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One of the most important and complex form of mathematics in human history is calculus. The two major branches are differential calculus and integral calculus. Differential calculus deals with instantaneous rates of change and the slopes of curves. This is found in many areas of life. Integral calculus deals with the accumulation of quantities and the areas under and between curves. They are related to each other, because they are bound in the fundamental theorem of calculus. Both branches use the notions of convergence of infinite sequences and infinite series to a well-defined limit. Infinitesimal calculus was created independently by the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Science, engineering, and economics heavily use calculus in our time. Involving mathematics education, calculus denotes courses of elementary mathematical analysis (which is devoted to the study of functions and limits). Mathematical analysis deals with metric space, differential equations, and other formulas. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine). Because such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus. The ancients introduced many ideas related to integral calculus too.

Pittsburgh is the place that is found in the Commonwealth of the great state of Pennsylvania. It is the county seat of Allegheny County. It has a population of about 301,048 people. It is the second largest city in Pennsylvania in terms of population. Known as the Steel City, Pittsburgh always had a strong, working class background. It is a city found in the southwest part of the state at the confluence of the Allegheny, Monongahela, and Ohio rivers. It has more than 300 steel related businesses and 446 bridges. It has 30 skyscrapers, two inclined railways, a pre-revolutionary fortification, and Point State Park at the confluence of the rivers. It is near the mineral rich Allegheny Mountains. Pittsburgh is a major manufacturing production of aluminum, glass, shipbuilding, petroleum, foods, sports, transportation, computing, autos, and electronics. Its culture is diverse with museums, medical centers, parks, research centers, and a cultural district filled with diversity. Many companies have a place in the city that deal with cyber defense, software engineering, robotics, energy research, and nuclear navy. Google, Apple Inc., Bosch, Facebook, Uber, Nokia, Autodesk, Microsoft, and IBM have investments in Pittsburgh. Carnegie Mellon University and the University of Pittsburgh have helped tons of people in the area. It is a city with 58 square miles and its highest elevation is 1,370 feet. Its lowest elevation is 710 feet. Pittsburgh has been called one of the most livable cities in America as found in the Economists’ Global Livability Ranking. It has been part of leadership in many other things as well. Birthed from the 1700’s, it has grown in enumerable ways. From the Steelers to civil rights activists, Pittsburgh has remained firmed in its commitment to excellence. The North Side, the West Side, and the East End encompass neighborhoods that give Pittsburgh its flair and creative spirit. Pittsburgh is an overly dynamic city.


From transportation to aesthetics, vehicles make our world more interesting. All of us have either driven a vehicle before, seen one, or traveled in one before. Billions of people live on this Earth, and we have many interests in our diverse, complicated lives. From the 19th century to the modern era of the 21st century, cars changed the cultures of the world. It was part of the era of modernization. It broke down barriers to allow people to travel into many areas in a short span of time. Once upon a time, cars ran mostly on gasoline, natural gas, or diesel. Today, cars can run on electrical power, hydrogen, solar, and vegetable oil. There are even self-propelled cars today. Insurance, computerized devices, and car repair shops deal with vehicle issues all of the time. One of the greatest joys in the world is to drive a car to a great destination where you can relax and have fun. From the modern car in 1886, which was created by German inventor Karl Benz, to the futuristic cars of the 21st century, people of every age are fans of them. The irony is that cars are more complex with lighting and other devices, but they are easier to drive today than back in the day. The balance is that we enjoy cars and we use policies that help maintain roads, land use, and regulate congestion at the same time. About one billion cars are in use worldwide.



An international sport that deals with competition, teamwork, and other forms of fair play describes volleyball. Volleyball is played among 2 teams of six players. The separation of the net is common. The team with the most scores wins the game. It was created by 1895. It has been part of the Summer Olympic Games since 1964 at Tokyo. Volleyball deals with strategy too. Many players on the team are strong on offensive or defense. Some are great strikers while others were great blockers. The rules of the game are very important. A player on one of the teams starts a rally by serving the ball. The ball can be tossed or released. Then, someone hit it with hand of arm from behind the back boundary line of the court, over the net, and into the receiving team’s court. The receiving team must not let the ball be grounded within their court. The team may touch the ball up to 3 times, but individual players may not touch the ball twice consecutively. Typically, the first two touches are used to set up for an attack, an attempt to direct the ball back over the net in such a way that the serving team is unable to prevent it from being grounded in their court. The rally continues, with each team allowed as many as three consecutive touches, until either (1): a team makes a kill, grounding the ball on the opponent's court and winning the rally; or (2): a team commits a fault and loses the rally. The team that wins the rally is awarded a point and serves the ball to start the next rally.

Volleyball has a long history. During the winter of 1895, in Holyoke, Massachusetts, William G. Morgan created a new game. He was a YMCA physical education director. His new game was called Mintonette. This name is derived from the game of badminton. This pastime was to be played indoors by any number of players. It took some of the characteristics from tennis and handball. Mintonette was created as an indoor sport. At the same time, basketball was created in the city of Springfield, Massachusetts. Mintonette was created with rules by William G. Morgan. The rules called for a net that was 6 ft. 6 in. (1.98 m) high, a 25 ft. × 50 ft. (7.6 m × 15.2 m) court, and any number of players. A match was composed of nine innings with three serves for each team in each inning, and no limit to the number of ball contacts for each team before sending the ball to the opponents' court. In case of a serving error, a second try was allowed. Hitting the ball into the net was considered a foul (with loss of the point or a side-out)—except in the case of the first-try serve. After an observer, Alfred Halstead, noticed the volleying nature of the game at its first exhibition match in 1896, played at the International YMCA Training School (now called Springfield College), the game quickly became known as volleyball (it was originally spelled as two words: "volley ball"). Volleyball rules were slightly modified by the International YMCA Training School and the game spread around the country to various YMCAs.

By Timothy