The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.

There is growing interest in undergraduate research, given its benefits to students, faculty members, and the institution. For higher education scholars, faculty, and administrators, this book logically synthesizes the literature to demonstrate its impact on facilitation of learning and engagement and to chart a course for expanding and improving these opportunities. This book provides a comprehensive overview of undergraduate research as a "high-impact practice" in postsecondary education, from its theoretical underpinnings and research-base, to student participation and faculty incentives. This important resource offers analysis of the current state of undergraduate research, explores challenges and unresolved questions affecting undergraduate research, and provides implications for research and practice.

Although many articles and books have been written about conducting research with undergraduates, there is a dearth of research on the process of publishing with undergraduates. Thus, in this research topic, we assembled a collection of 43 articles from 98 researchers worldwide who are passionate about—and have had success in—publishing high quality peer-reviewed journal articles with undergraduates. The diverse articles represent a wide range of practices to help researchers publish with undergraduates, including structuring the curriculum to promote undergraduate research and publication, optimizing research experiences for undergraduates, training students in implementing advanced techniques, accessing special populations, or conducting research in off-campus settings, addressing institutional and career challenges for faculty, and increasing inclusion and diversity. Each article provides a unique and diverse perspective that nevertheless resonates across contexts and situations. We hope that the ideas, models, techniques, and practices in these articles will motivate and inspire readers to begin, continue, or rethink how they engage undergraduates in publishable research; we also hope to stimulate empirical and quantitative research on the effectiveness of these ideas, models, techniques, and practices.

This research aims to identify the effects that an undergraduate research journal, specifically the James Madison Undergraduate Research Journal (JMURJ), has on its past and present student editors' career readiness. I began by exploring the existing literature surrounding undergraduate research, undergraduate research journals, and other studies done to measure the effects that these undergraduate research journals have on students at various institutions. Then, I conducted a survey on current and past members of the JMURJ editorial board, using a specific set of questions to determine if an undergraduate research journal such as the one at James Madison University was assisting/had already assisted students in recognizing their career skillsets. Using the feedback from this survey, I was able to identify common trends and their implications, as well as potential limitations to this study. Due to the highly specific nature of undergraduate research journals and their localized environments, the methodology used for this research is not meant to be replicated by other journals, but rather used as a resource for the current editorial board members of JMURJ. The current study also serves as a current assessment of how and how well the JMURJ approach serves students as an undergraduate research journal, so that it can be of use to JMURJ, other board members and journals, and to other universities committed to undergraduate research.

Speaking directly to the growing importance of research experience in undergraduate mathematics programs, this volume offers suggestions for undergraduate-appropriate research projects in mathematical and computational biology for students and their faculty mentors. The aim of each chapter is twofold: for faculty, to alleviate the challenges of identifying accessible topics and advising students through the research process; for students, to provide sufficient background, additional references, and context to excite students in these areas and to enable them to successfully undertake these problems in their research. Some of the topics discussed include: • Oscillatory behaviors present in real-world applications, from seasonal outbreaks of childhood diseases to action potentials in neurons • Simulating bacterial growth, competition, and resistance with agent-based models and laboratory experiments • Network structure and the dynamics of biological systems • Using neural networks to identify bird species from birdsong samples • Modeling fluid flow induced by the motion of pulmonary cilia Aimed at undergraduate mathematics faculty and advanced undergraduate students, this unique guide will be a valuable resource for generating fruitful research collaborations between students and faculty.