Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.

This fifth entry in the highly acclaimed Math Girls series focuses on the mathematics of Évariste Galois, the nineteenth-century wunderkind who revolutionized mathematics with work he performed while still a teenager. Mathematicians before him had discovered solutions to general second-, third-, and fourth-degree equations, but a similar quintic formula that would allow knowing the solutions to any fifth-degree equation had eluded mathematicians for centuries. Through his ingenious approach of bridging the worlds of groups and fields, young Galois not only showed that such a formula was impossible, he newly developed group theory and the branch of mathematics that today bears his name. Join Miruka and friends to see how Galois developed his theory, along with related topics such as geometric constructions and the angle trisection problem, derivation of the cubic formula, reducible and irreducible polynomials, group theory and field theory, symmetric polynomials, roots of unity, sets and cosets, cyclotomic polynomials, vector spaces, extension fields, and symmetric groups. The book concludes with a tour through Galois's first paper, in which he describes for the first time the necessary and sufficient conditions for a polynomial to be algebraically solved using radicals. Math Girls 5: Galois Theory has something for anyone interested in mathematics, from advanced high school to college students and educators.

This fourth entry in the highly acclaimed Math Girls series focuses on the mathematics of computer science and analysis of algorithms. Algorithms generally strive to take the shortest route to their goal, so how is it that adding a random element to how they work can improve their performance? Further, how can we apply mathematics to quantitatively compare the performance of different algorithms? Is it possible to predict the limits of how well an algorithm can perform, without coding and running it on an actual computer? New math girl and talented programmer Lisa will join Miruka and friends to explore these and other questions, applying what they learn to well-known algorithms such as bubble sort and quicksort. Other topics explored in this book include the Monty Hall problem, permutations and combinations, Pascal's triangle, the definition of probability, sample spaces, probability distributions, random variables, expected values, big-O notation, matrices, linear transformations, matrix diagonalization, random walks, the 3-SAT problem, and the P-versus-NP problem. Math Girls 4: Randomized Algorithms has something for anyone interested in mathematics and computer science, from advanced high school students to college students and educators.

From the author of Math Girls comes an exciting new series for learning and reviewing important skills for taking on advanced mathematics This first volume, Math Girls Talk About Equations and Graphs, develops topics such as using variables in equations, polynomials, setting up systems of equations, proportions and inverse proportions, the relation between equations and their graphs, parabolas, intersections, and tangent lines. These topics are introduced through conversations between the characters from Math Girls, offering a fun way to learn this serious content. Each chapter comes with review problems and answers, and an appendix gives more challenging, open-ended problems for learners wanting to push the limits of their understanding. This book is most suited to middle- or high-school students who have learned basic algebra, or older readers who want to brush up on forgotten math skills. This series came about through requests from readers who enjoyed the excitement of learning aspects of the Math Girls series, but found themselves unprepared to keep up with the mathematical content. We hope that the books in this series will help young mathematicians firm up vital math skills that will allow them to excel in more advanced studies.

This sixth entry in the highly acclaimed Math Girls series focuses on the Poincaré Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of Königsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the Möbius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincaré Conjecture. Math Girls 6: The Poincaré Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.

Math Girls Talk About Trigonometry explores a variety of fun and informative topics in trigonometry, from basics like defining the sine and cosine functions, to less frequently seen topics like Lissajous curves and different ways of deriving the value of pi. These topics are introduced through conversations between the characters from the Math Girls series, offering a fun way to learn this serious content. Each chapter comes with review problems and answers, and an appendix gives more challenging, open-ended problems for readers wanting to push the limits of their understanding. This book is the third in a series aimed at preparing students for advanced mathematics studies.

