Jaume Aguadé – författare

This textbook compiles lessons from the Foundations of Mathematics course at the Autonomous University of Barcelona. It is designed to introduce students beginning their mathematics studies to the major overarching ideas in the field—such as symmetry, structure, equivalence, abstraction, generalization, analogy, and computability. It also aims to familiarize students with the structure of mathematical discourse—how mathematics is written—and to support them in the challenging task of developing the rigor and creativity required of a professional mathematician.In this work, readers will encounter the big ideas and fundamental principles that shape mathematical discourse, including logic, group theory, Peano's axioms, Russell's paradox, the prime number theorem, RSA cryptography, Euler's formula, and more. After each part, a set of carefully selected exercises helps students to gain greater exposure to—and confidence in—the rigors of mathematics.Guided by aesthetic and playful principles, this book offers a gentle, passionate, and joyful approach to some of the most essential concepts in mathematics. It provides enjoyment for teachers, students, and anyone with an inclination toward the subject, and is particularly appealing to high-achieving high school students seeking to delve into college-level mathematics.

This book contains a collection of articles summarizing together the state of knowl- edge in a broad portion of modern homotopy theory. These articles were assembled during 1998 and 1999, on the occasion of an emphasis semester organized by the Centre de Recerca Matematica (CRM) and its highlight, the 1998 Barcelona Con- ference on Algebraic Topology (BCAT). First of all, we are indebted to all the authors for submitting their work, and to the referees for their help in the selec- tion and for their generous contribution to the content of the articles. Many talks given during the CRM semester or at the conference focused on aspects of the following topics: abstract stable homotopy, model categories, homotopical localizations and cellular approximations, p-compact groups, mod- ules over the Steenrod algebra, classifying spaces for proper actions of discrete groups, K-theory and other generalized cohomology theories, cohomology of fi- nite and profinite groups, Hochschild homology, configuration spaces, Lusternik- Schnirelmann category, stable and unstable splittings.Other talks treated multi- disciplinary subjects related to quantum field theory, differential geometry, homo- topical dynamics, tilings, and various aspects of group theory. In addition, an advanced course on Classifying Spaces and Cohomology of Groups was organized by the CRM in the days preceding the conference. Lecture notes from this course will be published by Birkhauser Verlag as the first volume of a newly created CRM Advanced Course series.

The papers in this collection, all fully refereed, originalpapers, reflect many aspects of recent significant advancesin homotopy theory and group cohomology.From the Contents: A. Adem: On the geometry and cohomologyof finite simple groups.- D.J. Benson: Resolutions andPoincar duality for finite groups.- C. Broto and S. Zarati:On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C.Ravenel: Morava K-theories of classifying spaces andgeneralized characters for finite groups.- K. Ishiguro:Classifying spaces of compact simple lie groups and p-tori.-A.T. Lundell: Concise tables of James numbers and somehomotopyof classical Lie groups and associated homogeneousspaces.- J.R. Martino: Anexample of a stable splitting: theclassifying space of the 4-dim unipotent group.- J.E.McClure, L. Smith: On the homotopy uniqueness of BU(2) atthe prime 2.- G. Mislin: Cohomologically central elementsand fusion in groups.

The papers in this collection, all fully refereed, originalpapers, reflect many aspects of recent significant advancesin homotopy theory and group cohomology.From the Contents: A. Adem: On the geometry and cohomologyof finite simple groups.- D.J. Benson: Resolutions andPoincar duality for finite groups.- C. Broto and S. Zarati:On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C.Ravenel: Morava K-theories of classifying spaces andgeneralized characters for finite groups.- K. Ishiguro:Classifying spaces of compact simple lie groups and p-tori.-A.T. Lundell: Concise tables of James numbers and somehomotopyof classical Lie groups and associated homogeneousspaces.- J.R. Martino: Anexample of a stable splitting: theclassifying space of the 4-dim unipotent group.- J.E.McClure, L. Smith: On the homotopy uniqueness of BU(2) atthe prime 2.- G. Mislin: Cohomologically central elementsand fusion in groups.