Bøger i MAA Textbooks serien

Offers a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to illustrate mathematical rigour.

Demonstrates that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem.

Provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All results are carefully, clearly, and rigorously proven. The exposition is very accessible.

Organised around carefully sequenced problems, Linear Algebra and Geometry will help students build both the tools and the habits that provide a solid basis for further study in mathematics. This volume uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Starting with Euclid's Elements, this book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered these two objects are analysed and highlighted.

Cultivates the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book.

Designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included - logic, sets, proof writing, relations, counting, number theory, and graph theory - in a manner that promotes development of a mathematical mindset.

An accessible, well-written textbook for an honours course in multivariable calculus for mathematically strong first- or second-year university students. The treatment carefully balances theoretical rigour, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles.

A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course.