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This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.

Groups are a means of classification, via the group action on a set, but also the object of a classification. Hoelder's program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups;

This book addresses the relationship between algebraic formulas and geometric images. In spite of the simplicity and importance of this problem, it remains unsolved to this day although, as the book shows, many remarkable results have been discovered.

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation.

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. complete metric spaces and function spaces; It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

This primer covers a remarkably wide range of topics in discrete calculus, from combinatorics to recurrence relations. With examples and exercises throughout, the text's clarity and rigor are informed by extensive teaching experience and academic discussion.