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Foreword by David Eisenbud Introduction by Zvezdelina Stankova Geometric re-constructions. Part I Along optimal paths and integer grids Rubik's cube. Part II by Tom Davis Knotty mathematics by Maia Averett Multiplicative functions. Part I The infinite-raffle challenge Introduction to group theory Monovariants. Part II Jumping fleas and Conway's checkers Geometric re-constructions. Part II Bits of geometry, physics & trigonometry Complex numbers. Part II Introduction to inequalities. Part I Arithmetic, geometric, and power means Multiplicative functions. Part II Dirichlet product and Mobius inversion Monovariants. Part III Smoothing inequalities Geometric re-constructions. Part III Optimal bridges and infinitely many squares Epilogue Symbols and notation Abbreviations Bibliography Index

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**Zvezdelina Stankova's** immediate neighbors in ** , ** are **30** individuals in **10** households.

Zvezdelina Stankova ’92, a professor of mathematics at Mills College and the University of California, Berkeley, was one of three university math teachers to receive the 2011 Deborah and Franklin Tepper Haimo Award. The award, presented by the Mathematical Association of America at the joint annual meeting of the MAA and the American Mathematical Society, recognizes math professors whose effectiveness in teaching reaches beyond the bounds of their home institutions.