Suppose you have five muffins that you want to divide and give to Alice, Bob, and Carol. You want each of them to get 5/3. You could cut each muffin into 1/3-1/3-1/3 and give each student five 1/3-sized pieces. But Alice objects! She has large hands! She wants everyone to have pieces larger than 1/3.Is there a way to divide five muffins for three students so that everyone gets 5/3, and all pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a division where the smallest piece is 5/12. Is there a better division? Spoiler alert: No.In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up m muffins for s students so that everyone gets m/s muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.This problem takes us through much mathematics of interest, for example, combinatorics and optimization theory. However, the math is elementary enough for an advanced high school student.
In 1840, prosperous farming families left North and South Carolina to trek in covered wagons to the unsettled Arkansas River Valley. Absorbing to read and rich with colorful detail, this is a story of the peopling of the western frontier and the ways in which hardship, religion, and a shared past bound settlers together into a lasting community.
Few North Carolinians have been as well known or as widely respected as William Friday (1920-2012). The former president of the University of North Carolina remained prominent in public affairs in the state and elsewhere throughout his life and ranked as one of the most important American university presidents of the post-World War II era. In the second edition of this comprehensive biography, William Link traces Friday's long and remarkable career and commemorates his legendary life. Friday's thirty years as president of the university, from 1956 to 1986, spanned the greatest period of growth for higher education in American history, and Friday played a crucial role in shaping the sixteen-campus UNC system during that time. Link also explores Friday's influential work on nationwide commissions, task forces, and nonprofits, and in the development of the National Humanities Center and the growth of Research Triangle Park. This second edition features a new introduction and epilogue to enrich the narrative, charting the later years of Friday's career and examining his legacy in North Carolina and nationwide.
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