Much of natural science and engineering, and certain areas of social science, depend on solving problems that have a large mathematical component. In this course, we study a variety of analytical techniques, drawn from linear algebra, complex analysis, and the theory of differential equations, as well as a number of numerical methods, and we use these techniques to solve typical (but interesting!) problems from science and engineering. But problem solving is much more than knowing a set of techniques. It is equally important to be able to imagine the solution to a problem before applying any sophisticated methods, and to know how to choose an efficient approach. The course aims to enhance the students' skills in these aspects of problem solving as well. No background in science is assumed. Evaluation will be based on homework, two hour exams, and a final exam. Prerequisites: Mathematics 210 and basic knowledge of one programming language.