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'Points, questions, stories, and occasional rants introduce the 24
chapters of this engaging volume. With a focus on mathematics and
peppered with a scattering of computer science settings, the
entries range from lightly humorous to curiously thought-provoking.
Each chapter includes sections and sub-sections that illustrate and
supplement the point at hand. Most topics are self-contained within
each chapter, and a solid high school mathematics background is all
that is needed to enjoy the discussions. There certainly is much to
enjoy here.'CHOICEEver notice how people sometimes use math words
inaccurately? Or how sometimes you instinctively know a math
statement is false (or not known)?Each chapter of this book makes a
point like those above and then illustrates the point by doing some
real mathematics through step-by-step mathematical techniques.This
book gives readers valuable information about how mathematics and
theoretical computer science work, while teaching them some actual
mathematics and computer science through examples and exercises.
Much of the mathematics could be understood by a bright high school
student. The points made can be understood by anyone with an
interest in math, from the bright high school student to a Field's
medal winner.
'Points, questions, stories, and occasional rants introduce the 24
chapters of this engaging volume. With a focus on mathematics and
peppered with a scattering of computer science settings, the
entries range from lightly humorous to curiously thought-provoking.
Each chapter includes sections and sub-sections that illustrate and
supplement the point at hand. Most topics are self-contained within
each chapter, and a solid high school mathematics background is all
that is needed to enjoy the discussions. There certainly is much to
enjoy here.'CHOICEEver notice how people sometimes use math words
inaccurately? Or how sometimes you instinctively know a math
statement is false (or not known)?Each chapter of this book makes a
point like those above and then illustrates the point by doing some
real mathematics through step-by-step mathematical techniques.This
book gives readers valuable information about how mathematics and
theoretical computer science work, while teaching them some actual
mathematics and computer science through examples and exercises.
Much of the mathematics could be understood by a bright high school
student. The points made can be understood by anyone with an
interest in math, from the bright high school student to a Field's
medal winner.
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.
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.
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