The Foundations of Mathematics
This book is study of philosophy and concepts of mathematics. It emphasis on logics proofs and development of general concepts based on set theory
It has been framed with the many years of experience of solving potential difficulties, teaching and research. Author has put his knowledge of teaching first year under graduate students and studies about the perception of students for mathematics. This book explains about inspiration behind the foundational material of students, experiences of school mathematics and suggests some ways to students to make sense of formal ideas
It is the revised edition in which author has put forward step not only by making transition from fundamental to formal methods but also by reversing the process using structure theorems to proof the significance of formal systems that have visual and symbolic interpretation for enhancing mathematical thinking.
In this second edition new chapter has been added under the title theory of groups
In the earlier edition, there was extending counting to infinite cardinal numbers so the successive edition extents the real numbers to large ordered field. It connects intuitive ideas of calculus to the formal epsilon-delta methods of analysis.
This book has been written with simple and graphically based approach not the conventional one; it makes the notion of straightforward and infinitesimal natural. This book illuminates the wider world of mathematical thinking which consist formal definition and new ways of defining, proofing, symbolising and visualizing and mathematics above the past expectations