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