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Basic Mathematics by Serge Lang - Physics Forums Basic Mathematics by Serge Lang - Physics Forums
The author has an impressive knack for presenting the important and interesting ideas of algebra in just the ‘right’ way, and he never gets bogged down in the dry formalism which pervades some parts of algebra.Note: Subsection pages for each chapter have not been added yet, but should be considered when the pages grow. The basic topics covered doesn't necessarily mean that the book will be easy; this was my first introduction to proofs, and to trying to create my own (which I often failed at doing).
Basic Mathematics by Serge Lang | Goodreads
This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. Lang's Algebra, a graduate-level introduction to abstract algebra, was a highly influential text that ran through numerous updated editions. It covers topics such as real numbers, solving equations, logic, geometry, trigonometry, functions, complex numbers, induction, and determinants.Later he moved into diophantine approximation and transcendental number theory, proving the Schneider–Lang theorem.
Serge Lang | Open Library Serge Lang | Open Library
Despite support for Huntington from the Academy's social and behavioral scientists, Lang's challenge was successful, and Huntington was twice rejected for Academy membership. Even then, one might say that full rigor hasn't been achieved until one has presented a way to formalize the concept of proof to such an extent that the correctness of any given proof can be verified by an algorithm. His extensive file criticizing Nobel laureate David Baltimore was published in the journal Ethics and Behaviour in January 1993 [12] and in his book Challenges. Se você é alguém que busca aprender matemática com este livro, leia somente as explicações e busque exercícios em outros lugares. These points are almost always ones where he reasonably feels full rigor isn't desirable considering his readership.
These points are almost always ones where he reasonably feels full rigor isn't desirable, in view of his readership. If you're exceptionally concerned about rigor, you can get the full story on the set-theoretical foundations of mathematics from a book like Introduction to Set Theory, by Jech and Hrbacek. The single most important aspect of this (after typical courses in high school algebra) is skill with inequalities, and that's why one of the books I recommended was An Introduction to Inequalities by Beckenbach and Bellman. I went through most of this book due to MicroMass's recommendation a little while ago, and really enjoyed my first introduction to real mathematics, and not the garbage I was/am being taught in middle/high school. Judged purely on geometric content, I don't have any reason to think Hobson would be less good than Durell.