A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning

Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.

This essential book:
* Clearly explains the relationship between definitions, conjectures, theorems, corollaries,...

The essentials of point-set topology, complete with motivation and numerous examples

Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.

Along with the standard point-set topology topics--connected...

Praise for the first edition

"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries."
-CHOICE

As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing-with extensive use in computing science,...

A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of...

Praise for the First Edition

." . .recommended for the teacher and researcher as well as for graduate students. In fact, it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second...

Praise for the First Edition:

"This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds."
--SIAM Review

A practical introduction to nonlinear PDEs and their real-world applications

Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers...

Requiring minimal background knowledge from the reader, this book provides a sense of unity in the subject's development and fully explains the essential concepts, outlining the logic behind the steps to familiarise the reader with the theories. All the important topics are covered, from linear spaces to the major theorems.

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance

Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems.

Unifying perspectives are provided throughout the text, bringing together and categorizing different types of...

Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry's history to illustrate how crucial proof writing is to the job of a mathematician.

Mathematical Methods in Biology uniquely covers both deterministic and probabilistic models, including algorithms in the MATLAB platform. The book focuses mostly in one area of the life sciences, focusing mainly on theoretical ecology.