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## Mathematical Capillarity

This will be an introduction to the mathematical shape and stability conditions used to study liquids filling thin tubes, drops resting on plates, and suspended drops hanging from various solid structures. Configurations of floating objects may also be discussed.

Crosslisted with Math 8803-MCU.

## Mathematical Capillarity

This will be an introduction to the mathematical shape and stability conditions used to study liquids filling thin tubes, drops resting on plates, and suspended drops hanging from various solid structures. Configurations of floating objects may also be discussed.

Crosslisted with Math 4803-MCU

## Nonlinear Algebra

This is a course that introduces a few tools of Nonlinear Algebra with the view toward solving systems of polynomial equations. Apart from regular components (such as HW and exams), applied problems from various areas (automatic theorem proving, robotics, computer vision, systems biology/chemistry, etc.) will be assigned as group projects.

1. Systems of polynomial equations

2. Numerical homotopy continuation

3. Rings, ideals, and Gr¨obner bases

4. Algebra-geometry correspondence

## Measure Theory for Scientists and Engineers

An introduction to measure theory and Lebesgue integration with a focus on topics that tend to be of the most utility in science and engineering. The three course series MATH 6579, 6580, and 6221 is designed to provide a high level mathematical background for engineers and scientists.

This course is equivalent to MATH 6337. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.