This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides …
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinit…
Provability, Computability and Reflection.
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Proceedings of the 13th Asian Logic Conference
by Yu, Liang, Feng, Qi, Kim, Byunghan, Zhao, Xishun
Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to an…
"Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and Linear Algebra. It prepares students for the proofs they will need to analyse and write, the ax…
This is an introduction to proofs book for the course offering a transition to more advanced mathematics. It contains logic, sets, functions, relations, the construction of rational, real and complex numbers and their properties. It also has a chapter on cardinality and a chapte…
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions,…
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions,…
"Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathema…
Annotation
The authors have written an introduction to logic taking Godel's incompleteness theorem as a starting point. The book should interest everyone from mathematicians to philosophers and readers who wish to understand the foundations and limitations of rational thinking. It is used …
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.
