The Modified Covering Problem on Paths and Trees

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Transcript The Modified Covering Problem on Paths and Trees

Department of Mathematical Sciences Family Orientation Welcome to the Best Math Department in the Army!

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Agenda

• Overview / History of USMA • Things to know about the Department • Tour of the Department • Mathlete Luncheon 2

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West Point (a strategic goal)

• Oct. 6, 1777 Battle of Ft. Montgomery • Oct. 7, 1777 Battle of Saratoga • Washington wanted to prevent British from splitting the colonies. He considered it “key to the continent and “the most important post in America” • Jan. 1778 work begins on Fortress West Point

The post itself, at 16,000 acres, is slightly larger than Manhattan USNA = 338 acres USAFA = 18,000 acres

History of West Point

• In 1780, the commander of the post, Maj. Gen. Arnold offered it to be traded to the British port 10,000 gold pounds and a general’s commission in the Royal Army • In 1793 Washington held a Cabinet meeting to discuss an academy.

“The establishment of a military academy, upon a respectable and extensive basis, has ever been considered by me to be an object of the highest national importance.”

-George Washington (Dec. 12, 1799) Congress had concerns about creating a military aristocracy.

• March 16,1802 − Academy founded under Jefferson − The Army established the Corps of Engineers as a separate, permanent branch, and gave the engineers responsibility for finding and operating the U.S. Military Academy at West Point. (caused problems that were changed in 1812)

Sylvanus Thayer, USMA 1808 “Father of the Military Academy”

• Assistant Professor of Mathematics USMA, 1809-1811 • Knew WP did not have quality mathematicians, scientists, and engineers to meet the requirements of a top-notch engineering school (America’s 1 st engineering school).

• Visited technical and military schools in France and England, 1815-1817 • Superintendent (1817-1833) – In less than a decade, established the Academy as one of the premier educational programs in the world.

The Thayer Method of Teaching

“a quiet revolution in American education” • Cadets prepare; no lectures • Every cadet is graded every day • Small sections of 10-12 • Sections grouped by performance • Professors have to turn in weekly reports • Instituted demerits which were based on conduct in military training and academic effort • Limited summer vacations to once – between 2 nd and 3 rd year.

• By 1823, applications lead to over 1000 a year for 250 openings • A major problem in Thayer’s merit system (Jefferson Davis and Edgar Allan Poe)

Thayer’s Legacy

• After Thayer resigned, he left a school that had become world famous – a model for other American schools in science and engineering.

– Virtually all 19th century American engineering schools were started with West Point educated faculty or adopted its texts. • Founded the Thayer School of Engineering at Dartmouth, 1867

Robert Edward Lee, USMA 1829

• Taught mathematics as a cadet as a third and second classman. • Superintendent 1848-1852 • Civil War General – Acknowledged as one of the Army’s best officers.

– Offered command of the Union Army in 1861.

Ulysses S. Grant, USMA 1843

• Applied four times to become an instructor in Mathematics, but was turned down.

• Prof Church believed Grant’s mediocre performance in mathematics did not qualify him to teach in the department.

• “It is easier to become President of the US than to become an instructor in the Department of Mathematical Sciences.”

Douglas MacArthur, USMA 1903* (Superintendent 1919-1922)

• If Sylvanus Thayer was the Father of the Military Academy, then MacArthur was its “savior.” − “How long are we going on preparing for the war of 1812?“ - MacArthur – "During the great war, West Pointers were unable to adapt to new methods in the field... because of their stifling training.” President emeritus of Harvard University, Dr. Charles Eliot. • The country’s needs had changed.

– A new type of officer was needed, one possessing • An understanding of human feelings • A comprehensive grasp of world and national affairs.

• MacArthur made reforms in an institution that was highly resistant to change.

– Modernized the curriculum – Formalized the honor code - Truth was always expected but it was never written down and there was no investigating or enforcing agency – Created a system of intramural athletics – Liberalized regulations; more privileges, ensured they came in contact with civilians, gave them $5 / month to spend, granted upperclassman leave on weekends… – Changed the basis for final class standings. • Grades included military bearing and efficiency, leadership, personality, athletic performance, and cadet participation in extracurricular activities. He bought a new spirit to the Academy, a willingness to experiment, to break with tradition, to question everything.

Omar N. Bradley USMA, 1915

"Whatever the case, I know I benefited from

this prolonged immersion in math. The study of mathematics, basically a study of logic, stimulates one's thinking and greatly improves one's power of reasoning. In later years, when I was faced with infinitely complex problems, mathematics helped me

think more clearly and logically."

- Instructor of Mathematics at USMA, 1920-24 14

ROBERT E.

LEE Class of 1829 ULYSSES S.

