Permutations. Teams should be able to compute the number of permutations and combinations of n objects taken m at a time. They should also have memorized the first eight (or so) values of the factorial function to make this easier.
Logarithms. Teams should be familiar with basic operations of logarithmic math: simplifying the logarithm of a product, difference, or power, and converting from one base to another.
Complex Math. Teams should be familiar with the symbol i representing the imaginary square root of -1, basic operations on complex numbers, graphing complex numbers, and converting complex numbers to magnitude-angle form.
Divisibility Rules. Teams should be able to quickly apply the divisibility rules for small integers (2 through 11) to large integers.
Polynomial Math. Teams should be able to quickly add, subtract, multiply, divide, factor, and find the roots of low-degree polynomials.
Calculus. Teams should be able to find the derivative, integral, slope-at-a-point, local extrema, and critical points of polynomial, trigonometric, and other common functions.
You Gotta Know These Jewish Holidays
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Rosh Hashanah Celebrated on the first and second days of Tishrei, Rosh Hashanah marks the beginning of the Jewish year. It is believed that on this day, people's souls are judged, and God "temporarily" decides their fate. Between Rosh Hashanah and Yom Kippur, the Day of Atonement, are the Ten Days of Repentment, when people are given a chance to reflect and repent. On Rosh Hashanah, it is customary to wear white clothes and eat apples, honey, and pomegranates. Other customs include the blowing of the shofar (an instrument made from a ram's horn) and the ceremony of Tashlich, in which Jews throw bread crumbs into running water to symbolize the cleansing of their sins, is also performed.
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Yom Kippur Celebrated on the tenth day of Tishrei, it is the Jewish Day of Atonement; at the end of Yom Kippur, it is believed that one's fate is sealed. Jews are required to abstain from eating, drinking, washing, and sex. Forbidden fashions include jewelry, makeup, and leather shoes. One traditionally wears white clothes to symbolizing purity from sin. In the afternoon, the Book of Jonah is read. A full day of prayers begins with the Kol Nidre, an ancient incantation that forgives Jews from vows or promises unwittingly made during the past year. As on Rosh Hashanah, the shofar is blown.
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Sukkot Celebrated on the 15th of Tishrei, Sukkot commemorates the sukkot (booths) that the Israelites lived in following the Exodus from Egypt; it also celebrates the harvest. Traditionally, Jews build booths, in which they live and eat for seven days. In synagogue, four symbolic species (the palm, the etrog [a large yellow citrus], myrtle, and willow) are waved in seven directions. Each night, in the sukkah, it is traditional to invite a Biblical figure to be your guest for that night.
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Hanukkah This festival lasts for eight days, starting on the 25th day of Kislev (the third month). It celebrates the victory of the small Maccabee army against the large Greek army of Antiochus, as well as the recapture and purification of the Temple in Jerusalem (ca. 168 BC). It is traditional to light the eight-branched Menorah each night and spin the dreidel. Exchanging presents is only a recent tradition developed in the U.S.
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Purim Celebrated on the 14th of Adar (the sixth month) and commemorating the victory of the Jews, led by Esther and Mordechai, against Haman, who tried to destroy the Jews because of his anger at Mordechai. The story, recorded in the Book of Esther (read from a one-handed scroll called a megillah), takes place in Shushan, the capital city of the kingdom of the Persian King Ahasueras. On Purim, it is traditional to dress up, get drunk, give charity, eat triangular pastries called hamentaschen, and exchange gifts (Mishloach Manot) with friends.
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Passover (Pesach) Celebrated for seven days beginning on the 15th day of Nissan (the seventh month), Passover commemorates the Exodus from Egypt. It is also the ancient Hebrew New Year (superceded in that role by Rosh Hashanah). On the first two days, Jews have a festival dinner called a seder, where they retell the story of the Exodus, from a book called a hagaddah. Jews are required to abstain from eating or owning leavened bread for the duration of the festival; matzah (usually a square flat unleavened bread) is eaten instead. On Passover, the Song of Songs is recited. Passover also begins a cycle of seven weeks, called the Omer, a period of semi-mourning.
