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A resource for introductory calculus courses. It provides incorrect mathematical statements which require students to create counterexamples to disprove them.
An introduction to complex analysis, covering the standard course material and additional topics. This is an ideal book for a first course in complex analysis: for advanced undergraduates or graduate students. It includes both exercises with detailed solutions to aid understanding, and those without solutions as an additional teaching tool.
Combinatorics is the mathematics of counting. This text presents the topics covered in undergraduate courses in combinatorics and advanced discrete mathematics, as well as in some introductory graduate courses. Uniquely, it features over 350 reading questions that provide checkpoints for learning and prepare the reader for the end-of-section exercises.
A collection of articles introducing the core ideas of calculus. A resource for teachers of secondary school and undergraduate students.
A thorough guide to Euclidean geometry with a unique emphasis and methodology, for use as an undergraduate textbook.
An introductory guide to elementary number theory for advanced undergraduates and graduates.
An exploration of Voltaire's Micromegas which presents the mathematics behind the polar expedition and suggests some answers to Voltaire's riddle.
This book is arranged to show the development of the different branches of mathematics over time and contains many illustrations to support the text. In all, a short, innovative and easy-to-read history of mathematics.
What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society.
A concise guide to support an undergraduate real analysis course.
Mathematical Interest Theory gives an introduction to how investments vary over time, and this book provides a solid foundation for readers embarking on actuarial careers. It is among the recommended reading options for the Society of Actuaries/Casualty Actuarial Society FM/2 exam.
A collection of ingenious problems and their solutions from elementary mathematics.
Developed over a period of many years of working with students at the University of Texas, Austin, this book cultivates mathematical creativity and independence. The book is self contained, and assumes little formal mathematical background on the part of the reader.
This collection of sixteen original essays is the first to explore a range of new developments in the philosophy of mathematics, in a way mathematicians will understand. Coverage includes emerging questions in the field as well as recent thinking on classical ideas, all relevant to the teaching of mathematics.
A collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.
A collection of problems posed by Murray Klamkin over his career.
A compilation of 325 problems and solutions for high school students. A valuable resource for any mathematics teacher.
A compilation of 350 problems and solutions for early high school students. A valuable resource for any mathematics teacher.
A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.
This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. It is ideal for those interested in the history of mathematics.
A guide to the hidden byways of algebra, calculus and geometry, for the seasoned mathematical traveller.
A set of seemingly difficult problems that have simple, elegant solutions, thereby revealing the beauty of mathematics.
A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques. This book can be used as a textbook for an undergraduate course on calculus or as a reference for self-study.
Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.
This book studies the differential geometry of surfaces and aims to help students make the transition from the standard university curriculum to a type of mathematics that is a unified whole, by mixing geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences.
The classic book - back in print! Demonstrating the profound connections that join mathematics to the history of philosophy and of Western civilization, and containing nuggets collected from number theory, geometry, science, etc. We see the true purpose of mathematics - 'To delight the mind and help us understand the world.'
An anthology of articles ideal for use as a textbook supplement on a number theory course.
Describes techniques for solving problems in maxima and minima other than the methods of calculus.
A remarkable collection, which discusses not only Euler's well-known achievements in pure mathematics, but also his contributions in many other areas, from astronomy to music. Even readers already familiar with Euler and his work will find here much to enhance their appreciation of this extraordinary scientist and human being.
Uses the history of mathematics to facilitate active learning in the mathematics classroom.
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