Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, 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 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.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
A community college is a type of educational institution. The term can have different meanings in different countries: many community colleges have an “open enrollment” for students who have graduated from high school; the term refers to a higher educational institution that provides workforce education and college transfer academic programs. Some institutions maintain athletic dormitories similar to their university counterparts. In Australia, the term "community college" refers to small private businesses running short courses of a self-improvement or hobbyist nature. Equivalent to the American notion of community colleges are Tertiary and Further Education colleges or TAFEs. There are an increasing number of private providers, which are colloquially called "colleges". TAFEs and other providers carry on the tradition of adult education, established in Australia around the mid-19th century, when evening classes were held to help adults enhance their numeracy and literacy skills. Most Australian universities can be traced back to such forerunners, although obtaining a university charter has always changed their nature.
In TAFEs and colleges today, courses are designed for personal development of an individual and/or for employment outcomes. Educational programs cover a variety of topics such as arts, languages and lifestyle, they are scheduled to run two, three or four days of the week, depending on the level of the course undertaken. A Certificate I may only run for 4 hours twice a week for a term of 9 weeks. A full-time Diploma course might have classes 4 days per week for a year; some courses may be offered in the weekends to accommodate people working full-time. Funding for colleges may come from government grants and course fees. Many are not-for-profit organisations; such TAFES are located in metropolitan and rural locations of Australia. Education offered by TAFEs and colleges has changed over the years. By the 1980s many colleges had recognised a community need for computer training. Since thousands of people have increased skills through IT courses; the majority of colleges by the late 20th century had become Registered Training Organisations.
They offer individuals a nurturing, non-traditional education venue to gain skills that better prepare them for the workplace and potential job openings. TAFEs and colleges have not traditionally offered bachelor's degrees, instead providing pathway arrangements with universities to continue towards degrees; the American innovation of the associate degree is being developed at some institutions. Certificate courses I to IV, diplomas and advanced diplomas are offered, the latter deemed equivalent to an undergraduate qualification, albeit in more vocational areas; some TAFE institutes have become higher education providers in their own right and are now starting to offer bachelor's degree programs. In Canada, colleges are adult educational institutions that provide higher education and tertiary education, grant certificates and diplomas; as well, in Ontario, the 24 colleges of applied arts and technology have been mandated to offer their own stand-alone degrees as well as to offer joint degrees with universities through "articulation agreements" that result in students emerging with both a diploma and a degree.
Thus, for example, the University of Guelph "twins" with Humber College and York University does the same with Seneca College. More however, colleges have been offering a variety of their own degrees in business and technical fields; the academic and economic value of the college degree is still being tested in the marketplace. Each province has its own educational system, as prescribed by the Canadian federalism model of governance. In the mid-1960s and early 1970s, most Canadian colleges began to provide practical education and training for the emerging baby boom generation, for immigrants from around the world who were entering Canada in increasing numbers at that time. A formative trend was the merging of the separate vocational training and adult education institutions. Canadian colleges are either publicly funded or private post-secondary institutions. There are 150 institutions that are equivalent to the US community college in certain contexts, they are referred to as "colleges" since in common usage a degree-granting institution is exclusively a university.
In addition to graduate degrees, universities grant Associate's degrees and Bachelor's degrees, but in some regions and/or courses of study and universities collaborate so college students can earn transfer credits toward undergraduate university degrees. University degrees are attained through four years of study; the term associate degree is used in western Canada to refer to a two-year college arts or science degree, similar to how the term is used in the United States. In other parts of Canada the term advanced degree is used to indicate a 3- or 4-year college program. In the province of Quebec, three years is the norm for a university degree because a year of credit is earned in the CEGEP system; when speaking in English, people refer to all colleges as Cégeps, however the term is an acronym more applied to the French-language public system: Collège d'enseignement général et professionnel. The word College can refer to a private High School in Quebec. Canadian community college systemsList of colleges in Canada Colleges and Institutes Can
Canada is a country in the northern part of North America. Its ten provinces and three territories extend from the Atlantic to the Pacific and northward into the Arctic Ocean, covering 9.98 million square kilometres, making it the world's second-largest country by total area. Canada's southern border with the United States is the world's longest bi-national land border, its capital is Ottawa, its three largest metropolitan areas are Toronto and Vancouver. As a whole, Canada is sparsely populated, the majority of its land area being dominated by forest and tundra, its population is urbanized, with over 80 percent of its inhabitants concentrated in large and medium-sized cities, many near the southern border. Canada's climate varies across its vast area, ranging from arctic weather in the north, to hot summers in the southern regions, with four distinct seasons. Various indigenous peoples have inhabited what is now Canada for thousands of years prior to European colonization. Beginning in the 16th century and French expeditions explored, settled, along the Atlantic coast.
