The Essence Of Mathematics Through Elementary Problems

"It is increasingly clear that the shapes of reality - whether of the natural world, or of the built environment - are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself 'tick', and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems - with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works."--Publisher's website.

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.

A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

Between 1918 and 1921 an estimated 100,000 Jewish people were killed, maimed or tortured in pogroms in Ukraine. Hundreds of Jewish communities were burned to the ground and hundreds of thousands of people were left homeless and destitute, including orphaned children. A number of groups were responsible for these brutal attacks, including the Volunteer Army, a faction of the Russian White Army. The Pogroms in Ukraine, 1918-19: Prelude to the Holocaust is a vivid and horrifying account of the atrocities committed by the Volunteer Army, written by Nokhem Shtif, an eminent Yiddish linguist and social activist who joined the relief efforts on behalf of the pogrom survivors in Kiev. Shtif’s testimony, published in 1923, was born from his encounters there and from the weighty archive of documentation amassed by the relief workers. This was one of the earliest efforts to systematically record human rights atrocities on a mass scale. Originally written in Yiddish and here skillfully translated and introduced by Maurice Wolfthal, The Pogroms in Ukraine, 1918-19 brings to light a terrible and historically neglected series of persecutions that foreshadowed the Holocaust by twenty years. It is essential reading for academics and students in the fields of human rights, Jewish studies, Russian and Soviet studies, and Ukraine studies. Maurice Wolfthal has also written the award-winning translation of Bernard Weinstein’s The Jewish Unions in America, also published by Open Book Publishers.