The early twentieth century saw a significant effort to eliminate paradoxes in mathematics through Hilbert's program, aiming for a solid foundation for the discipline. However, this pursuit was dramatically challenged by Kurt Gödel, who demonstrated that achieving Hilbert's ambitions was impossible, revealing that contradictions are inherent in any mathematical system. This groundbreaking revelation reshaped the understanding of mathematics and its foundational principles.
Engaging conversations among characters from the Math Girls series introduce a range of trigonometry topics, from foundational sine and cosine functions to intriguing concepts like Lissajous curves and methods of deriving pi. Each chapter features review problems and answers, while an appendix presents challenging, open-ended questions for deeper exploration. As the third installment in the series, it aims to prepare students for advanced mathematics studies in a fun and accessible manner.
Originally published 2007 in Japan by Softbank Creative Corp., Tokyo.
Engaging with discrete math, this book explores intriguing topics such as the unique properties of prime numbers and clever methods for identifying multiples of 3 and 9. It delves into the concept of division remainders to tackle unusual problems and provides a comprehensive understanding of proof by mathematical induction. Designed for students, it combines fun with informative insights, making complex mathematical concepts accessible and enjoyable.
Focusing on the intriguing intersection of mathematics and computer science, this installment delves into the analysis of algorithms, particularly the benefits of incorporating randomness. It introduces Lisa, a new character, who joins her friends in exploring concepts like the Monty Hall problem, probability, and various algorithms including bubble sort and quicksort. The book also addresses complex topics such as big-O notation, linear transformations, and the P-versus-NP problem, making it a valuable resource for advanced students and educators interested in these fields.
Focusing on Évariste Galois, this installment of the Math Girls series explores his groundbreaking contributions to mathematics, particularly his work on polynomial equations and group theory. It delves into Galois's ingenious methods that revealed the impossibility of a quintic formula, while also covering related concepts like geometric constructions, the cubic formula, and symmetric polynomials. The narrative is designed for math enthusiasts from advanced high school students to educators, culminating in an examination of Galois's foundational paper on polynomial solutions.
This new series from the author of Math Girls focuses on essential skills needed for mastering advanced mathematics. It offers engaging content designed to help readers learn and review key concepts, making it an exciting resource for students looking to enhance their mathematical abilities.
Exploring the Poincaré Conjecture, this installment of the Math Girls series introduces readers to fundamental concepts of topology, starting with the historic Seven Bridges of Königsberg problem. Through the journey of Miruka and friends, readers encounter intriguing mathematical objects like the Möbius strip and Klein bottle, alongside essential topics such as homeomorphism, homotopy, and non-Euclidean geometries. The narrative also delves into differential equations, Fourier series, and concludes with Hamilton's Ricci flow, integral to Grigori Perelman's proof.