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36807 results in Cambridge Textbooks

Page 621 of 1841

  • 22 - International Organisations

  • Malcolm N. Shaw
  • Book:
    International Law
    Published online:
    01 July 2021
    Print publication:
    22 July 2021, pp 1133-1176

  • Summary

    The evolution of the modern nation-state and the consequent development of an international order founded upon a growing number of independent and sovereign territorial units inevitably gave rise to questions of international cooperation. The first major instance of organised international cooperation occurred with the Peace of Westphalia in 1648, which ended the thirty-year religious conflict of Central Europe and formally established the modern secular nation-state arrangement of European politics. Over a century later, the Napoleonic wars terminated with the Congress of Vienna in 1815, marking the first systematic attempt to regulate international affairs by means of regular international conferences. The Congress system lasted, in various guises, for practically a century and institutionalised not only the balance of power approach to politics, but also a semi-formal international order.

  • 10 - The Discriminant

  • from Part II - The Theory of Fields and Galois Theory
  • D. J. H. Garling, University of Cambridge
  • Book:
    Galois Theory and Its Algebraic Background
    Published online:
    05 August 2021
    Print publication:
    22 July 2021, pp 122-125

  • Summary

    Suppose that 𝐾 is a field whose characteristic is not 2, that 𝑓 is a normal separable monic polynomial of degree 𝑛 in 𝐾[𝑥] and that 𝐿 : 𝐾 is a splitting field extension for 𝑓. Then the Galois group Γ[𝐿 : 𝐾] acts on the set {α1, …, α𝑛} of roots of 𝑓 in 𝐿, and can therefore be identified with a subgroup of Σ𝑛.

  • 2 - Integral Domains

  • from Part I - The Algebraic Background
  • D. J. H. Garling, University of Cambridge
  • Book:
    Galois Theory and Its Algebraic Background
    Published online:
    05 August 2021
    Print publication:
    22 July 2021, pp 25-53

  • Summary

    The second main topic of Galois theory is the study of polynomials. The collection of all polynomials with integral coefficients forms an integral domain, and integral domains provide an appropriate setting for the study of divisibility and factorization.

Algebra
  • Notes from the Underground
  • Paolo Aluffi
  • Published online:
    19 July 2021
    Print publication:
    03 June 2021
  • From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.

Design Optimization using MATLAB and SOLIDWORKS
  • Krishnan Suresh
  • Published online:
    17 July 2021
    Print publication:
    29 April 2021
  • A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including constrained non-linear, linear-programming, least-squares, multi-objective, and global optimization problems.

The Cambridge Illustrated History of Warfare
  • 2nd edition
  • Edited by Geoffrey Parker
  • Published online:
    15 July 2021
    Print publication:
    15 July 2021
  • The new edition of The Cambridge Illustrated History of Warfare, written and updated by a team of nine distinguished military historians, examines how war was waged by Western powers across a sweeping timeframe, beginning with classical Greece and Rome, moving through the Middle Ages and the early modern period, down to the wars of the twenty-first century in Afghanistan, Iraq, and Syria. The book stresses five essential aspects of the Western way of war: a combination of technology, discipline, and an aggressive military tradition with an extraordinary capacity to respond rapidly to challenges and to use capital rather than manpower to win. Although the focus remains on the West, and on the role of violence in its rise, each chapter also examines the military effectiveness of its adversaries and the regions in which the West's military edge has been - and continues to be - challenged.

  • 4 - The Mechanics of Deeper Learning

  • from Part II - Pluriliteracies: Building a Pedagogical Approach for Deeper Learning
  • Do Coyle, University of Edinburgh, Oliver Meyer, Johannes Gutenberg Universität Mainz, Germany
  • Book:
    Beyond CLIL
    Published online:
    22 June 2021
    Print publication:
    15 July 2021, pp 42-85

  • Summary

    A basic tenet of our pluriliteracies model is that deeper learning is fundamental for an individual’s learning progression and development. This is not new. However, closer investigation reveals the complex and dynamic nature of the processes involved. Whilst a great deal has been written about deeper learning and its importance for engaging learners ‘through discovering and mastering existing knowledge and then creating new knowledge’, (Fullan & Langworthy, 2014, p. 2), there is little to guide in-depth understanding of the nature of those processes – that is, what it means to master existing knowledge and create new knowledge which can then be ‘translated’ into pedagogic practices to support and ‘grow’ classroom learning. In seeking to understand better the nature of deeper learning and its implications for learning and teaching, two strands have emerged: the mechanics or cognitive-linguistic processes through which deeper learning evolves, and the drivers of and for deeper learning. We define drivers as those factors that promote or inhibit the processes or mechanics of deeper learning, such as student and teacher engagement.

Page 621 of 1841