Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve
Originally published in 1936, this textbook was primarily designed for students of applied mathematics to provide a solid foundation for studies on the practical side of the subject. The book, whilst carefully keeping the groundwork of pure mathematics, covering key elementary aspects of the subject, such as quadratic equations, in the main explores the 'generally understood technical allusions, illustrations, and graded applications'. The book provides multiple useful and challenging exercises and is shaped and established around the syllabus at the time of publication. Chapters are broad in scope, detailed and clearly written; chapter titles include, 'Curved graphs', 'Trigonometry ratios and exercises' and 'Loci'. Aiming to achieve a 'logical sequence of leading theorems, clear deductions and concise, practical applications', this textbook will be of great value to students of engineering mathematics as well as to anyone with an interest in physics, materials science and the history
A deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Originally published in 1911, this practical textbook of exercises was primarily aimed at school students and was intended to provide an accessible yet challenging 'informal course' on solid geometry for classwork, homework and revision. The book is divided into three principal sections: chapters 1-6 discuss the main properties of lines and planes, chapters 7-13 examine properties of the principal solid figures, including mensuration, whilst chapters 14-16 consider coordinates in three dimensions, plan, elevation and perspective, also known as descriptive geometry. The book covers key theorems, whilst cataloguing useful geometry questions focused on developing a broad understanding of the subject. Intended as educational rather than technical material and a practical, systematic supplement to school lessons, this book will be of great value to scholars of mathematics as well as to anyone with an interest in the history of education.
