Describe how children can take different paths in development and reach similar destinations; understand the developmental differences between children as a set of strengths and challenges that are highly sensitive to environmental context; explore how events in children’s lives can trigger a cascade of later consequences.

In this chapter, we study vector spaces and their basic properties and structures. We start by stating the definition and discussing examples of vector spaces. Next we introduce the notions of subspaces, linear dependence, bases, coordinates, and dimensionality. And then we consider dual spaces, direct sums, and quotient spaces. Finally, we cover normed vector spaces.

Each process to resolving intrastate conflicts requires different strategies and objectives. Yet, as conflicts continue to increase, researchers have asked if peacekeeping is truly possible. Furthermore, is peace from these approaches stable and durable? The role of third parties in ending intrastate wars or post-conflict instability is central to these processes, where organizations and states play a critical role in ushering in peace during and following civil wars. Over the last three decades a strong trend in third-party attempts to resolve intrastate conflict has emerged. Here, mediation and peacekeeping have played a pivotal role in addressing crises within various countries since the end of the Cold War. From mediation to peacekeeping, this chapter expands upon the different forms and interventions that prevent and resolve conflict, all of which incorporate various sociopolitical and international legal principles in the process. It highlights the benefits and consequences of each intervention, what institutions utilize these principles, and how international humanitarian law has changed since World War II.

In this chapter, we consider linear mappings over vector spaces. We begin by stating the definition and discussing the structural properties of linear mappings. Then we introduce the notion of adjoint mappings and illustrate some of their applications. Next we focus on linear mappings from a vector space into itself and study a series of important concepts such as invariance and reducibility, eigenvalues and eigenvectors, projections, nilpotent mappings, and polynomials of linear mappings. Finally, we discuss the use of norms of linear mappings and present a few analytic applications.

Readers will understand what is meant by inviscid flow, and why it is useful in aerodynamics, including how to use Bernoulli’s equation and how static and dynamic pressure relate to each other for incompressible flow. Concepts are presented to describe the basic process in measuring (and correcting) air speed in an airplane. A physical understanding of circulation is presented and how it relates to predicting lift and drag. Readers will be presented with potential flow concepts and be able to use potential flow functions to analyze the velocities and pressures for various flow fields, including how potential flow theory can be applied to an airplane.

Across Australia and beyond, early childhood education (ECE) services play a significant role in the everyday lives of infants, toddlers and their families. For some decades, the enrolment of infants and toddlers has increased to the extent that, in today’s Australian society, around 40% of birth to 24-month-olds and nearly 60% of two-year-olds spend at least part of their week in an early childhood service. More still balance ECE service attendance with informal care arrangements with family members and friends. With these figures echoed across many countries worldwide, the widespread uptake of infant and toddler early childhood programs has meant that this generation of infants and toddlers and their families are experiencing a markedly different start to life than previous generations. It is now the norm for infant–toddler care to be spread across multiple contexts both within and outside of the walls of the family home, and for the responsibility for early learning to be shared between family and non-familial adults.

Describe how children think and behave differently in groups; explain the roles of collaboration, self-identity, and categorisation in creating and sustaining groups; understand how group differences can be reduced via intergroup contact, cooperation, and empathy.

Civil wars are complex events that alter the group trajectories and lives of everyone directly and indirectly involved. Studying these devastating crises effectively requires understanding and using multiple approaches. This book explores various theoretical explanations for the onset of civil wars, highlighting patterns in conflict dynamics over time and in different regions. For instance, the “greed” perspective suggests that rebels are driven by profit, treating rebellion as an economic opportunity. Another perspective centers on grievances, where rebel leaders mobilize due to collective political, economic, social, cultural, or identity-related grievances. Often these grievances stem from the government exclusion of minorities, unequal opportunities, and restrictions on collective group rights, particularly in states with weak institutions. A further perspective, the capacity-and-opportunity model, focuses on how material resources play a vital role in financing violence through a materialistic lens. Across all themes, this text serves as a means for providing a comprehensive analysis of civil wars, covering their onset, duration, destructiveness, outcome, and recurrence.

In this chapter, we present a few selected subjects that are important in applications as well but are not usually included in a standard linear algebra course. These subjects may serve as supplemental or extracurricular materials. The first subject is the Schur decomposition theorem, the second is about the classification of skew-symmetric bilinear forms, the third is the Perron–Frobenius theorem for positive matrices, and the fourth concerns the Markov or stochastic matrices.

The loss of human life and physical injuries through violence are an inherent consequence of armed conflict, including civil wars. Deliberate atrocities – such as war crimes, crimes against humanity, genocide, politicide and “ethnic cleansing” – have been a conspicuous feature of many wars. Civil wars – whether correctly or incorrectly from an empirical perspective – have often been regarded as particularly vicious, transgressing all norms of decency in the frequency and type of atrocities. This chapter explores several key questions that have arisen in the conflict analysis field in relation to atrocities in civil war – and war generally. Are atrocities specifically associated with certain “types” of civil war, such as separatist, ideological, intercommunal, or resource conflict? Are there patterns in terms of which types of actors – state or non-state rebel groups – are more likely to perpetrate atrocities? What motivates individuals and groups to perpetrate atrocities, and what “role,” if any, do such atrocities play in armed conflict? Do atrocities play a strategic role, or are they better understood as a manifestation of individual and group sadism, revenge, and hate or fear, spread in the contemporary era by social media? Are all combatants capable of perpetuating atrocities in the “right” circumstances? The chapter concludes with a discussion of the international norms that have emerged over the last century – which prohibit war crimes, crimes against humanity, and genocide – and the calls for accountability and justice after mass atrocities that have arguably made a significant although limited impact on conduct in war. As a part of this, “transitional justice” has emerged as an important topic, designed to address the societal impact and legacy of atrocities.