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Shavu'ot Celebrated on the sixth day of Sivan (the ninth month), the 50th day of the Omer, after Passover; the word Shavu'ot means "weeks," hence the name Pentecost. Shavu'ot commemorates the giving of the Torah to the Israelites at Mt. Sinai, as well as the beginning of the harvest in ancient Israel. Sukkot, Passover, and Shavu'ot are the three pilgrimages, when Jews would all gather at the Temple each year; on Shavu'ot, Jews would dedicate their first harvest fruits to the Temple. The Book of Ruth is read in synagogue on Shavu'ot, and it is traditional to study all night on this festival.
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The Ninth of Av This is a day of mourning for the destructions of both the First and Second Temples. It is traditional to fast and to keep oneself in a solemn mood. The Book of Lamentations and the Book of Job are read, traditionally while sitting on the floor and with candles as the only lights, as Jews are supposed to refrain from physical comfort.
You Gotta Know These Civil War Battles and Campaigns
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Fort Sumter (April 12, 1861). Built on an island in 1829, the fort was one of three that the United States maintained in the harbor of Charleston, South Carolina. In order to claim true independence from the Union, Jefferson Davis decided that the forts needed to be taken; a Confederate force under P.G.T. Beauregard ordered the small Union garrison, controlled by Major Robert Anderson, to surrender. Anderson refused, shots were fired, and the Union commander surrendered two days later, with only one soldier killed. The Union made two unsuccessful attempts to recapture the fort with ironclad ships in 1863, but Confederate forces finally abandoned Sumter when they left Charleston in February 1865.
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First Bull Run / First Manassas (July 21, 1861). Fought at a creek near Manassas, Virginia (30 miles west of Washington D.C.), this was the first major showdown of the war. Beauregard led an army against Union commander Irwin McDowell and received reinforcements from Joseph Johnston's troops (whom Union General Robert Patterson failed to detain). The Confederacy routed the Union when Thomas Jackson's brigade held the left line at Henry House Hill; this effort earned him the nickname "Stonewall." Congressmen and reporters, who had expected to watch a Union victory, fled in panic back to D.C.
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Hampton Roads (March 9, 1862). A channel in southeastern Virginia was the site of the first major fight between two ironclad ships. The Confederates raised an old wooden boat, the Merrimack, and fit it with ten guns and iron armor plates. Renaming the Virginia, it was captained by Franklin Buchanan. The Union countered by constructing a large oval with a rotating gun, called the Monitor and piloted by John Worden. The Virginia tore through Union wooden ships (Cumberland, Congress, Minnesota) but when the Monitor arrived, the two ironclads fought to a stalemate - thus the Union maintained its blockade. The South deliberately destroyed the Virginia two months later, while the Monitor sank in a storm off Cape Hatteras in December 1862.
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Shiloh / Pittsburg Landing (April 6-7, 1862). This was named after a church in Pittsburg Landing, Tennessee (100 miles southwest of Nashville). Confederate commander Albert Sidney Johnston led a force north from Corinth, Mississippi. Ulysses S. Grant, who had just captured Fort Donelson, brought five Union divisions to face him. At first, the South led the attack, but Union troops held the "Hornets' Nest" for hours, killing Johnston in the process. Beauregard took over, but by the second day Northern Generals Don Carlos Buell and Lew Wallace (who wrote Ben-Hur) brought reinforcements, causing the Confederates to retreat. More than 13,000 Union and 10,000 Confederate soldiers lost their lives.
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Peninsular Campaign (March - July 1862). Union commander George McClellan devised this plan to capture the Confederate capital at Richmond, Virginia by sending 110,000 men up the peninsula between the York and James rivers. Advised of Northern maneuvers, Southern commander Joseph Johnston detached a force to defend the peninsula. He also sent a small unit (led by Stonewall Jackson) that crushed Union reinforcements in the West. After Johnston was wounded at Seven Pines (June 1), Davis replaced him with Robert E. Lee. Lee concentrated his force north of the Chickahominy River; in the Seven Days' Battles (June 25-July 1), the Confederates broke through Union defenses, leading to McClellan's retreat down the James toward Harrison's Landing, and failure of the campaign.
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Second Bull Run / Second Manassas (August 29-30, 1862). This resounding victory by Lee and Jackson pushed Union forces back to Washington, D.C. President Lincoln had replaced McClellan with John Pope, who would supposedly be united with the Army of the Potomac, commanded by Henry Halleck. Lee maneuvered Jackson's troops behind those of Pope; Jackson detained Pope's men at Manassas while Lee sent James Longstreet to crush Pope's left flank. Halleck's army was supposed to land at Aquia, but instead retreated to defend Washington, ceding all of Virginia to the Confederacy and marking a low point in the Union effort.
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Antietam / Sharpsburg (September 17, 1862). The bloodiest day of the Civil War: 12,000 Union men lost their lives, as did 10,000 Confederates. Lee planned a northern invasion into Maryland but a Union soldier discovered those battle plans wrapped around three cigars. Instead, Lee marched his army toward Sharpsburg Creek. Meanwhile, Jackson's forces captured Harper's Ferry, Virginia, and rushed to reunite with Lee. McClellan had a large enough force to capture the entire rebel army but did not use all of his troops nor coordinate one solid attack. Antietam thus was actually a series of five skirmishes; in one of them, dubbed "The Bloody Lane," 2000 Union soldiers fell in a few minutes. As it was, Union forces drove the Confederates back across the Potomac.
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Fredericksburg / Marye's Heights (December 13, 1862). At this site, about 50 miles south of Washington, Union commander Ambrose Burnside (who had replaced McClellan) tried to take the initiative and cross the Rappahannock River in a march toward Richmond. He met Lee's forces, which were well entrenched in the hills behind the town. With a superior position, Lee routed the Union army; 13,000 Northern troops fell there, while only 5000 Confederates were killed. After the battle, Burnside's troops were forced to make "The Mud March" up the Rappahannock, made foul by weather and dead and wounded bodies.
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Vicksburg Campaign (April 29 - July 4, 1863). This campaign was launched by Grant to take control of the Mississippi River and cut off the western Confederate states from the east. Grant ordered regiments led by James McPherson, John McClernand, and William Tecumseh Sherman through bayous west of the Mississippi to Hard Times. They were up against rebel forces under Joseph Johnston and John Pemberton. Sherman and McPherson drove Johnston from Jackson, Mississippi on May 14, and the Union scored a victory at Champion's Hill two days later, but could not drive the Southerners out of Vicksburg, so Grant laid siege to the town. Outnumbered 71,000 to 20,000 and on the brink of starvation, Pemberton finally surrendered his men; Johnston withdrew east.
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Chancellorsville (May 1-4, 1863). Victory for the South, but with great cost, as Stonewall Jackson lost his life. Lincoln called on "Fighting Joe" Hooker to command the Union army; Hooker took a force of 134,000 and provoked Lee and Jackson's 60,000 men into battle. Jackson moved around Hooker and counterattacked the Union flank on May 2. That night, while Jackson was on reconnaissance, his own men mistook him for a Northerner and shot him; he died of pneumonia eight days later. The following morning, a cannonball blast hit the Chancellor House, knocking Hooker unconscious; Union troops led by John Sedgwick then retreated. Casualties for the North outnumbered those of the South, 17,000 to 13,000.
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Gettysburg (July 1-3, 1863). This marked both the farthest northward advancement by the Confederacy and the turning point that led to its defeat. Lee, along with Longstreet, A.P. Hill, and Richard Ewell, led the southern Pennsylvania attack; J.E.B. Stuart was supposed to monitor Union movement with his cavalry but strayed so far east of Gettysburg that his force did not return (exhausted) until the second day. George Meade replaced Hooker as leader of the Union side; Southern forces drove Northerners through the town but could not secure key positions at Cemetery Ridge and Little and Big Round Tops. Low on supplies, on the final day Lee ordered an attack on the center; George Pickett led his famous "charge" through open fields, where the Union mowed down one-third of his 15,000 men. The Confederates lost 20,000 and Lee retreated to Virginia.
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Chattanooga Campaign (September-November 1863). It began when Union General William Rosecrans forced Confederate commander Braxton Bragg out of the city on September 9. Ten days later, at Chickamauga (in Georgia), Bragg and Longstreet turned the tables by whipping Rosecrans, forcing him into a siege position at Chattanooga. Only George Thomas (the "Rock of Chickamauga") saved Rosecrans from annihilation. Well-developed railroad networks, however, allowed Grant, Hooker, and Sherman to bring reinforcements. On November 24, Hooker took Lookout Mountain in the southwest, in the "Battle Above the Clouds." The next day, Thomas ran right over the Southern force at Missionary Ridge, securing Tennessee for the North.
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Wilderness Campaign (May 5 - June 12, 1864). The first clash between Grant and Lee, this series of conflicts started with the Battle of the Wilderness (50 miles northwest of Richmond), where Southern leaders A.P. Hill and Ewell held the line, and over 17,000 Northerners fell. At Spotsylvania Court House, Meade assaulted Lee's men, but they repelled Meade at the "Bloody Angle." The trenches in which much of the fighting took place were similar to those later seen in World War I. Advancing within ten miles of Richmond, Grant met Lee at Cold Harbor (June 3); he lost 7,000 men to Lee's 1,500 and withdrew across the James River, but with the entire campaign he severely reduced Confederate strength in a war of attrition.
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Petersburg Campaign (June 1864 - April 1865). After Cold Harbor, Grant moved south to lay siege to this railroad hub, 25 miles from Richmond. On July 30, Pennsylvania coal miners detonated four tons of powder in a tunnel underneath the Confederate line; this "Battle of the Crater" killed many defenders. Although the South maintained the city, its supplies ran thin in the winter of 1865. Grant finally destroyed the Confederate right flank at Five Forks (April 1-2), 14 miles southwest of Petersburg. This resounding defeat led to Lee's surrender to Grant at Appomattox Court House one week later, effectively ending the Civil War.
You Gotta Know These Latin American Authors
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Gabriel García Marquez (1928-present, Colombia; Nobel Prize for Literature 1982). The master of magic realism, his birthplace of Aracataca was the model for the fictional town of Macondo. The town played a prominent role in many of García Marquez's works, such as Leaf Storm and his seminal novel, One Hundred Years of Solitude (1967), which details the decline of the Buendía family over seven generations. A newspaper journalist in the 1950s, García Marquez exposed a naval scandal (chronicled in The Story of a Shipwrecked Sailor). Other prominent novels include In Evil Hour, Love in the Time of Cholera, and The General in His Labyrinth, a depiction of Simón Bolívar's final years.
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Pablo Neruda (1904-1973, Chile; Nobel 1971). Born Neftalí Reyes, he adopted the surname of the 19th century Czech poet Jan Neruda. Gabriela Mistral (see below) was the head of his school in the small city of Temuco. 1923 saw the publication of Neruda's best-known work, Twenty Love Poems and a Song of Despair, which led to diplomatic appointments. As a penniless consul in Burma in the 1930s, he wrote the surrealist collection Residence on Earth. He served in the Chilean senate in the 1940s, though government opponents forced him into exile over his Communist views. Crossing the Andes on horseback inspired his epic Canto general (1950). He died of cancer days after his friend Salvador Allende was executed.
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Jorge Luis Borges (1899-1986, Argentina). One-quarter English, Borges learned that language before he learned Spanish. Educated in Europe during World War I, he met a circle of avant-garde poets in Spain, which inspired him to found the ultraismo movement and publish the collection Fervor of Buenos Aires (1923) when he returned to Argentina. While working in a library, Borges developed his greatest short stories, collected in A Universal History of Infamy (1935), Ficciones (1944), and The Aleph (1949). By his fifties, a disorder inherited from his father had taken Borges's eyesight, but in 1962 he completed the influential story collection Labyrinths.
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Isabel Allende (1942-present, Chile). Actually born in Peru, at age three she moved to her mother's native Chile. A successful news reporter in her twenties, she and her family fled to Venezuela after General Augusto Pinochet deposed and executed her uncle Salvador Allende, setting up a dictatorship. Her formal literary career began at age 40, when she published The House of the Spirits, a magic realist work that chronicles several generations of the Trueba family. Other works of fiction include the short-story collection Eva Luna (1989) and Paula (1995), which detailed Allende's care for her terminally ill daughter.
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Gabriela Mistral (1889-1957, Chile; Nobel 1945). The first Latin American to win the Nobel Literature Prize, Mistral was actually named Lucila Godoy Alcayaga, but took her pen name from the Italian and French poets Gabriele D'Annunzio and Frédéric Mistral respectively. At first a prominent educator, she wrote "Sonnets of Death" (1914) after the suicide of her fiancé. Those sonnets later appeared in her most famous collection, Desolation (1922). A native Chilean, she served as a diplomat both in the United States and Europe. Langston Hughes translated a portion of Mistral's poetry into English just after she died.
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Octavio Paz (1914-1998, Mexico; Nobel 1990). A prominent poet and essayist, Paz supported leftist causes in Mexico; he fought briefly for the Republicans during the Spanish Civil War. He published the poetry collection Luna silvestre at age 19, and his 584-line poem The Sun Stone deals with the planet Venus, an important symbol to the Aztecs. While studying in Los Angeles, Paz observed flamboyantly dressed Mexican-American pachucos ("zoot-suiters"), who inspired him to write about Mexico and its Native American/mestizo heritage in his pivotal essay collection, The Labyrinth of Solitude (1950). Another prose work, In the Light of India (1997), reflected Paz's part-(East) Indian heritage.
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José Martí (1853-1895, Cuba). Best known as a poet and a revolutionary, Martí fought tirelessly for Cuban independence. Imprisoned at age sixteen and exiled from the island several times, he settled in New York for the last fifteen years of his life, where he wrote essays on Walt Whitman, Jesse James, and the threat of Latin American economic dependence on the United States. His Ill-Omened Friendship (1885) is considered the first Spanish modernist novel, and his poetry collections include Our America and Simple Verses; the poem "Guantanamera" was the inspiration for several songs. Martí was killed in a skirmish at Dos Ríos while participating in an invasion with other Cuban exiles.
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Mario Vargas Llosa (1936-present, Peru). While attending military school in Lima, Vargas Llosa wrote the play The Escape of the Inca (1952), but the harsh treatment he received there was the basis for his best-known novel, The Time of the Hero. Conversation in the Cathedral (1969) was Vargas Llosa's serious take on living under the dictatorship of Manuel Odría, while in 1977 he published the lighter, autobiographical Aunt Julia and the Scriptwriter, about soap operas. Other important works include The War of the End of the World and A Fish in the Water, which discusses his political career; Vargas Llosa ran for president of Peru in 1990 but was defeated by Alberto Fujimori.
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Miguel Asturias (1899-1974, Guatemala; Nobel 1967). Asturias left his native Guatemala in 1923 to study in Paris. There he discovered Mayan mythology, and translated the Popol Vuh into Spanish; the theme would pervade his work, such as 1963's Mulata de tal. He most famous novel, El señor presidente (1946), was a satire against the oppressive Guatalemalan dictatorship. Asturias also completed a trilogy that blasted exploitation by the American-led United Fruit Company, and the short-story collection Weekend in Guatemala (1956), based on the CIA-led overthrow of president Jacobo Arbenz's liberal government.
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Carlos Fuentes (1928-present, Mexico). Though born into a well-to-do family, Fuentes has often dealt with the betrayed ideals from the Mexican Revolution of 1910, the subject of both his first novel, Where the Air is Clear (1958), and his most successful book, The Death of Artemio Cruz (1962). Other notable novels include Terra nostra, set during the reign of King Philip II of Spain, and The Old Gringo, which portrays Ambrose Bierce's last days in Mexico. Fuentes has also penned absurdist plays and essay collections on Mexican and American art and literature.
You Gotta Know These Tennis Players
Men
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Rod Laver (1938-present). Australia produced many talented players (Emerson, Rosewall, Newcombe, Stolle, Hoad) but Laver was the best of all. He weighed just 145 pounds in his playing days but his massive left arm generated incredible topspin shots. The only player to win the Grand Slam twice - in 1962 as an amateur, and in 1969 as a professional - Laver took 11 major singles titles overall. Turning pro in 1963, Laver won five U.S. Pro Championships; had he been allowed to play the majors from '63 to '67, he likely would hold the wins record instead of Pete Sampras. Martina Navratilova and Sampras both idolized Laver, the first to earn $1 million in a career.
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Pete Sampras (1971-present). "Pistol Pete" burst onto the scene in 1990, when he became the youngest man ever to win the U.S. Open. He would take five U.S. Opens and two Australian Opens, but his greatest accomplishments came on the Wimbledon grass. Starting in 1993 he won the tournament seven times in eight years, losing only to Richard Krajicek in the quarterfinals in 1996. The last Wimbledon win (2000) gave Sampras the all-time men's major record, passing Roy Emerson's 12. Married to actress Bridgette Wilson, Sampras silenced his critics (who thought he was washed up) by defeating Andre Agassi for the 2002 U.S. Open title -- then he retired.
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