The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic.

After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves.

Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

Alberti never mentions Florence in De pictura. This is intentional as the tract not so much ignores as merely suggests previous periods of art, and Alberti’s refusal to specify those interludes, such as Romanesque, Gothic, or medieval, reflects the need for a humanist audience to have all precepts couched in the domain of antiquity. His cryptic indication of sources consequently demands forensic scrutiny of his visual paradigm before Florence. The text itself invites this. In the face of no hard evidence or documentation, Alberti’s claim in De pictura to be an ostensible painter begs the query as to where or with whom he began his study of draftsmanship, either in the studio or in practice. Although he had left Padua for Bologna by 1420, conjecture suggests that while in Padua he may have seen and even studied the art of genius before and contemporary to his age.

This chapter is an introduction to a minimalist approach to German syntax. It starts with very basic concepts (like lexical items, categories, complements, specifiers, modifiers, derivations, and Merge), and goes on to carefully develop accounts of basic structure building (external Merge) and of movement (internal Merge). Furthermore, the concept of Agree is introduced, as are two fundamental principles of derivational syntax: the Strict Cycle Condition and the Cyclic Principle. Various kinds of movement types are analyzed in detail (among them wh-movement, scrambling, pronoun fronting, topicalization, relativization, and extraposition). The notion of successive-cyclic long-distance movement is introduced, and four different morpho-syntactic reflexes of movement are identified for German. Next, the role of edge features and improper movement is clarified. Finally, a concept of cyclic Agree is postulated for Agree relations in German syntax that are not strictly local.

Introduction

There was a time in political science and in political philosophy when emotionality and rationality were regarded as opposites and when the presence of emotions as such (especially of ‘passions’) in politics was seen as inappropriate, if not as outright suspect. Since the nineteenth century, many even liked to think that emotionality in politics was a preserve of unruly mobs and crowds. In democratic theory, politics was predominantly conceived as an arena in which various actors were basically pursuing their interests in a deliberate and rational way. Therefore, rational choice theory and coalition formation theory came to be seen as the best instruments to explain democratic politics according to most political scientists.

Since the ‘affective turn’ started in politics and in political thinking in the 1980s – spearheaded by philosophers such as Martha Nussbaum and Chantal Mouffe – this time is no more: emotions are increasingly appealed upon and taken seriously as objects of analysis (Nussbaum 2013; Mouffe 2005). Since then it is no longer possible in politics to criticize political opponents by simply unmasking that their beliefs and actions are based on emotions – and this obviously also holds for right-wing, exclusionary populism because political feelings are as old as modern politics itself (Frevert et al. 2022). Instead, the task of the critics of populism is to analyse the emotional repertoire used by populists in a comparative-historical perspective and to explain why it is successful in terms of mobilizing electoral support (Tietjen 2022; Demertzis 2019).

In this chapter, I address these issues by asking whether the emotions that populism appeals to form a specific set that distinguishes populism from other ideologies or discourses, especially from ethnic nationalism and nativism. However, in order to answer this first question, I first need to clarify the definitions of populism, ethnic nationalism, and nativism that I adopt. I depart from the well-known definition of populism formulated by Cas Mudde and Cristóbal Kaltwasser and indicate the problems connected with this kind of definition in the light of ethnic nationalism. Then I elucidate the concept of ethnic nationalism and its relationship to populism because at least in Western Europe and in the United States of America (USA) they both appear to be very closely related.

This chapter studies the interlocked biographies of three interwar figures: Charlie Chaplin, Charles Lindbergh, and Mickey Mouse. All three achieved renown as changemakers and the title “greatest of all time” in their various social/cultural arenas. More importantly, for this chapter, all three figures undergo a steep decline, forcing the American public to reconsider the contours of greatness. Chaplin is branded a Communist. Lindbergh a Nazi. Mickey Mouse is eventually seen as too unmasculine to support patriotism during World War II and is therefore swapped by Walt Disney for Donald Duck. The chapter highlights the historical contingencies of greatness.

Services preferential trade agreements (PTAs) have grown rapidly since the turn of the millennium, going from exception to common occurrence. In recent years, they have increasingly linked a number of larger economies. The chapter reviews the main innovations brought by PTAs in the global governance of services trade, and highlights some limits. The contribution of services PTAs is analysed along three key angles, against the background of the multilateral trading system: 1) market access commitments; 2) rulemaking; and 3) architecture and liberalisation modalities. While WTO+ market access commitments have been an important feature of services PTAs early on, progress on rulemaking has been modest. In terms of architecture, services PTAs have produced major advances in relation to liberalisation modalities, with negative-list agreements outnumbering the General Agreement on Trade in Services (GATS)-type positive-list agreements. Recently, agreements between larger economies have been associated with several architectural innovations, moving away from the simple choice between the traditional positive and negative listing models. Overall, this has resulted in the extension of some of the key features of the negative-list approach to new countries and served to further emphasise, sometimes through innovative solutions, the importance of transparency of market access conditions across sectors and modes.

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic.

After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves.

Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

This chapter presents an overview of the book’s theory, empirics, and contributions to the study of Japanese politics. The theory is in two parts. First, I make the case that when politicians run for office in electoral districts divisible into groups of voters, from whom electoral support is discernible and to whom central government resources are deliverable, they can pull those groups into clientelistic exchanges, in which the amount of money groups receive is tied to how they vote. Second, I consider the nuts and bolts of how a politician can go about tying a group’s resource allocation to its electoral support. I elucidate one method that politicians in a dominant party will be able to use. The chapter then presents an overview of the empirical strategy used to test the theory, which uses regression analyses of original data on resource allocations and voting behavior in Japanese municipalities, 1980–2014, buttressed by qualitative evidence. Finally, the chapter presents a summary of the headline findings for scholars of Japanese politics. Ultimately, the book helps to account for why a single party, Japan’s Liberal Democratic Party (LDP), has been able to win almost every election in Japan.