Introductory Math Courses
Single Variable Calculus
The 20Series:
This series covers differential calculus, integral calculus, and power series in one variable. It can be started at any point in the sequence for those with sufficient background. See the detailed list of topics.
Math 19 Calculus (3 units) covers properties and applications of limits, continuous functions, and derivatives. Calculations involve trigonometric functions, exponentials, and logarithms, and applications include max/min problems and curvesketching.
Math 20 Calculus (3 units) covers properties and applications of integration, including the Fundamental Theorem of Calculus and computations of volumes, areas, and arc length of parametric curves. An introduction to some basic notions related to differential equations (such as exponential growth/decay and separable equations) is also given.
Math 21 Calculus (4 units) covers limits at infinity and unbounded functions in the context of integration as well as infinite sums, including convergence/divergence tests and power series. Taylor series and applications are also covered.
It is often asked whether skipping Math 21 to go straight into Math 51 is harmless. The link above addresses this popular question.
Courses in Multivariable Mathematics
The department offers 3 sequences in multivariable mathematics.
The 50Series:
Math 51 Linear Algebra, Multivariable Calculus, and Modern Applications (5 units) covers linear algebra and multivariable differential calculus in a unified manner alongside applications related to many quantitative fields. This material includes the basic geometry and algebra of vectors, matrices, and linear transformations, as well as optimization techniques in any number of variables (involving partial derivatives and Lagrange multipliers).
Math 52 Integral Calculus of Several Variables (5 units) covers multivariable integration, and in particular Green’s Theorem and Stokes’ Theorem. This uses both linear algebra and matrix derivative material from Math 51.
Math 53 Ordinary Differential Equations with Linear Algebra (5 units) integrates further topics in linear algebra with ordinary differential equations. These further topics include using eigenvalues and eigenvectors to solve systems of differential equations.
**Math 52 and Math 53 can be taken in either order.
This series provides the necessary mathematical background for majors in all disciplines, especially for the Natural Sciences, Mathematics, Mathematical and Computational Science, Economics, and Engineering.
The table of contents and page of applications near the start of the course text provide more information; the course text is freely available to anyone with an SUNetId.
For those with a strong interest in math and a preference for more conceptual and theoretical understanding we recommend the following two sequences:
The 60CMSeries
Math 61CM62CM63CM Modern Mathematics: Continuous Methods (5 units each) This prooforiented threequarter sequence covers the material of 51, 52, 53, and additional advanced calculus, higherdimensional geometry, and ordinary and partial differential equations. This provides a unified treatment of multivariable calculus, linear algebra, and differential equations with a different order of topics and emphasis from standard courses. Students should know singlevariable calculus very well and have an interest in a theoretical approach to the subject.
This series provides the necessary mathematical background for majors in all disciplines, especially for the Natural Sciences, Mathematics, Mathematical and Computational Science, Economics, and Engineering.
The 60DMSeries
This prooforiented threequarter sequence covers the same linear algebra and multivariable optimization material as the 60CMseries but draws its motivation from topics in discrete math rather than from the more analytic topics as in the 60CMseries. Its discrete math coverage includes combinatorics, probability, some basic group theory, number theory, and graph theory. Students should have an interest in a theoretical approach to the subject.
This series provides the necessary mathematical background for majors in Computer Science, Economics, Mathematics, Mathematical and Computational Science, and most Natural Sciences and some Engineering majors. Those who plan to major in Physics or in Engineering majors requiring Math 50’s beyond Math 51 are recommended to take Math 60CM.
Learning Proof Writing
Many 100level mathematics courses assume familiarity with writing proofs, and if you plan to be a Math major then you should learn proof writing as soon as possible. Here is a list of courses to begin learning proofwriting:

Math 56

61CM or 61DM

Math 110

Math 113

Math 115
Math 104 also provides an introduction to proofwriting, but not at the same level as the above courses (a variety of proofs are covered, but students are not expected to write proofs of their own at the same level as some of those shown in class).
Please note: Math 104 and Math 113 do not assume background beyond the linear algebra covered in Math 51.
More Information
For more information about these courses see ExploreCourses for course descriptions and schedule. If you have further questions about which course to take, contact your academic advisor, or our Director of Undergraduate Studies.