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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.<b>Contents:</b> <ul><li>Preface</li><li>About the Authors</li><li>Acknowledgments</li><li>Five Muffins, Three Students; Three Muffins, Five Students</li><li>One Student! Two Students! Some Basic Theorems!</li><li>Our Plan</li><li>Three Students! Four Students! The Floor–Ceiling Theorem!</li><li>Finding Procedures</li><li>The Half Method</li><li>A Formula for ƒ(<i>m</i>,5)</li><li>The Interval Method</li><li>The Midpoint Method</li><li>The Easy Buddy–Match Method</li><li>The Hard Buddy–Match Method</li><li>The Gap and Train Methods</li><li>Scott Huddleston's Method</li><li><b><i>Appendices:</i></b><ul><li>Math Notation</li><li>Fair Division</li><li>ƒ(<i>m</i>,<i>s</i>) Exists! ƒ(<i>m</i>,<i>s</i>) is Rational! ƒ(<i>m</i>,<i>s</i>) is Computable!</li></ul></li><li>References</li><li>Index</li></ul><br><b>Readership:</b> High school and undergraduate students, computer scientists, mathematicians, and anyone interested in recreational mathematics. Fair Division;Muffins;Combinatorics0<b>Key Features:</b><ul><li>Fun mathematics for high school students</li><li>Material on Muffin Mathematics appears here for the first time</li><li>Unique book, since most other recreational math books are essays on separate topics</li></ul> Получить ссылку |
Morv mustikamuffinitega
Автор: Joanne Fluke
Год издания:
Minnesota osariigis asuv Lake Edeni linnake on iga-aastase talvekarnevali ettevalmistustoode tuhinat tais ning Hannah Swensen peab vihtuma oma menukas kohvikus, Cookie Jaris, valmis terve kupsisemae. Kahju ainult, et ametliku talvekarnevali tordi valmistamise au oli langenud kuulsale elustiili eksperdile, Connie Macile, ja see oli Hannah’ arvates kull veidi nigel mote. Hannah kahtlustab, et Connie Mac on paljuski samasugune nagu need maiused, mida naine oma kaabeltelevisiooni kokasaates valmistab – magusad, ohulised ja horgutava valimusega, kuid toenaoliselt kibeda maitsega.Hannah’ kahtlused leiavad kinnitust, kui Connie Maci limusiin linna veereb. Ilmneb, et Kupsetav Kullake on kamandav, kergesti arrituv ja udini domineeriv. Viimane tilk langeb karikasse siis, kui Hannah saabub Cookie Jari ja leiab eest soestunud talvekarnevali tordi ning sahvris lebava Connie Maci, keda oli surmav look tabanud tapselt siis, kui ta oli napanud soomiseks uhe Hannah’ kuulsa mustikamuffini.Jargmisena teatab politsei, et sulgeb Hannah’ pagaritookojale ligipaasu, kuna tegu on kuriteopaigaga. Hannah on ilma ahjudeta pagar ja talvekarneval on kohe-kohe algamas. Hannah ainsaks voimaluseks on haududa valmis plaan oma pagariari paastmiseks – paljastada ise tapja…Sisaldab seitse originaalset kupsise- ja magustoiduretsepti, mida proovida!
Mathematical Mindsets. Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Автор: Джо Боулер
Год издания:
Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.
Problems and Solutions in Mathematical Finance. Equity Derivatives, Volume 2
Автор: Eric Chin
Год издания:
Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. Review the fundamentals of equity derivatives Work through problems from basic securities to advanced exotics pricing Examine numerical methods and detailed derivations of closed-form solutions Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.
Problems and Solutions in Mathematical Finance. Stochastic Calculus
Автор: Eric Chin
Год издания:
Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance. Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance. This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance. Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.
Quantitative Business Valuation. A Mathematical Approach for Today's Professionals
Автор: Jay Abrams B.
Год издания:
Praise for the First Edition of Quantitative Business Valuation A Mathematical Approach for Today's Professionals «Jay Abrams' book is close to the equivalent of several graduate dissertations rolled into one book. For each topic (covered), he presents a scholarly summary of past research, new empirical research of his own, and his conclusions. It is a well-documented contribution to in-depth understanding of important business valuation issues, and should not be overlooked by the serious practitioner.» —Shannon Pratt, DBAManaging Director, Willamette Management AssociatesCoauthor, Valuing a Business «A must-read for the serious business appraiser.» —Jay E. Fishman, ASA, CBAPresident, Financial Research, Inc. «The problem of simplified valuation procedures and coherent theory still remains complex and is ever evolving. Jay Abrams deals very effectively with this complexity through the use of mathematical formulas. Input to his models is explained with clarity and effectiveness, which adds to the overall value of this advanced text on business valuation.» —Terry A. Isom, Chairman, National Association of Certified Valuation Analysts «Jay Abrams' book strives to provide mathematical modeling for what practitioners often do by reasoning alone. This book is a must-read for practitioners who are searching for additional techniques for dealing with some of business valuation's imponderables.» —David M. Bishop, FIBA, BVAL, ASA, MCBAPresident, American Business Appraisers, Inc. «Jay Abrams' book will not only challenge the top theoreticians in the field; his step-by-step explanations will make advanced quantitative techniques available to the many appraisers who are not capable of independently creating the underlying mathematical analysis.» —Kent Osborne, ASAChairman, Editorial Review Board of the American Society of Appraisers «While a proliferation of business valuation treatises and guides exists in the market, most are very general in nature and do nothing more than rehash fundamental concepts. I am unaware of any author who has stepped into the unknown as Jay Abrams has and compiled and developed a treatise of extremely useful analytical tools for the serious valuator.» —Robert J. Grossman, CPA/ABV, ASA, CVAPartner, Grossman Yanak & Ford «Jay Abrams develops unusual approaches which merit consideration when 'cookie cutter' methodologies are inadequate. This manuscript contributes to the dialogue among practitioners and strengthens the theoretical foundations of business valuation.» —Herbert T. SpiroPresident, American Valuation Group, Inc. «There is no question about it, the use of rigorous quantitative methods is the cure for subjective valuation analysis. This book not only satisfies this need—which has grown considerably in recent years—but is chock-full of new tools that have been carefully developed.» —Edward MurrayValuation Partner, Arthur Andersen, LLP
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