• is the study of,,,,,. Mathematics is used throughout the world as an essential tool in many fields, including,,, and the., the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as. Mathematicians also engage in, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. Leonhard Euler Image credit: Leonhard Euler (pronounced oiler; /ˈɔɪlər/) (April 15, 1707, - September 18, 1783, ) was a. He is considered to be the dominant mathematician of the and one of the greatest mathematicians of all time; he is certainly among the most prolific, with collected works filling over 70 volumes.

Discrete mathematics is the study of mathematical structures that are fundamentally discrete. In mathematics, they are useful in geometry and certain parts of topology, e.g. Biggs (2002-12-19).

Euler developed many important concepts and numerous lasting in diverse areas of, from to to. In the course of this work, he introduced many of modern mathematical terminologies, defining the concept of a, and its notation, such as sin, cos, and tan for the. Credit: A shows the distribution of in a population by plotting the percentage y of total income that is earned by the bottom x percent of households (or individuals).

Developed by economist in 1905 to describe, the curve is typically plotted with a diagonal line (reflecting a hypothetical 'equal' distribution of incomes) for comparison. This leads naturally to a derived quantity called the, first published in 1912 by, which is the ratio of the area between the diagonal line and the curve (area A in this graph) to the area under the diagonal line (the sum of A and B); higher Gini coefficients reflect more income inequality. Lorenz's curve is a special kind of used to characterize quantities that follow a, a type of.

More specifically, it can be used to illustrate the, a stating that roughly 80% of the identified 'effects' in a given phenomenon under study will come from 20% of the 'causes' (in the first decade of the 20th century showed that 80% of the land in Italy was owned by 20% of the population). As this so-called '80–20 rule' implies a specific level of inequality (i.e., a specific power law), more or less extreme cases are possible. For example, in the first half of the 2010s, 95% of the financial was held by the top 20% of wealthiest households (in 2010), the top 1% of individuals held approximately 40% of the wealth (2012), and the top 1% of earners received approximately 20% of the pre-tax income (2013). Observations such as these have brought income and wealth inequality into and have given rise to various slogans about.

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