Cambridge Igcse International Mathematics 3rd ed

Discrete mathematics becomes more and more important as the digital age goes forward. This newly revised third edition updates all areas of the subject.

Permutation group algorithms are indispensable in the proofs of many deep results, including the construction and study of sporadic finite simple groups. This work describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout.

Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties.