Many things in mathematics are groups. This is mostly because groups help to benefit from a brilliant idea of ‘a change that keeps interesting feature unchanged’. For example, equations. The ways of solving equations can be a group. Physical things can be studied as groups. There are important symmetries about physical things which are groups (this can be place, turn, time, energy, electric charge).
Sometimes, part of the group is also a group. In that case, the part is called a "subgroup". For example, there is this subgroup of the group of isometries of a square: only the turns of the square and the identity (not the reflections in a mirror). Many useful things can be proved about groups and their subgroups.
Chelsea Clinton
Chelsea Victoria Clinton (born February 27, 1980) is the only child of Bill Clinton, former President of the United States, and his wife, former Secretary of State, Hillary Clinton.
Clinton was born at Baptist Health Medical Center in Little Rock, Arkansas. She moved in to The White House when she was twelve years old when her father, Bill Clinton, became president. She has helped her mother, Hillary Clinton, many times by campaigning for people to elect her mother as the first woman President of the United States.
Clinton has a Bachelor of Arts in History. She also has a Master of Philosophy qualification. She went to university at Oxford University and Stanford University.
Clinton is vegetarian.
On November 30, 2009, it was announced that Clinton was engaged to Marc Mezvinsky, an investment banker. They married on July 31, 2010. On November 14, 2011, Clinton announced joining as a "special correspondent" for NBC News. She will continue as a PhD student.
On September 2014, Clinton gave birth to a daughter Charlotte. She was gave birth to a eldest son Aiden on June 2016.
Her youngest son, Jasper, was born in New York on July 2019.
Crich
Crich ( "kryech") is a village in the English county of Derbyshire. It is the home of the National Tramway Museum in the Crich Tramway Village.
At the top of Crich Hill is a tower. The tower was built to remember members of the regiment who died in battle, particularly in World War I.
The tower was built in 1923 on the site of an older tower called Crich Stand. The Memorial Tower is the end of an annual pilgrimage on the first Sunday in July. It is above sea level. The tower has 52 steps to the top. From the top of the tower, eight counties and landmarks such as the Humber Bridge and Lincoln Cathedral can be seen.
Crich is mentioned in 1009 by Ethelred the Unready when he gives away Weston-on-Trent to his minister.
A workhouse opened in 1734 and had 40 people. The workhouse accepted poor people from places, including Melbourne, Pentrich, Willington, Mercaston and Denby.
The television series "Peak Practice" and the 2007 movie ""And When Did You Last See Your Father"" were filmed in Crich.
Edwardian period
The Edwardian era in the United Kingdom is the period which included the reign of King Edward VII (1901–1910). The "Edwardian era" usually includes some years before and after his reign, up to the First World War.
King Edward VII was very different from Queen Victoria. Victoria had become almost a recluse after her husband died. On the other hand, Edward was an important leader. Edward and his fashionable friends followed the art and fashions of other European countries. Edward enjoyed travelling, and his visits to Paris improved relations between the two countries.
The United Kingdom was a powerful nation in the nineteenth century. There was progress in British science and industry at this time. The British Empire was large. The Royal Navy was the most powerful navy in the world at that time.
The prosperity of the Edwardian era was built on trade and manufacturing. These were the main industries at the time:
The extent of this trade was big. Railways all over the world were built by the British. They were equipped with machinery made in Britain. Germany also became a powerful nation, and the United States was already becoming an industrial giant. By Edward VII's time. Both of these countries were as industrially advanced.
Most British people in the "Edwardian era" were sure that British progress would continue. They were certain that the United Kingdom would continue to be very powerful. The era came to an unexpected end with the First World War. Economically and in human terms, this was a disaster for most of the European nations.
There was a lot of inequality in society in the United Kingdom in the Edwardian era, as there always had been. Rich people and poor people had very different living standards at this time.
Most adult men could vote, but women could not. Suffragettes were fighting for the right to vote.
Objectivity (philosophy)
Objectivity is a philosophical opinion or method that believes that reality exists outside of the human mind. People can separate their own ideas and opinions from the observations they make. Objective observations are true no matter who makes the observation. Being objective helps people focus on things that everyone can agree on.
The Scientific method claims objectivity but see epistemology, the philosophy of science and the work of Karl Popper. The opposite of objectivity is subjectivity.
Rod Paige
Roderick Raynor "Rod" Paige (born June 17, 1933), served as the 7th United States Secretary of Education from 2001 to 2005. He was the first African American to serve as the nation's education chief. He earned a bachelor's degree from Jackson State University in Mississippi and a Master's degree and an Ed.D from Indiana University Bloomington. He also holds an honorary doctoral degree from the University of Houston presented to him in 2000.
Paige was sitting with George W. Bush at the Emma E. Booker Elementary School in Sarasota, Florida, when Bush received the news that a second plane had hit the World Trade Center in the September 11, 2001 attacks.
On November 15, 2004, Paige announced his resignation after overseeing the President's education agenda for four years. White House domestic policy adviser Margaret Spellings was nominated as his successor. The U.S. Senate confirmed her on January 20, 2005 after Bush's inauguration for a second term.
Joshua Bolten
Joshua Brewster Bolten (born August 16, 1954) was the White House Chief of Staff serving U.S. President George W. Bush. Bolten replaced Andrew Card on April 14, 2006.
Alan Stephenson Boyd
Alan Stephenson Boyd (July 20, 1922 – October 18, 2020) was an American politician and lawyer. He was the first United States Secretary of Transportation, appointed by Lyndon Johnson in November 1966.
He was appointed to the Civil Aeronautics Board in 1959 by Dwight Eisenhower and promoted to chairman by John F. Kennedy.
When the Richard M. Nixon administration took power, Boyd left the government and became the president of the Illinois Central Railroad, a position he held from 1969 to 1972.
Boyd died at a retirement home in Seattle, Washington on October 18, 2020 at the age of 98.
Mary Peters (politician)
Mary E. Peters (born December 4, 1948) was the United States Secretary of Transportation. She is the second woman and first Arizonan to hold the position. Peters joined the Arizona Department of Transportation in 1985, and was appointed by Gov. Jane Dee Hull to serve as its director in 1998. In 2006, President Bush appointed Peters as the Co-Vice Chairwoman of the National Surface Transportation Policy and Revenue Study Commission.
President-elect
A President-elect is a political candidate who has been elected president but who has not yet taken office.
Flag of Australia