Basic Elements of Real Analysis


Book Description

From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.




Exploring General Equilibrium


Book Description

An incisive, unconventional assessment of general equilibrium theory; with a previously unpublished paper. Fischer Black is known for his brilliance as well as his sometimes controversial opinions. Highly respected for his scholarly writings in finance, he now moves into different territory with this incisive, unconventional assessment of general equilibrium theory and what that theory reveals about business cycles, growth, and labor economics. The general equilibrium approach, Black asserts, can be used to explain most of the economy's behavior. It can explain business cycles and growth without using sticky prices, irrationality, economies of scale, or imperfect competition. It can explain the volatility of consumption, output, sales, investment, and inventories with axiomatic utility and constant-returns-to-scale production. It can explain temporary layoffs, job changes with and without intervening unemployment, and the behavior of vacancies. It can explain lower wages in part-time jobs, wages that increase rapidly with time on the job, and the forces that cause migration from poor to rich countries. Although the general equilibrium approach can't be tested in conventional ways, it can be used to generate examples that explain stylized facts—generalized observations from the real world—that have preoccupied macroeconomists for the last decade. Black contrasts his interpretation of these facts with conventional interpretations. Finally, he reviews a substantial body of literature on these topics.




A First Course in Real Analysis


Book Description

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.




Guidelines on the Management of Latent Tuberculosis Infection


Book Description

BACKGROUND: Latent tuberculosis infection (LTBI), defined as a state of persistent immune response to prior-acquired Mycobacterium tuberculosis antigens without evidence of clinically manifested active TB, affects about one-third of the world's population. Approximately 10% of people with LTBI will develop active TB disease in their lifetime, with the majority developing it within the first five years after initial infection. Currently available treatments have an efficacy ranging from 60% to 90%. Systematic testing and treatment of LTBI in at-risk populations is a critical component of WHO's eight-point framework adapted from the End TB Strategy to target pre-elimination and, ultimately, elimination in low incidence countries. OVERVIEW: Recognizing the importance of expanding the response to LTBI, in 2014 WHO developed Guidelines on the Management of Latent Tuberculosis Infection. The guidelines are primarily targeted at high-income or upper middle-income countries with an estimated TB incidence rate of less than 100 per 100 000 population, because they are most likely to benefit from it due to their current TB epidemiology and resource availability. The overall objective of the guidelines is to provide public health approach guidance on evidence-based practices for testing, treating and managing LTBI in individuals with the highest risk of progression to active disease. Specific objectives include identifying and prioritizing at-risk population groups for targeted intervention of LTBI testing and treatment, including defining an algorithm, and recommending specific treatment options. The guidelines are expected to provide the basis and rationale for the development of national guidelines for LTBI management based on available resources, epidemiology of TB including intensity of transmission, the health-care delivery system of the country, and other national and local determinants.







History of Madison County, Indiana, from 1820 to 1874


Book Description

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.




Index of Research Results


Book Description