110, 111, 112, 115, 116, or 120 must enter preference selection at the appropriate time to guarantee their place in a section.

Calculus courses

  • Math 110  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 112 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 115 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 116 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 118 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 differential calculus prior to Yale. 
  • Math 120 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.

Linear algebra 

MATH 222, MATH 225 and MATH 226 deal with linear algebra, the common language for a wide variety of applications involving many variables.
MATH 222 emphasizes computations and applications of linear algebra, and is especially useful for students who wish to major in engineering, social sciences, economics, and other fields. Students normally enroll in MATH 222 after completing MATH 120, but well prepared students may consider taking MATH 222 after MATH 115 or equivalent. 

MATH 225 and MATH 226 are proof-based courses focusing on geometric and conceptual issues and the logical structure of the subject. These are recommended for students who wish to major in mathematics and for students who intend to take higher-level mathematics courses. MATH 225 is typically taken by students who have completed multivariable calculus, or students who have completed integral calculus and have strong interest in proof-based mathematics courses. MATH 225 assumes no prior exposure to writing mathematical proofs. MATH 226 is an intensive version of MATH 225 for students with strong mathematical background who have some familiarity with writing mathematical proofs.

Introductory sequence into the math major

After integral calculus, students wishing to pursue study of mathematics typically enroll in MATH 225 (linear algebra and introduction to proofs), and MATH 255 (real analysis and introduction to proofs). MATH 225 and MATH 255 can be taken in either order, though it is recommended to take MATH 225 first. 
Most students complete multivariable calculus before enrolling in MATH 225, however, prospective mathematics majors and students with interest in abstract mathematics may consider enrolling in MATH 225 directly after MATH 115 or equivalent, and complete their vector analysis/multivariable calculus requirement with MATH 302. 
Students with a strong mathematical background that includes exposure to mathematical proofs are encouraged to consider the intensive version of the introductory sequence, MATH 226 and MATH 256.