GRANT Class of 1843 JOHN J.

PERSHING Class of 1886 DOUGLAS MACARTHUR Class of 1903

“Much of the history we teach was made by people we taught.”

GEORGE S.

PATTON, JR.

Class of 1909 DWIGHT D. EISENHOWER Class of 1915 OMAR N.

BRADLEY Class of 1915 H. NORMAN SCHWARZKOPF Class of 1956

JOHN P.

ABIZAID Class of 1973 MARTIN E. DEMPSEY Class of 1974 DAVID H. PETAEUS Class of 1974

“Much of the history we teach was made by people we taught.”

RAYMOND T. ODIERNO Class of 1976 STANLEY A. MCCHRYSTAL Class of 1976 ANNE F. MACDONALD Class of 1980 REBECCA S. HALSTEAD Class of 1981

Two West Point Grads served as US President: President Ulysses S. Grant (1869-1877) USMA 1843 President Dwight D. Eisenhower (1953-1961) USMA 1915 Four Heads of State: Jefferson Davis USMA1828 (1861-1865) Anastasio Somoza Debayle USMA 1946, Nicaragua (1967 –72, 1974-79) Fidel V. Ramos USMA1950,. Philippines (1992-1998) José María Figueres USMA1979, Costa Rica (1994-1998) Only Five “5 Star Generals”

Title “General of the Army”:

Douglas C. MacArthur USMA 1903 Henry H. Arnold (Gen of Air Force*) USMA 1907 Omar N. Bradley USMA 1915 Dwight D. Eisenhower USMA 1915 George C.Marshall * VMI 1901 18 Astronauts

West Point, 1980 - Present

• Better problem solvers, decision makers, critical and creative thinkers, and more culturally diverse… • Changed the overarching intellectual goal:

Graduates anticipate and respond effectively to the uncertainties of a changing technological, social, political, economic world.

• Summer programs - 519 Cadets in 37 Countries • Semester Abroad - 140 Cadets in 10 countries, (up from 1 cadet in 2001)

West Point Leaders

IG USMA Superintendent LTG Huntoon Chaplain Diversity EO SJA G-1 G-3 USMA Chief of Staff COL Stafford G-5 G-6 G-8 Director Strategic Communications Ms. Fitzgerald PAO Protocol BAND DAA AOG Dean Of the Academic Board BG Trainor Commandant United States Corps of Cadets BG Rapp Director Intercollegiate Athletics Mr. Corrigan Director of Admissions COL McDonald Commander US Army Garrison West Point COL Tarsa Commander Keller Army Community Hospital COL Land

Necessary Components of an Officer

Physically Fit Great Intellectual Capacity Militarily Competent Solid Moral/Ethical Foundation Socially Adept Grounded in an individual’s self-concept

Present Day

• 4400 cadets from all 56 U.S. states and territories, as well as 36 foreign countries • Provides the Army with approximately 1000 second lieutenants each year • Of the newly minted 2LTs - West Point contributes approximately 20% , ROTC 60%, OCS 20%.

• As a minimum, graduates serve five years on active duty and three years in a reserve status 21

Typical Class (2015)

13,954 Applicants 4,344 Nominated 2,554 Qualified

1,249 Admitted

97 Valedictorians 122 Class Presidents 704 Team Captains 1,090 Varsity Letters 17% Women 10% Hispanics 11% African Americans 6.5% Asians 14 International Cadets 17 Combat Veterans 22

Three Developmental Programs

Academic (55%)

Core Academic Curriculum Majors Program Clubs Advanced Developmental Activities

Military (30%)

Summer Training Military Leadership Simon Center – PME2 Military Science Courses Clubs

Physical (15%)

Department of Physical Education Physical Testing Club Sports Company Athletics Character in Sports

(Note: % s reflects weighted averages of the Cadet Performance Score) 23

Army Officer Bachelor of Science Degree

Majors in Engineering Math and Science Humanities and Social Sciences

(Each with 8 to 12 Electives)

8 Military Science 7 Physical Education 3 English 4 History 2 Leadership 1 Philosophy/Ethics 2-4 Foreign Language* 3 Social Sciences 1 Law 4 Math 2 Chemistry 1 Physical Geography 2 Information Technology 2 Physics 3 Engineering Science/Design The Core

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Academic Development

The Academic Curriculum

First Year Chemistry x 2 History x 2 Math x 2 Information Technology English x 2 Psychology Second Year Physics x 2 Philosophy Math x 2 Foreign Language x 2 Economics American Politics Geography Third Year Leadership International Relations English Foreign Language x 2 Information Technology Engineering x 1 Electives in major x 3-5 Fourth Year Military History x 2 Law Engineering x 2 Electives in major x 5-8 Physical Education Military Science Physical Education Military Science Physical Education Military Science Physical Education Military Science 25

