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Undergraduate Convexity: Problems and Solutions

Mikkel Slot Nielsen and Victor Ulrich Rohde
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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The story begins with Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker, by Niels Lauritzen, published in 2013. As our reviewer pointed out, this is a concrete and hands-on introduction to convexity theory. It includes quite a few exercises.

The book under review was written by two of Lauritzen’s teaching assistants. It is basically a solutions manual for the main textbook. For each chapter of the original book, the authors have provided short introductions reminding the reader of the main ideas. These are followed by statements and solutions of all the problems. The solutions start off very detailed and then become more succinct, on the assumption that the readers’ ability will increase as they work through the problems. This approach makes this book almost able to stand alone, but it will be most useful for those who are working through (or teaching from) Lauritzen’s Undergraduate Convexity.

Fernando Q. Gouvêa is the editor of MAA Reviews. As Carter Professor of Mathematics at Colby College, he has had only a few opportunities to tell students about convexity.

  • Fourier–Motzkin Elimination
  • Affine Subspaces
  • Convex Subsets
  • Polyhedra
  • Computations with Polyhedra
  • Closed Convex Subsets and Separating Hyperplanes
  • Convex Functions
  • Differentiable Functions of Several Variables
  • Convex Functions of Several Variables
  • Convex Optimization
  • Appendices: Analysis; Linear (In)dependence and the Rank of a Matrix