The Foundations of Mathematics
With the shifting of school mathematics to the university mathematics problems of the students have risen as they face difficulties in mathematics due to untouched experience with proofs, logics, abstract development of general concepts, set theory due to algorithmic and informal attitude for mathematics at school.
Many years of experience of author through teaching first year undergraduates and researches for finding the ways in which the students and mathematicians think and perceive the mathematical problems, have added advantages for the readers in this book.
the second edition of the book is the one forward step than its previous edition by not only making the intuitive and formal approach of mathematical methods but also by reversing the process of using structure theorems to prove the formal methods. These included formal systems have visual and symbolic interpretations that can enhance the mathematical perception.
In this new edition new chapter has been added on the basis of theory of groups. It also extends the real numbers rigorously to large ordered fields. This book highlights the foundations of math in which formal definitions and proof lead to amazing ways of defining, explaining, visualizing and symbolizing math beyond the earlier expectations.