The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.

Understanding how to apply maths to economic and business problems is an essential skill for any economics student, but can be daunting. This textbook takes the fear factor out of maths, starting with the basics and building knowledge in small steps, not giant leaps

This publication, written and developed by experienced Caribbean teachers and advisors, has been designed to meet the requirements of maths syllabuses from across the region. It includes worked examples, objectives and explanation boxes, overviews of chapters, real life case studies, assessments and reviews and progessive exercises that support the development of crtical thinking skills and independent learning among Caribbean maths students at the lower secondary level.

Check out the gang at Maths Land High School . You can trust them to give kids of 9-12 years a helping hand with the Maths Basics. Felicity Factor, Anita Addition, Donna Decimal and Max Multiple are just some of the characters on hand to help kids get those top grades. Unlike other maths books, Maths Land High School provides mathematical activities in a fun way, that complies with the National Curriculum. It aims to enable the child to reach level 4 rising to level 5. The presentation of the book with its cartoon drawings make this a fun book that children will want to use. It can be used to reinforce math programmes used in schools or as a homework activity. It is written by a tutor who is well informed on the needs of children reaching the requirements of key stage 2 and 3 and 11+ examinations. The book focuses on basic mathematical skills - adding, take away and divide. It introduces some elementary fractions, percentages, decimals, weights, measurements, shapes and averages. It focuses on the areas that children find most difficult.

Asking key questions about how policies and systems impact on children’s early years and rethinking the ways in which young children’s learning and development becomes integral to policy, this insightful text challenges the common misconception that policy development and pedagogical implementation are separate endeavours. Challenging the Intersection of Policy with Pedagogy explores symbiotic dynamics between policy and practice in the early years to consider the implications of policies relating to documentation, professional well-being, mentoring, the role of the family, language development and diversity. Written to provoke group discussion and extend thinking, opportunities for international comparison, points for reflection and editorial provocations will help students, educators, integrated service providers and policy makers engage critically with a variety of understandings of how policy and practice interact. Considering the role of learning environment, the practitioner, the wider community and policy, chapters are divided into four key sections which reflect major influences on practice and pedagogy: Being alongside children Those who educate Embedding families and communities Working with systems Considering diverse settings and contexts, perspectives, policies and systems, this text will enhance understanding, support self-directed learning and provoke and transform thinking at both graduate and postgraduate levels, particularly in the field of early childhood education and care.

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Godel stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Godel's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Godel's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Godel's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators."