Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

Students pursue problems they’re curious about, not problems they’re told to solve. Creating a math classroom filled with confident problem solvers starts with challenges discovered in the real world, not a sequence of prescribed problems. In this groundbreaking book, Gerald Aungst offers five powerful principles for instilling a culture of learning in your classroom: Conjecture, Collaboration, Communication, Chaos, and Celebration. Aungst shows how to: Embrace collaboration and purposeful chaos to engage students in productive struggle Put each chapter’s principles into practice using a variety of strategies, activities, and technology tools Introduce lasting changes in your classroom through a gradual shift in processes and behaviors

Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of Étienne Bézout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them. The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in 2008. This book is the official record of the conference and includes supplements of collated texts of Seki's original writings with notes in English on these texts. Hikosaburo Komatsu (Professor emeritus, The University of Tokyo), one of the editors, is known for partial differential equations and hyperfunction theory, and for his study on the history of Japanese mathematics. He served as the President of the International Congress of Mathematicians Kyoto 1990.

“Of high merit”—Scientific American This stimulating approach to several branches of modern mathematics is geared to those with no background beyond elementary algebra and geometry. Its nine essays by leading mathematicians—including Oswald Veblen, Gilbert Ames Bliss, L. E. Dickson, and David Eugene Smith—cover the foundations of geometry, modern pure geometry and non-Euclidean geometry, fundamental propositions of algebra, algebraic equations, functions, fundamentals of calculus, and number theory. Each essay provides wide coverage, with proofs of important results and descriptions of leading methods. 1911 ed.

Ulam, famous for his solution to the difficulties of initiating fusion in the hydrogen bomb, devised the well-known Monte-Carlo method. Here he presents challenges in the areas of set theory, algebra, metric and topological spaces, and topological groups. Issues in analysis, physical systems, and the use of computers as a heuristic aid are also addressed.

Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed. Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional statements; and biconditional sentences. Subsequent chapters focus on switching circuits; multibase arithmetic; finite systems; relations, vectors, and matrices; tessellations; and linear programming. The book concludes with an analysis of motion geometry and rubber sheet geometry, paying particular attention to radial enlargement and composite reflections as well as topological equivalence, networks for maps, and incidence matrices. This monograph is intended for students, parents, and teachers who are interested in modern mathematics.

The field of education is in constant flux as new theories and practices emerge to engage students and improve the learning experience. Globalization has created new challenges for mathematics educators as they are compelled to respond to the shifting patterns and practices of everyday life and stay abreast of the latest research in education, curriculum, development, and technologies. Globalized Curriculum Methods for Modern Mathematics Education is a comprehensive and timely publication that contains the latest research in mathematics education and modern globalized curriculum development and technologies. The book examines subjects such as teaching competencies, digital games for teaching and learning mathematics, and the challenges and prospects of globalized science curriculum. This is an ideal resource for educators, academicians, teachers, policy makers, researchers, and graduate-level students seeking to further their research in mathematics education.

In-depth overview, geared toward undergraduates of all backgrounds, covers natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.

Discover modern solutions to ancient mathematical problems with this engaging guide, written by a mathematics enthusiast originally from South Vietnam. Author Dat Phung To provides a theory that defines the partial permutations as the compositions of the permutations nPn=n!. To help you apply it, he looks back at the ancient mathematicians who solved challenging problems. Unlike people today, the scholars who lived in the ancient world didnt have calculators and computers to help answer complicated questions. Even so, they still achieved great works, and their methods continue to hold relevance. In this textbook, youll find fourteen ancient problems along with their solutions. The problems are arranged from easiest to toughest, so you can focus on building your knowledge as you progress through the text. Fourteen Ancient Problems also explores partial permutations theory, a mathematical discovery that has many applications. It provides a specific and unique method to write down the whole expansion of nPn = n! into single permutations with n being a finite number. Take a thrilling journey throughout the ancient world, discover an important theory, and build upon your knowledge of mathematics with Fourteen Ancient Problems.

All materials that would be covered in this book were the collection of in-depth mathematical research. Hopefully, the inclusion of such new findings could help to uproot all unnecessary errors, mistakes of the past mathematical literatures and philosophy. Last but not least, hopefully reading through this book would be a rewarding experience.