Management
Management (or managing) is the administration of an organization, whether it is a business, a not-for-profit organization, or government body. Management includes the activities of setting the strategy of an organization and coordinating the efforts of its employees (or of volunteers) to accomplish its objectives through the application of available resources, such as financial, natural, technological, and human resources. The term "management" may also refer to those people who manage an organization.
Public
In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of such groupings. This is a different concept to the sociological concept of the Öffentlichkeit or public sphere. The concept of a public has also been defined in political science, psychology, marketing, and advertising. In public relations and communication science, it is one of the more ambiguous concepts in the field. Although it has definitions in the theory of the field that have been formulated from the early 20th century onwards, it has suffered in more recent years from being blurred, as a result of conflation of the idea of a public with the notions of audience, market segment, community, constituency, and stakeholder.
Public Administration
Public Administration is the implementation of government policy and also an academic discipline that studies this implementation and prepares civil servants for working in the public service. As a "field of inquiry with a diverse scope" whose fundamental goal is to "advance management and policies so that government can function". Some of the various definitions which have been offered for the term are: "the management of public programs"; the "translation of politics into the reality that citizens see every day"; and "the study of government decision making, the analysis of the policies themselves, the various inputs that have produced them, and the inputs necessary to produce alternative policies."
Management
Management of many is the same as management of few. It is a matter of organization.
Sun Tzu (c. 6th century BC) The Art of War
Public Administration
Public administration is that part of the science of administration which has to do with government, and thus concerns itself primarily with the executive branch, where the work of government is done, though there are obviously administrative problems also in connection with the legislative and the judicial branches. Public administration is thus a division of political science, and one of the social sciences.
Luther H. Gulick, "Science, values and public administration." Papers on the Science of Administration (1937). p. 189.
Public Administration
Decision theory can be pursued not only for the purposes of building foundations for political economy, or of understanding and explaining phenomena that are in themselves intrinsically interesting, but also for the purpose of offering direct advice to business and governmental decision makers. For reasons not clear to me, this territory was very sparsely settled prior to World War II. Such inhabitants as it had were mainly industrial engineers, students of public administration, and specialists in business functions, none of whom especially identified themselves with the economic sciences...
Herbert A. Simon, "Rational decision making in business organizations." Nobel Prize lecture 1978, published in: The American economic review 69(4) (1979): 493-513;