What's the big deal about Fermat's last theorem? Yuri asked. It's famous, I said. So simple anyone can understand it, but it took centuries for mathematicians to prove it's true. * * * With a note scribbled in the margin of a book in the 1600s, Fermat set in motion centuries of effort spent unraveling this enigma. It would require 358 years and the development of entirely new fields of mathematics to provide a definitive solution to what is now recognized as one of the greatest mathematical problems of all time. In this second book in the Math Girls series, you'll join Miruka, Tetra, and new math girl Yuri in explorations of number theory, abstract algebra, modular arithmetic, methods of proof, and other intriguing mathematical topics, leading up to a whirlwind tour of the modern proof of Fermat's last theorem. Math Girls 2: Fermat's Last Theorem has something for anyone interested in mathematics, from advanced high school students to college math majors and educators. Praise for Math Girls ...the type of book that might inspire teens to realize how much interesting mathematics there is in the world-not just the material that is forced upon them for some standardized test. Recommended -CHOICE: Current Reviews for Academic Libraries Imagine the improbable: high-school students getting together on their own - not in a Math Club or Math Circle, not in preparation for any Math Olympiad or regular test, not on the advice of any of their teachers, not as part of any organized program - to talk about pure math, math more interesting than the math found in their textbooks. The three students in this book do that for the sheer love of it. That to me is the beauty and fascination of this novel for young people, mostly young people interested in math. -Marion Cohen, Arcadia University, MAA Reviews Sometimes the math goes over your head-or at least my head. But that hardly matters. The focus here is the joy of learning, which the book conveys with aplomb. -Daniel Pink, NYT and WSJ best-selling author of Drive and A Whole New Mind if you have a...teenager who's really into math, this is a really interesting choice -Carol Zall, Public Radio International, The World Math Girls provides a fun and engaging way to learn and review mathematical concepts...the characters' joy as they explore and discover new and old ideas is infectious. -review, Experiments in Manga blog

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Gödel stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Gödel's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Gödel's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Gödel's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators.

Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Gödel stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Gödel's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Gödel's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Gödel's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators.

Math Girls Talk About Integers introduces students to a variety of fun and informative topics in discrete math, including curious features of the prime numbers, tricks for checking for multiples of 3 and 9 (and why those tricks work ), using division remainders to solve some unusual problems, and an in-depth look at proof by mathematical induction. These topics are introduced through conversations between the characters from Math Girls, offering a fun way to learn this serious content. Each chapter comes with review problems and answers, and an appendix gives more challenging, open-ended problems for readers wanting to push the limits of their understanding.

This fourth entry in the highly acclaimed Math Girls series focuses on the mathematics of computer science and analysis of algorithms. Algorithms generally strive to take the shortest route to their goal, so how is it that adding a random element to how they work can improve their performance? Further, how can we apply mathematics to quantitatively compare the performance of different algorithms? Is it possible to predict the limits of how well an algorithm can perform, without coding and running it on an actual computer? New math girl and talented programmer Lisa will join Miruka and friends to explore these and other questions, applying what they learn to well-known algorithms such as bubble sort and quicksort. Other topics explored in this book include the Monty Hall problem, permutations and combinations, Pascal's triangle, the definition of probability, sample spaces, probability distributions, random variables, expected values, big-O notation, matrices, linear transformations, matrix diagonalization, random walks, the 3-SAT problem, and the P-versus-NP problem. Math Girls 4: Randomized Algorithms has something for anyone interested in mathematics and computer science, from advanced high school students to college students and educators.

This fifth entry in the highly acclaimed Math Girls series focuses on the mathematics of Évariste Galois, the nineteenth-century wunderkind who revolutionized mathematics with work he performed while still a teenager. Mathematicians before him had discovered solutions to general second-, third-, and fourth-degree equations, but a similar quintic formula that would allow knowing the solutions to any fifth-degree equation had eluded mathematicians for centuries. Through his ingenious approach of bridging the worlds of groups and fields, young Galois not only showed that such a formula was impossible, he newly developed group theory and the branch of mathematics that today bears his name. Join Miruka and friends to see how Galois developed his theory, along with related topics such as geometric constructions and the angle trisection problem, derivation of the cubic formula, reducible and irreducible polynomials, group theory and field theory, symmetric polynomials, roots of unity, sets and cosets, cyclotomic polynomials, vector spaces, extension fields, and symmetric groups. The book concludes with a tour through Galois's first paper, in which he describes for the first time the necessary and sufficient conditions for a polynomial to be algebraically solved using radicals. Math Girls 5: Galois Theory has something for anyone interested in mathematics, from advanced high school to college students and educators.

This sixth entry in the highly acclaimed Math Girls series focuses on the Poincaré Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of Königsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the Möbius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincaré Conjecture. Math Girls 6: The Poincaré Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.

