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Finishing Noninear Programming: Guler, Chapter 9.
Class notes (pretty incomplete, to be used just as a study guide), here and here.…
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Consider a Morse function on \(f:\Real^n\to \Real\) with controlled behavior at infinity, – say, \(f=|x|^2\) near infinity. Assume further that all critical values \(a_1<a_2<\ldots<a_k\) are distinct and that all indices of critical points are \(0\) or \(1\). (Condition obviously holds in one variable.)
Clearly, there are many function that satisfy these conditions. In the (again, most transparent) univariate case, the enumeration of topological types of functions with given critical values is the subject of a nice thread of papers by Arnold on “snakes” (see, e.g., here), relating them to enumeration of ramified coverings of Riemannian spheres, up-down sequences and other cute objects.…
What is your math department strength? One of those rather polarizing questions, or an opportunity to gossip without guilt.
Still, important to understand where your department is on the map, if one wants to steer it in some particular direction, or to keep it where it is.
I wrote a short python script, using BeautifulSoup (thank you!) and campus-wide subscription to MathSciNet (thank you too!) – and downloaded the raw numbers: how many items (whichever MathSciNet is indexing: articles, books, theses,…) are authored by folks from ‘1-IL’ (our code) vs.…
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Simplex method (see Matousek/Gaertner, Understanding and using linear programming.
Starting Noninear Programming: Guler, Chapter 9.
Class notes (pretty incomplete, to be used just as a study guide), here and here.
Homework (due by midnight of Sunday, Mar. 10).
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Linear Programming: Guler, Chapter 6 and Matousek/Gaertner, Understanding and using linear programming.
Class notes (pretty incomplete, to be used just as a study guide), here and here.
Exercises
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Finishing Guler, Chapter 4 and covering Chapter 6.
Class notes (pretty incomplete, to be used just as a study guide), here and here.
Exercises:
Finishing Guler, Chapter 3 and starting Chapter 4.
Class notes (pretty incomplete, to be used just as a study guide), here and here.
Using linear constraints compatibility in packing problems, see e.g. here.
Exercises:
Following Chapter 2 of Guler.
Class notes (pretty incomplete, to be used just as a study guide), here and here.
Exercises:
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