A Bridge to Higher Mathematics

The goal of this unique text is to provide an ＂experience＂ that would facilitate a better transition for mathematics majors to the advanced proof-based courses required for their major.

If you feel like you love mathematics but hate proofs, this book is for you. The change from example-based courses such as Introductory Calculus to the proof-based courses in the major is often abrupt, and some students are left with the unpleasant feeling that a subject they loved has turned into material they find hard to understand.

The book exposes students and readers to some fundamental content and essential methods of constructing mathematical proofs in the context of four main courses required for the mathematics major - probability, linear algebra, real analysis, and abstract algebra.

Following an optional foundational chapter on background material, four short chapters, each focusing on a particular course, provide a slow-paced but rigorous introduction. Students get a preview of the discipline, its focus, language, mathematical objects of interest, and methods of proof commonly used in the field. The organization of the book helps to focus on the specific methods of proof and main ideas that will be emphasized in each of the courses.

The text may also be used as a review tool at the end of each course and for readers who want to learn the language and scope of the broad disciplines of linear algebra, abstract algebra, real analysis, and probability, before transitioning to these courses.

James R. Kirkwood holds a Ph.D. in mathematics from the University of Virginia. He has authored and co-authored twenty published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics, many published by CRC Press. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory. He is the recipient of many awards for his teaching and research, including the Outstanding Faculty Award of the State Council of Higher Education for Virginia--the Commonwealth’s highest honor for faculty at Virginia’s public and private colleges and universities.

Raina S. Robeva is a Professor of Mathematics at Randolph-Macon College in Virginia. She holds a Ph.D. in mathematics from the University of Virginia and is the lead author/editor of several textbooks and volumes in mathematical biology. She has led numerous educational and professional development initiatives at the interface of mathematics and biology sponsored by NSF, NIH, and MAA among others. Robeva is the founding Chief Editor of Frontiers in Systems Biology, a specialty journal in the Frontiers portfolio of open-access publications. In 2014 she was awarded the Outstanding Faculty Award of the State Council of Higher Education for Virginia.