# More Information on Math 205a-b

**A score of 5 on the AP Calculus BC exam is required to enter this sequence.**

Math 2500-2501 (formerly 205a-b) is a two-semester alternative to Math 2300 (formerly 175), Second Year Accelerated Calculus, and Math 2600 (formerly 204) or 2410 (formerly 194), Linear Algebra, for the most mathematically talented and motivated entering students. All the material from Math 2300 and 2600 is covered in Math 2500-2501, but Math 22500-2501 goes further and deeper and takes an integrated approach to multivariable calculus and linear algebra. Math 2500 and 2501 are four credit hours each semester, whereas Math 2300 and 2600 are three-credit-hour courses.

Here is the official catalog description:

**2500. Multivariable Calculus and Linear Algebra. **Vector algebra and geometry; linear transformations and matrix algebra. Real and complex vector spaces, systems of linear equations, inner product spaces. Functions of several variables and vector-valued functions: limits, continuity, the derivative. Extremum and nonlinear problems, manifolds. Multiple integrals, line and surface integrals, differential forms, integration on manifolds, theorems of Green, Gauss, and Stokes. Eigenvectors and eigenvalues. Emphasis on rigorous proofs. Enrollment limited to first-year students with test scores of 5 on the Calculus BC advanced placement examination or the approval of the director of undergraduate studies. Credit is not given for both 2500-2501 and 2300, 2410, or 2600.

**Who should take Math 2500-2501?**

All qualified prospective mathematics majors should take the course. Qualified science and engineering students with a strong interest in mathematics should consider it. The main criteria are that the student has a 5 on the AP Calculus BC exam, an excellent background in single-variable calculus, and a fascination with the theoretical side of mathematics.

**More information:** For more information, contact the current course instructor.

Updated JAR, April 21, 2015

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