Conclusion

This book offers a survey of mathematical topics. However, there is much more for you to explore. Catastrophe theory, the Chinese Remainder Theorem, combinatorics, and complex analysis. Equivalence relations, Euclid’s elements, and Euler’s formula. The Fields Medal and Four-color Theorem. Galois theory, the gambler’s fallacy, geodesic domes, the geometry of spacetime, and group theory. The Ham Sandwich Theorem. Isomorphisms. Linear algebra. The Mandelbrot set, mathematical induction, matrices, and the monster group. The parallel postulate, Pascal’s triangle, perfect numbers, permutation groups, pi, the Poincare Conjecture, projective geometry, public-key cryptography, and Pythagoras’ Theorem. Quaternions. Regression analysis. Set theory, squaring the circle, and surreal numbers. Truth tables, turning machines, and turning a sphere inside out. Venn diagrams. Wavelets. Zero. The list never ends....

Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian

We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.