The Core Mathematics Program

MA103 COL Kobylski, MAJ Weld MA100 MAJ Jackson MA104 LTC Lunday, MAJ Trujillo MA101 MAJ Jackson MA153 LTC Outing, MAJ Swedberg MA205 COL Hartley, MAJ LaCasse MA206 LTC Jackson, MAJ Cummiskey MA104 LTC Lunday, MAJ Trujillo MA205 COL Hartley, MAJ LaCasse MA255 LTC Outing, MAJ Swedberg MA206 LTC Jackson, MAJ Cummiskey MA206 LTC Jackson, MAJ Cummiskey 26

Cadet Academic Schedule

Morning

0630 0705-0720 0730-1155 1210-1235

Afternoon

1250-1345 1355-1600 1615-1830 1830-1930

Evening

1930-2330 2330 2400

Event

Reveille Breakfast Classes Lunch Values Classes, Labs, Tests Classes Athletics, Drill and Ceremony Dinner Evening Study Period (ESP) Taps Lights Out

Faculty Blend of Excellence

Faculty Blend of Excellence

Teaching Scholarship Service Faculty Development

Rotating Military 55%

Cadet Development

Civilian Faculty 27%

Five Domains of Faculty Excellence

• Teaching – Number one priority – Not easy, not 9-5 • Scholarship - May start in 2 nd year • Service – Committees, the Department and the Community – Additional Department Responsibilities • Cadet Development – Professionally – TAC for a day, Academic Officer in Charge – Socially • Faculty Development - Usually starts in 2 nd year 29

Department Daily Routine • Mornings – Teaching • Afternoons – Lesson Preparation – Daily – Course Meetings – Tuesdays – Faculty development - Wed / Thurs • As Required – Additional Instruction (AI) – Grading

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Average Instructor Schedule

Morning

0630-0730 0715-0730 0730-1155 1155-1245

Event

Arrive Work Transition to Classroom Teaching Lunch

Afternoon

1250-1345 1345-1600 1600-UTC Cadet Development / Additional Instruction (AI) Meetings / Lesson Prep / AI / Scholarship Cadet Development / Lesson Prep

Evening

1930-2330 Academic Officer In-Charge (1-2 x Semester) 31

Supporting Cadets, the Academy, and Our Country

• National Leader in Mathematics Education – National Science Foundation Grants – Participation in the National Joint Meetings of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA)

“The West Point mathematics department is broadly viewed as one of the most creative mathematics departments in the country. The attention to student mathematical growth in problem solving, the thoughtful use of technology, and the use of applications is a national model that others could well emulate.”

Dr. Liz Teles, NSF • Junior Faculty are Combat Proven Leaders • Active Support to the Global War on Terrorism 32

Summer Planning

• 1 st Summer: FDW • 2 nd and 3 rd Summers (Approximately 10 weeks): Buckner, Research, or the Q-course, Course Prep, and leave • Final Summer: Summer School (STAP) and Out processing 33

D/Math Social Calendar

Date 3 Jul 18 Jul 15 or 16 Aug 15 Sep Sep – Nov Dec Dec Mar - Apr TBD May Event Location Welcome Picnic Boat Ride Softball Game / Welcome Back Picnic P6’s Quarters South Dock PX Fields Tailgate Pig Roast Other Tailgates Children’s Christmas Party TBD Various Math Adult Holiday Party / Progressive Dinner TBD Bowling Spring Formal Farewell Bash WP B. Alley TBD TBD

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Other Important Dates

13 Aug 13-17 Aug 18 Aug

20 Aug 16 Aug

CBT (Plebe) March Back Reorganization Week Acceptance Day Parade

First Day of Class for Cadets First Day, West Point Schools

2 Sep

5 Sep

22-25 Nov 8 Dec Band Concert at Trophy Point (1812 Overture)

First Day, O’Neill High School

Thanksgiving Leave Army-Navy Football Game 17-21 Dec Term End Exams

22 Dec - 3 Jan Winter Leave for Cadets 22 Dec - 6 Jan 22 Dec - 1 Jan

3-7 Jan

Winter Leave for West Point Schools Winter Leave for O’Neill High School

Winter Reorganization Week 8 Jan 8-10 March First Day of Classes for Second Term Plebe Parent Weekend 11-17 March 10 May 11-17 May 25 May 5 Jun Spring Leave (Cadets and West Point Schools) Last day of Classes for Cadets Term End Exams Graduation USMA Class of 2013 Last Day, West Point Schools 35

Math Spouse’s Activities

• Coffees • Bunko group • Lunch group • Various department committees

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Questions / Comments?