As a consequence of various armed conflicts, France ceded nearly all of its colonies in North America in 1763. In 1867, with the union of three British North American colonies through Confederation, Canada was formed as a federal dominion of four provinces; this began an accretion of provinces and territories and a process of increasing autonomy from the United Kingdom. This widening autonomy was highlighted by the Statute of Westminster of 1931 and culminated in the Canada Act of 1982, which severed the vestiges of legal dependence on the British parliament. Canada is a parliamentary democracy and a constitutional monarchy in the Westminster tradition, with Elizabeth II as its queen and a prime minister who serves as the chair of the federal cabinet and head of government; the country is a realm within the Commonwealth of Nations, a member of the Francophonie and bilingual at the federal level. It ranks among the highest in international measurements of government transparency, civil liberties, quality of life, economic freedom, education.
It is one of the world's most ethnically diverse and multicultural nations, the product of large-scale immigration from many other countries. Canada's long and complex relationship with the United States has had a significant impact on its economy and culture. A developed country, Canada has the sixteenth-highest nominal per capita income globally as well as the twelfth-highest ranking in the Human Development Index, its advanced economy is the tenth-largest in the world, relying chiefly upon its abundant natural resources and well-developed international trade networks. Canada is part of several major international and intergovernmental institutions or groupings including the United Nations, the North Atlantic Treaty Organization, the G7, the Group of Ten, the G20, the North American Free Trade Agreement and the Asia-Pacific Economic Cooperation forum. While a variety of theories have been postulated for the etymological origins of Canada, the name is now accepted as coming from the St. Lawrence Iroquoian word kanata, meaning "village" or "settlement".
In 1535, indigenous inhabitants of the present-day Quebec City region used the word to direct French explorer Jacques Cartier to the village of Stadacona. Cartier used the word Canada to refer not only to that particular village but to the entire area subject to Donnacona. From the 16th to the early 18th century "Canada" referred to the part of New France that lay along the Saint Lawrence River. In 1791, the area became two British colonies called Upper Canada and Lower Canada collectively named the Canadas. Upon Confederation in 1867, Canada was adopted as the legal name for the new country at the London Conference, the word Dominion was conferred as the country's title. By the 1950s, the term Dominion of Canada was no longer used by the United Kingdom, which considered Canada a "Realm of the Commonwealth"; the government of Louis St. Laurent ended the practice of using'Dominion' in the Statutes of Canada in 1951. In 1982, the passage of the Canada Act, bringing the Constitution of Canada under Canadian control, referred only to Canada, that year the name of the national holiday was changed from Dominion Day to Canada Day.
The term Dominion was used to distinguish the federal government from the provinces, though after the Second World War the term federal had replaced dominion. Indigenous peoples in present-day Canada include the First Nations, Métis, the last being a mixed-blood people who originated in the mid-17th century when First Nations and Inuit people married European settlers; the term "Aboriginal" as a collective noun is a specific term of art used in some legal documents, including the Constitution Act 1982. The first inhabitants of North America are hypothesized to have migrated from Siberia by way of the Bering land bridge and arrived at least 14,000 years ago; the Paleo-Indian archeological sites at Old Crow Flats and Bluefish Caves are two of the oldest sites of human habitation in Canada. The characteristics of Canadian indigenous societies included permanent settlements, complex societal hierarchies, trading networks; some of these cultures had collapsed by the time European explorers arrived in the late 15th and early 16th centuries and have only been discovered through archeological investigations.
The indigenous population at the time of the first European settlements is estimated to have been between 200,000
The United States of America known as the United States or America, is a country composed of 50 states, a federal district, five major self-governing territories, various possessions. At 3.8 million square miles, the United States is the world's third or fourth largest country by total area and is smaller than the entire continent of Europe's 3.9 million square miles. With a population of over 327 million people, the U. S. is the third most populous country. The capital is Washington, D. C. and the largest city by population is New York City. Forty-eight states and the capital's federal district are contiguous in North America between Canada and Mexico; the State of Alaska is in the northwest corner of North America, bordered by Canada to the east and across the Bering Strait from Russia to the west. The State of Hawaii is an archipelago in the mid-Pacific Ocean; the U. S. territories are scattered about the Pacific Ocean and the Caribbean Sea, stretching across nine official time zones. The diverse geography and wildlife of the United States make it one of the world's 17 megadiverse countries.
Paleo-Indians migrated from Siberia to the North American mainland at least 12,000 years ago. European colonization began in the 16th century; the United States emerged from the thirteen British colonies established along the East Coast. Numerous disputes between Great Britain and the colonies following the French and Indian War led to the American Revolution, which began in 1775, the subsequent Declaration of Independence in 1776; the war ended in 1783 with the United States becoming the first country to gain independence from a European power. The current constitution was adopted in 1788, with the first ten amendments, collectively named the Bill of Rights, being ratified in 1791 to guarantee many fundamental civil liberties; the United States embarked on a vigorous expansion across North America throughout the 19th century, acquiring new territories, displacing Native American tribes, admitting new states until it spanned the continent by 1848. During the second half of the 19th century, the Civil War led to the abolition of slavery.