From the author of Math Girls comes an exciting new series for learning and reviewing important skills for taking on advanced mathematics This first volume, Math Girls Talk About Equations and Graphs, develops topics such as using variables in equations, polynomials, setting up systems of equations, proportions and inverse proportions, the relation between equations and their graphs, parabolas, intersections, and tangent lines. These topics are introduced through conversations between the characters from Math Girls, offering a fun way to learn this serious content. Each chapter comes with review problems and answers, and an appendix gives more challenging, open-ended problems for learners wanting to push the limits of their understanding. This book is most suited to middle- or high-school students who have learned basic algebra, or older readers who want to brush up on forgotten math skills. This series came about through requests from readers who enjoyed the excitement of learning aspects of the Math Girls series, but found themselves unprepared to keep up with the mathematical content. We hope that the books in this series will help young mathematicians firm up vital math skills that will allow them to excel in more advanced studies.

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt G del stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. G del's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of G del's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: G del's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators.

This fourth entry in the highly acclaimed Math Girls series focuses on the mathematics of computer science and analysis of algorithms. Algorithms generally strive to take the shortest route to their goal, so how is it that adding a random element to how they work can improve their performance? Further, how can we apply mathematics to quantitatively compare the performance of different algorithms? Is it possible to predict the limits of how well an algorithm can perform, without coding and running it on an actual computer? New math girl and talented programmer Lisa will join Miruka and friends to explore these and other questions, applying what they learn to well-known algorithms such as bubble sort and quicksort. Other topics explored in this book include the Monty Hall problem, permutations and combinations, Pascal's triangle, the definition of probability, sample spaces, probability distributions, random variables, expected values, big-O notation, matrices, linear transformations, matrix diagonalization, random walks, the 3-SAT problem, and the P-versus-NP problem. Math Girls 4: Randomized Algorithms has something for anyone interested in mathematics and computer science, from advanced high school students to college students and educators.

This sixth entry in the highly acclaimed Math Girls series focuses on the Poincaré Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of Königsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the Möbius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincaré Conjecture. Math Girls 6: The Poincaré Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.

What's the big deal about Fermat's last theorem? Yuri asked. It's famous, I said. So simple anyone can understand it, but it took centuries for mathematicians to prove it's true. * * * With a note scribbled in the margin of a book in the 1600s, Fermat set in motion centuries of effort spent unraveling this enigma. It would require 358 years and the development of entirely new fields of mathematics to provide a definitive solution to what is now recognized as one of the greatest mathematical problems of all time. In this second book in the Math Girls series, you'll join Miruka, Tetra, and new math girl Yuri in explorations of number theory, abstract algebra, modular arithmetic, methods of proof, and other intriguing mathematical topics, leading up to a whirlwind tour of the modern proof of Fermat's last theorem. Math Girls 2: Fermat's Last Theorem has something for anyone interested in mathematics, from advanced high school students to college math majors and educators. Praise for Math Girls! ...the type of book that might inspire teens to realize how much interesting mathematics there is in the world-not just the material that is forced upon them for some standardized test. Recommended -CHOICE: Current Reviews for Academic Libraries Imagine the improbable: high-school students getting together on their own - not in a Math Club or Math Circle, not in preparation for any Math Olympiad or regular test, not on the advice of any of their teachers, not as part of any organized program - to talk about pure math, math more interesting than the math found in their textbooks. The three students in this book do that for the sheer love of it. That to me is the beauty and fascination of this novel for young people, mostly young people interested in math. -Marion Cohen, Arcadia University, MAA Reviews Sometimes the math goes over your head-or at least my head. But that hardly matters. The focus here is the joy of learning, which the book conveys with aplomb. -Daniel Pink, NYT and WSJ best-selling author of Drive and A Whole New Mind if you have a...teenager who's really into math, this is a really interesting choice -Carol Zall, Public Radio International, The World Math Girls provides a fun and engaging way to learn and review mathematical concepts...the characters' joy as they explore and discover new and old ideas is infectious. -review, Experiments in Manga blog

Math Girls Talk About Trigonometry explores a variety of fun and informative topics in trigonometry, from basics like defining the sine and cosine functions, to less frequently seen topics like Lissajous curves and different ways of deriving the value of pi. These topics are introduced through conversations between the characters from the Math Girls series, offering a fun way to learn this serious content. Each chapter comes with review problems and answers, and an appendix gives more challenging, open-ended problems for readers wanting to push the limits of their understanding. This book is the third in a series aimed at preparing students for advanced mathematics studies.