Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Bystander

A bystander is a person who, although present at some event, does not take part in it; an observer or spectator.

In media

In music

Other meanings

See also

Khan Academy

Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.

History

The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.

In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.

Bystander effect

The bystander effect, or bystander apathy, is a social psychological phenomenon that refers to cases in which individuals do not offer any means of help to a victim when other people are present. The probability of help is inversely related to the number of bystanders. In other words, the greater the number of bystanders, the less likely it is that any one of them will help. Several variables help to explain why the bystander effect occurs. These variables include: ambiguity, cohesiveness and diffusion of responsibility.

Social psychology research

The bystander effect was first demonstrated in the laboratory by John Darley and Bibb Latané in 1968 after they became interested in the topic following the murder of Kitty Genovese in 1964. These researchers launched a series of experiments that resulted in one of the strongest and most replicable effects in social psychology. In a typical experiment, the participant is either alone or among a group of other participants or confederates. An emergency situation is staged and researchers measure how long it takes the participants to intervene, if they intervene. These experiments have found that the presence of others inhibits helping, often by a large margin. For example, Bibb Latané and Judith Rodin (1969) staged an experiment around a woman in distress. 70 percent of the people alone called out or went to help the woman after they believed she had fallen and was hurt, but when there were other people in the room only 40 percent offered help.