Modern Real Analysis, Second Edition

Mathematics

Mathematics Education in a Context of Inequity, Poverty and Language Diversity: Giving Direction and Advancing the Field by Mamokgethi Phakeng
Mathematical Aspects of Multi–Porosity Continua ByBrian Straughan
Modern Real Analysis, Second Edition By William P. Ziemer
Jean-Marie De Koninck, Armel Mercier, “1001 Problems in Classical Number Theory”
A History of Mathematics

Mathematics Education in a Context of Inequity, Poverty and Language Diversity: Giving Direction and Advancing the Field by Mamokgethi Phakeng

English | 16 July 2016 | ISBN: 3319388231 | 180 Pages | EPUB (True) | 1.88 MB

This volume is dedicated to the career of Jill Adler and the role she has played in growing mathematics education research in South Africa, Africa and beyond. Her work epitomises what is referred to as the ‘engaged scholar’: i.e. doing rigorous and theoretically rich research at the cutting edge of international work in the field which at the same time contributes to critical areas of local and regional need in education. Jill is one of the world’s leading experts in mathematics education research and her exemplary career is a continuous source of inspiration for generations of researchers and students. The chapters in this volume are authored by Jill’s former PhD students, a few select colleagues from different parts of the world that she collaborated with as well as leading scholars who she worked with in PME, ICMI and in her many international assignments. In essence, this volume celebrates Jill’s contribution not only to mathematics education but also to our contributions as her friends and colleagues. Topics covered include language and mathematics, teacher education, and the dilemma of an activist researcher engaging in issues that matter hugely to the participants in the research, students and teachers in post-apartheid schooling, whilst also setting up the separation that is needed for good research

Mathematical Aspects of Multi–Porosity Continua ByBrian Straughan

English | PDF | 2017 | 214 Pages | ISBN : 3319701711 | 2.96 MB

This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.
Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion.
This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.

Modern Real Analysis, Second Edition By William P. Ziemer

English | PDF,EPUB | 2017 | 389 Pages | ISBN : 3319646281 | 13.21 MB

This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations.
This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.

Jean-Marie De Koninck, Armel Mercier, “1001 Problems in Classical Number Theory”

2007 | ISBN-10: 0821842242 | 336 pages | PDF | 9 MB

In the spirit of The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice or an experienced mathematician, anyone fascinated by numbers will find a great variety of problems–some simple, others more complex–that will provide them with a wonderful mathematical experience.

A History of Mathematics

English | 2 Jun. 2005 | ISBN: 0198529376 | 296 Pages | PDF | 4 MB

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians.