General Daniel Harvey Hill in the Civil War

General Daniel Harvey Hill in the Civil War Daniel Harvey Hill: Early Life Career: Born in the York District of South Carolina on July 21, 1821, Daniel Harvey Hill was the son Solomon and Nancy Hill.   Educated locally, Hill received an appointment to West Point in 1838 and  graduated four years later in the same class as  James Longstreet,  William Rosecrans,  John Pope, and  George Sykes.   Ranked 28th in a class of 56, he accepted a commission in the 1st US Artillery.   With  the outbreak of the  Mexican-American War  four years later, Hill traveled south with  Major General Winfield Scotts army.   During the campaign against Mexico City, he earned a brevet promotion to captain for his performance at the  Battles of Contreras  and  Churubusco.   A brevet to major followed his actions at the  Battle of Chapultepec. Daniel Harvey Hill - Antebellum Years: In 1849, Hill elected to resign his commission and left the 4th US Artillery to accept a teaching post at Washington College in Lexington, VA.   While there, he befriended Thomas J. Jackson who was then serving as a professor at the Virginia Military Institute.   Actively engaged in education over the next decade, Hill also taught at Davidson College before receiving an appointment as superintendent of the North Carolina Military Institute.   In 1857, his ties to Jackson tightened when his friend  married his sisters wife.   Skilled in mathematics, Hill was well-known in the South for his texts on the subject. Daniel Harvey Hill - The Civil War Begins: With the beginning of the Civil War in April 1861, Hill received command of the 1st North Carolina Infantry on May 1.   Dispatched north to the Virginia Peninsula, Hill and his men played a key role in defeating Major General Benjamin Butlers Union forces at the Battle of Big Bethel on June 10.   Promoted to brigadier general the following month, Hill moved through a number of posts in Virginia and North Carolina later that year and into early 1862.   Elevated to major general on March 26, he assumed command of a division in General Joseph E. Johnstons army in Virginia.   As Major General George B. McClellan moved to the Peninsula with the Army of the Potomac in April, Hills men took part in opposing the Union advance at the Siege of Yorktown. Daniel Harvey Hill - Army of Northern Virginia: In late May, Hills division played a central role in the Battle of Seven Pines.   With the ascent of General Robert E. Lee to command of the Army of Northern Virginia, Hill saw action during the Seven Days Battles in late June and early July including Beaver Dam Creek, Gaines Mill, and Malvern Hill.   As Lee moved north following the campaign, Hill and his division received orders to remain in the vicinity of Richmond.   While there, he was tasked with negotiating an agreement for the exchange of prisoners of war. Working with Union Major General John A. Dix, Hill concluded the Dix-Hill Cartel on July 22.   Rejoining Lee following the Confederate victory at Second Manassas, Hill moved north into Maryland. While north of the Potomac, Hill exercised independent command and his men comprised the armys rearguard as it moved north and west.   On September 14, his troops defended Turners and Foxs Gaps during the Battle of South Mountain.   Three days later, Hill performed well at the Battle of Antietam as his men turned back Union assaults against the sunken road.   Following the Confederate defeat, he retreated south with his division serving in Jacksons Second Corps.   On December 13, Hills men saw limited action during the Confederate victory at the Battle of Fredericksburg. Daniel Harvey Hill - Sent West: In April 1863, Hill departed the army to begin recruiting duty in North Carolina.   Following the death of Jackson after the Battle of Chancellorsville a month later, he was irritated when Lee did not appoint him to corps command.   After protecting Richmond from Union efforts, Hill instead received orders to join General Braxton Braggs Army of Tennessee with the provisional rank of lieutenant general.   Taking command of a corps consisting of the divisions of Major Generals Patrick Cleburne and John  C. Breckinridge, he led it effectively at the Battle of Chickamauga that September.   In the wake of the triumph, Hill and several other senior officers openly expressed their unhappiness with Braggs failure to capitalize on the victory.   Visiting the army to resolve the dispute, President Jefferson Davis, a longtime friend of Bragg, found in the commanding generals favor.   When the Army of Tennessee underwent a reorganization, Hill was intentionally left without a comma nd.   In addition, Davis decided not to confirm his promotion his promotion to lieutenant general. Daniel Harvey Hill - Later War: Reduced to major general, Hill served as volunteer aide-de-camp in the  Department of North Carolina and Southern Virginia in 1864.   On January 21, 1865, he assumed command of the  District of Georgia, Department of South Carolina, Georgia, and Florida.   Possessing few resources, he moved north and led a division in Johnstons army during the final weeks of the war.   Taking part in the Battle of Bentonville in late March, he surrendered with the rest of the army at Bennett Place the following month.    Daniel Harvey Hill - Final Years: Settling in Charlotte, NC in 1866, Hill edited a magazine for three years.   Returning to education, he became president of the University of Arkansas in 1877.   Known for his effective administration, he also taught classes in philosophy and political economy.   Resigning in 1884 due to health issues, Hill settled in Georgia.   A year later, he accepted the presidency of the  Georgia Agriculture and Mechanical College.   In this post until August 1889, Hill again stepped down due to ill health.   Dying at Charlotte on September 23, 1889, he was buried at the Davidson College Cemetery. Selected Sources: Civil War: Daniel Harvey HillCMHLC: Daniel Harvey HillNorth Carolina History Project: Daniel Harvey Hill

Worksheet for Chebyshevs Inequality

Worksheet for Chebyshev's Inequality Chebyshev’s inequality says that at least 1 -1/K2 of data from a sample must fall within K standard deviations from the mean, where ​​K is any positive real number greater than one. This means that we don’t need to know the shape of the distribution of our data. With only the mean and standard deviation, we can determine the amount of data a certain number of standard deviations from the mean. The following are some problems to practice using the inequality. Example #1 A class of second graders has a mean height of five feet with a standard deviation of one inch. At least what percent of the class must be between 4’10† and 5’2†?​​ Solution The heights that are given in the range above are within two standard deviations from the mean height of five feet. Chebyshev’s inequality says that at least 1 – 1/22 3/4 75% of the class is in the given height range. Example #2 Computers from a particular company are found to last on average for three years without any hardware malfunction, with a standard deviation of two months. At least what percent of the computers last between 31 months and 41 months? Solution The mean lifetime of three years corresponds to 36 months. The times of 31 months to 41 months are each 5/2 2.5 standard deviations from the mean. By Chebyshev’s inequality, at least 1 – 1/(2.5)62 84% of the computers last from 31 months to 41 months. Example #3 Bacteria in a culture live for an average time of three hours with a standard deviation of 10 minutes. At least what fraction of the bacteria live between two and four hours? Solution Two and four hours are each one hour away from the mean. One hour corresponds to six standard deviations. So at least 1 – 1/62 35/36 97% of the bacteria live between two and four hours. Example #4 What is the smallest number of standard deviations from the mean that we must go if we want to ensure that we have at least 50% of the data of a distribution? Solution Here we use Chebyshev’s inequality and work backward. We want 50% 0.50 1/2 1 – 1/K2. The goal is to use algebra to solve for K. We see that 1/2 1/K2. Cross multiply and see that 2 K2. We take the square root of both sides, and since K is a number of standard deviations, we ignore the negative solution to the equation. This shows that K is equal to the square root of two. So at least 50% of the data is within approximately 1.4 standard deviations from the mean. Example #5 Bus route #25 takes a mean time of 50 minutes with a standard deviation of 2 minutes. A promotional poster for this bus system states that â€Å"95% of the time bus route #25 lasts from ____ to _____ minutes.† What numbers would you fill in the blanks with? Solution This question is similar to the last one in that we need to solve for K, the number of standard deviations from the mean. Start by setting 95% 0.95 1 – 1/K2. This shows that 1 - 0.95 1/K2. Simplify to see that 1/0.05 20 K2. So K 4.47. Now express this in the terms above. At least 95% of all rides are 4.47 standard deviations from the mean time of 50 minutes. Multiply 4.47 by the standard deviation of 2 to end up with nine minutes. So 95% of the time, bus route #25 takes between 41 and 59 minutes.