Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

This third edition of a popular, well-received text offers undergraduates an opportunity to obtain an overview of the historical roots and the evolution of several areas of mathematics. The selection of topics conveys not only their role in this historical development of mathematics but also their value as bases for understanding the changing nature of mathematics. Among the topics covered in this wide-ranging text are: mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, the real numbers system, sets, logic and philosophy and more. The emphasis on axiomatic procedures provides important background for studying and applying more advanced topics, while the inclusion of the historical roots of both algebra and geometry provides essential information for prospective teachers of school mathematics. The readable style and sets of challenging exercises from the popular earlier editions have been continued and extended in the present edition, making this a very welcome and useful version of a classic treatment of the foundations of mathematics. "A truly satisfying book." — Dr. Bruce E. Meserve, Professor Emeritus, University of Vermont.

Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people who want to gain a thorough understanding of the fundamental concepts of mathematics will find this book a good reference.

In this brief treatise, Carus traces the roots of his belief in the philosophical basis for mathematics and analyzes that basis after a historical overview of Euclid and his successors. He then examines his base argument and proceeds to a study of different geometrical systems, all pulled together in his epilogue, which examines matter, mathematics, and, ultimately, the nature of God.

This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

This book was written in an attempt to make available an introductory treatment of the foundations of mathematics and of concepts that are basic to mathematical knowledge.

This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

We are pleased to present the revised edition of the series Foundation Mathematics for Primary Classes (Books 1-5}. This series is based on the latest curriculum prepared and recommended by the Council for the Indian School Certificate Examinations, New Delhi. The new curriculum for Classes 1 to 5 is designed to ensure that children build a solid foundation in mathematics by connecting and applying mathematical concepts in a variety of ways. This curriculum aims to develop a number of mathematical skills and processes among children. Main objectives of teaching and learning mathematics at primary level are to : • Develop the mathematical thinking and problem solving skills and apply these to formulate and solve problems. • Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines. • Develop the necessary process skills for the acquisition and application of mathematical concepts. • Create love and interest towards mathematics. • Make effective use of a variety of mathematical tools in the learning and application of mathematics. • Reason logically, communicate mathematically, and learn cooperatively and independently. The present series has been developed and designed keeping the above objectives in mind. This child-friendly series teaches Mathematics in such an interesting and comprehensive manner that even an average child has no difficulty in grasping the fundamental concepts of Mathematics. The Salient Features of this Series are : • A graded and spiralling approach, keeping in mind the age and level of understanding of the student. • Eye-catching illustrations and child-friendly layout to kindle the imagination of the child and create an interest in the subject. • Each chapter begins with the heading Let Us Recall, which refreshes the concepts learnt in the previous class. • The fact box Remember highlights the important points. • Concept detailing helps in conceptual understanding that refers to grasp of ideas. • Interactive exercises help in kids participation. This level of engagement makes it easier for kids to retain information. • Value Based Questions are meant to inculcate moral values in the children. • Review Exercise at the end of each chapter checks the retention capacity and the level of understanding of the students. • Assignments under the heading Mental Matbs not only enhance the mathematical and calculation skills of the students but also fortify the concepts already learned. • Let's Play introduces games that improves critical thinking, problem solving, interaction and collaboration with peers. • Maths Lab Activities are meant to learn mathematical concepts through various activities. • Two Model Test Papers, one for Half Yearly Examination and other for Annual Examination have also been added in each book. It is hoped that the series will meet the requirements of the students, teachers and parents alike. Suggestions and constructive criticism for the improvement of the books would be highly appreciated. -The Publishers