Fun with Mathematical Inequalities


Zoom link: 979 9501 1494 (email me for password)

This course is being offered as a part of the Science Honors Program in Fall 2021.

Inequalities can be found throughout all of mathematics—from Euclid's Elements to operations research and financial mathematics. This course will focus on developing problem solving skills, especially in the context of mathematical inequalities. Class discussions and problem solving will be a major part of the course. No special mathematical background is required, though some knowledge of calculus and some exposure to (or enthusiasm for) proofs will be helpful.

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when topics notes problems
10/9 10am-12:00pm Introduction, the Cauchy–Schwarz inequality pdf pdf
10/16 10am-12:00pm The AM-GM inequality, thinking in high dimensions pdf pdf
10/23 10am-12:00pm Why high dimensions can be counterintuitive pdf
10/30 10am-12:00pm Metrics and metric spaces pdf pdf
11/6 10am-12:00pm (Guest lecture) Joanna Tao on Ramsey theory pdf
11/13 10am-12:00pm Convexity and Jensen's inequality pdf
11/20 10am-12:00pm Applications of Jensen's inequality pdf
12/4 10am-12:00pm Reverse Cauchy-Schwarz, Chebyshev's order inequality pdf
12/11 10am-12:00pm (Bonus) The Halting Problem, computability and complexity theory pdf