By the end of the century, the United States had extended into the Pacific Ocean, its economy, driven in large part by the Industrial Revolution, began to soar. The Spanish–American War and World War I confirmed the country's status as a global military power; the United States emerged from World War II as a global superpower, the first country to develop nuclear weapons, the only country to use them in warfare, a permanent member of the United Nations Security Council. Sweeping civil rights legislation, notably the Civil Rights Act of 1964, the Voting Rights Act of 1965 and the Fair Housing Act of 1968, outlawed discrimination based on race or color. During the Cold War, the United States and the Soviet Union competed in the Space Race, culminating with the 1969 U. S. Moon landing; the end of the Cold War and the collapse of the Soviet Union in 1991 left the United States as the world's sole superpower. The United States is the world's oldest surviving federation, it is a representative democracy.
The United States is a founding member of the United Nations, World Bank, International Monetary Fund, Organization of American States, other international organizations. The United States is a developed country, with the world's largest economy by nominal GDP and second-largest economy by PPP, accounting for a quarter of global GDP; the U. S. economy is post-industrial, characterized by the dominance of services and knowledge-based activities, although the manufacturing sector remains the second-largest in the world. The United States is the world's largest importer and the second largest exporter of goods, by value. Although its population is only 4.3% of the world total, the U. S. holds 31% of the total wealth in the world, the largest share of global wealth concentrated in a single country. Despite wide income and wealth disparities, the United States continues to rank high in measures of socioeconomic performance, including average wage, human development, per capita GDP, worker productivity.
The United States is the foremost military power in the world, making up a third of global military spending, is a leading political and scientific force internationally. In 1507, the German cartographer Martin Waldseemüller produced a world map on which he named the lands of the Western Hemisphere America in honor of the Italian explorer and cartographer Amerigo Vespucci; the first documentary evidence of the phrase "United States of America" is from a letter dated January 2, 1776, written by Stephen Moylan, Esq. to George Washington's aide-de-camp and Muster-Master General of the Continental Army, Lt. Col. Joseph Reed. Moylan expressed his wish to go "with full and ample powers from the United States of America to Spain" to seek assistance in the revolutionary war effort; the first known publication of the phrase "United States of America" was in an anonymous essay in The Virginia Gazette newspaper in Williamsburg, Virginia, on April 6, 1776. The second draft of the Articles of Confederation, prepared by John Dickinson and completed by June 17, 1776, at the latest, declared "The name of this Confederation shall be the'United States of America'".
The final version of the Articles sent to the states for ratification in late 1777 contains the sentence "The Stile of this Confederacy shall be'The United States of America'". In June 1776, Thomas Jefferson wrote the phrase "UNITED STATES OF AMERICA" in all capitalized letters in the headline of his "original Rough draught" of the Declaration of Independence; this draft of the document did not surface unti
Southwest Tennessee Community College
Southwest Tennessee Community College is a community college operated by the Tennessee Board of Regents in Memphis, Tennessee, USA. As the product of a merger between two colleges in 2000, the school has two campuses in Memphis and several satellite centers; the college resulted from the 2000 merger between two institutions, the former Shelby State Community College and the former State Technical Institute at Memphis. Nathan Essex, the school's founding president, announced in 2014 that he would retire the next summer; the merger was an attempt to reduce the overhead of maintaining two separate institutional managements and a recognition of the increasing convergence of academic and technical education. It has made credits earned at the former Technical Institute more transferable to other institutions of higher learning, an additional goal of the merger. Southwest is one of the largest two-year colleges operated by the Tennessee Board of Regents. Southwest Tennessee Community College is a comprehensive, public, open-access college.
