A “bridge” course can help ensure a smooth transition as a student transitions from lower-division calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and other related topics. This course’s textbook, Introduction to Mathematical Structures and Proofs, is also suitable for independent study. A variety of fundamental mathematical structures are introduced in this book. It also looks at the tricky balancing act between rigor and intuition and the adaptable thinking needed to prove a nontrivial result. In short, this book aims to increase the reader’s mathematical maturity.
A section on graph theory, many new parts on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers are among the new content in this second edition (including a section on the arithmetic of the Gaussian integers). For instructors using the material for a course, solutions to the problems with even numbers are accessible on springer.com.