Southwest is accredited by the Commission on Colleges of the Southern Association of Colleges and Schools. Dr. Charles M. Temple Dr. M. Douglas Call Dr. Nathan Essex Dr. Tracy D. Hall Southwest has several campuses and centers; these include: Macon Cove Campus- located in Northeast Memphis Union Avenue Campus- located in Downtown Memphis Gill Center- located in Frayser Maxine A. Smith Center- located in Southeast Memphis Millington Center- located in Millington, Tennessee Whitehaven Center- located in Whitehaven The college maintains collegiate sports teams in the following sports: Men's Basketball Women's Basketball Baseball Softball Women's Soccer CheerleadingThe mascot is the Saluqi. Both basketball teams have a winning tradition and advance to the national tournaments. Basketball games are played at the Verties Sails Gymnasium on the Union Avenue Campus. Saluqi Baseball is played at USA Stadium in Tennessee. Southwest Tennessee Community College official site
Memphis is a city located along the Mississippi River in southwestern Shelby County, United States. The 2017 city population was 652,236, making Memphis the largest city on the Mississippi River, second-largest city in Tennessee, as well as the 25th largest city in the United States. Greater Memphis is the 42nd largest metropolitan area in the United States, with a population of 1,348,260 in 2017; the city is the anchor of West Tennessee and the greater Mid-South region, which includes portions of neighboring Arkansas and Mississippi. Memphis is the seat of the most populous county in Tennessee; as one of the most historic and cultural cities of the southern United States, the city features a wide variety of landscapes and distinct neighborhoods. The first European explorer to visit the area of present-day Memphis was Spanish conquistador Hernando de Soto in 1541 with his expedition into the New World; the high bluffs protecting the location from the waters of the Mississippi would be contested between the Spanish and the English as Memphis took shape.
Modern Memphis was founded in 1819 by three prominent Americans: John Overton, James Winchester, future president Andrew Jackson. Memphis grew into one of the largest cities of the Antebellum South as a market for agricultural goods, natural resources like lumber, the American slave trade. After the American Civil War and the end of slavery, the city experienced faster growth into the 20th century as it became among the largest world markets for cotton and lumber. Home to Tennessee's largest African-American population, Memphis played a prominent role in the American civil rights movement and was the site of Dr. Martin Luther King, Jr.'s 1968 assassination. The city now hosts the National Civil Rights Museum—a Smithsonian affiliate institution. Since the civil rights era, Memphis has grown to become one of the nation's leading commercial centers in transportation and logistics; the city's largest employer is the multinational courier corporation FedEx, which maintains its global air hub at Memphis International Airport, making it the second-busiest cargo airport in the world.
Today, Memphis is a regional center for commerce, media and entertainment. The city has long had a prominent music scene, with historic blues clubs on Beale Street originating the unique Memphis blues sound during early 20th century; the city's music has continued to be shaped by a multi-cultural mix of influences across the blues, rock n' roll and hip-hop genres. Memphis barbecue has achieved international prominence, the city hosts the World Championship Barbecue Cooking Contest, which attracts over 100,000 visitors to the city annually. Occupying a substantial bluff rising from the Mississippi River, the site of Memphis has been a natural location for human settlement by varying cultures over thousands of years; the area was known to be settled in the first millennium A. D. by people of the Mississippian Culture, who had a network of communities throughout the Mississippi River Valley and its tributaries. They built complexes with large earthwork ceremonial and burial mounds as expressions of their sophisticated culture.
The historic Chickasaw Indian tribe, believed to be their descendants occupied the site. French explorers led by René-Robert Cavelier, Sieur de La Salle and Spanish explorer Hernando de Soto encountered the Chickasaw tribe in that area in the 16th century. J. D. L. Holmes, writing in Hudson's Four Centuries of Southern Indians, notes that this site was a third strategic point in the late 18th century through which European powers could control United States encroachment and their interference with Indian matters—after Fort Nogales and Fort Confederación: "... Chickasaw Bluffs, located on the Mississippi River at the present-day location of Memphis. Spain and the United States vied for control of this site, a favorite of the Chickasaws."In 1795 the Spanish Governor-General of Louisiana, Francisco Luis Héctor de Carondelet sent his Lieutenant Governor, Manuel Gayoso de Lemos, to negotiate and secure consent from the local Chickasaw so that a Spanish fort could be erected on the bluff. Holmes notes that consent was reached despite opposition from "disappointed Americans and a pro-American faction of the Chickasaws", when the "pro-Spanish faction signed the Chickasaw Bluffs Cession and Spain provided the Chickasaws with a trading post…".
Fort San Fernando de las Barrancas remained a focal point of Spanish activity until, as Holmes summarizes: he Treaty of San Lorenzo or Pinckney's Treaty of 1795, all of the careful, diplomatic work by Spanish officials in Louisiana and West Florida, which has succeeded for a decade in controlling the Indians, was undone. The United States gained the right to navigate the Mississippi River and won control over the Yazoo Strip north of the thirty-first parallel; the Spanish dismantled the fort, shipping its iron to their locations in Arkansas. In 1796, the site became the westernmost point of the newly admitted state of Tennessee, located in what was called the Southwest United States; the area was still occupied and controlled by the Chickasaw nation. Captain Isaac Guion led an American force down the Ohio River to claim the land, arriving on July 20, 1797. By this time, the Spanish had departed; the fort's ruins went unnoticed twenty years when Memphis was laid out as a city, after the United States government paid the Chickasaw for land.
The city of Memphis was founded on May 22, 1819 by John Overton, James Winchester and Andrew Jackson. They named it after the ancient capita