This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.
A Mathematician's Practical Guide to Mentoring Undergraduate Research is a complete how-to manual on starting an undergraduate research program. Readers will find advice on setting appropriate problems, directing student progress, managing group dynamics, obtaining external funding, publishing student results, and a myriad of other relevant issues. The authors have decades of experience and have accumulated knowledge that other mathematicians will find extremely useful.
'The collection transcends the traditional institutional division lines (private, public, large, small, research, undergraduate, etc.) and has something to offer for readers in every realm of academia. The collection challenges the reader to think about how to implement and improve undergraduate research experiences, what such experiences mean to students and faculty, and how such experiences can take a permanent place in the modern preparation of undergraduate mathematics and STEM majors. The book is an open invitation to learn about what has worked and what hasn’t in the inspiration, and has the potential to ignite initiatives with long-lasting benefits to students and faculty nationwide.' See Full ReviewNotices of the AMS“The US National Science Foundation (NSF) Research Experiences for Undergraduates (REU) program in mathematics is now 25 years old, and it is a good time to think about what it has achieved, how it has changed, and where this idea will go next.”This was the premise of the conference held at Mt. Holyoke College during 21-22 June, 2013, and this circle of ideas is brought forward in this volume. The conference brought together diverse points of view, from NSF administrators, leaders of university-wide honors programs, to faculty who had led REUs, recent PhDs who are expected to lead them soon, and students currently in an REU themselves. The conversation was so varied that it justifies a book-length attempt to capture all that was suggested, reported, and said. Among the contributors are Ravi Vakil (Stanford), Haynes Miller (MIT), and Carlos Castillo-Chavez (Arizona, President's Obama Committee on the National Medal of Science 2010-2012).This book should serve not only as a collection of speakers' notes, but also as a source book for anyone interested in teaching mathematics and in the possibility of incorporating research-like experiences in mathematics classes at any level, as well as designing research experiences for undergraduates outside of the classroom.
The first student-centred guide on how to write projects and case studies in mathematics, with particular attention given to working in groups (something maths undergraduates have not traditionally done). With half of all universities in the UK including major project work of significant importance, this book will be essential reading for all students on the second or final year of a mathematics degree, or on courses with a high mathematical content, for example, physics and engineering.
Descriptions of summer research programs: The AIM REU: Individual projects with a common theme by D. W. Farmer The Applied Mathematical Sciences Summer Institute by E. T. Camacho and S. A. Wirkus Promoting research and minority participantion via undergraduate research in the mathematical sciences. MTBI/SUMS-Arizona State University by C. Castillo-Chavez, C. Castillo-Garsow, G. Chowell, D. Murillo, and M. Pshaenich Summer mathematics research experience for undergraduates (REU) at Brigham Young University by M. Dorff Introducing undergraduates for underrepresented minorities to mathematical research: The CSU Channel Islands/California Lutheran University REU, 2004-2006 by C. Wyels The REUT and NREUP programs at California State University, Chico by C. M. Gallagher and T. W. Mattman Undergraduate research at Canisius. Geometry and physics on graphs, summer 2006 by S. Prassidis The NSF REU at Central Michigan University by S. Narayan and K. Smith Claremont Colleges REU, 2005-07 by J. Hoste The first summer undergraduate research program at Clayton State University by A. Lanz Clemson REU in computational number theory and combinatorics by N. Calkin and K. James Research with pre-mathematicians by C. R. Johnson Traditional roots, new beginnings: Transitions in undergraduate research in mathematics at ETSU by A. P. Godbole Undergraduate research in mathematics at Grand Valley State University by S. Schlicker The Hope College REU program by T. Pennings The REU experience at Iowa State University by L. Hogben Lafayette College's REU by G. Gordon LSU REU: Graphs, knots, & Dessins in topology, number theory & geometry by N. W. Stoltzfus, R. V. Perlis, and J. W. Hoffman Mount Holyoke College mathematics summer research institute by M. M. Robinson The director's summer program at the NSA by T. White REU in mathematical biology at Penn State Erie, The Behrend College by J. P. Previte, M. A. Rutter, and S. A. Stevens The Rice University Summer Institute of Statistics (RUSIS) by J. Rojo The Rose-Hulman REU in mathematics by K. Bryan The REU program at DIMACS/Rutgers University by B. J. Latka and F. S. Roberts The SUNY Potsdam-Clarkson University REU program by J. Foisy The Trinity University research experiences for undergraduates in mathematics program by S. Chapman Undergraduate research in mathematics at the University of Akron by J. D. Adler The Duluth undergraduate research program 1977-2006 by J. A. Gallian Promoting undergraduate research in mathematics at the University of Nebraska-Lincoln by J. L. Walker, W. Ledder, R. Rebarber, and G. Woodward REU site: Algorithmic combinatorics on words by F. Blanchet-Sadri Promoting undergraduate research by T. Aktosun Research experiences for undergraduates inverse problems for electrical networks by J. A. Morrow Valparaiso experiences in research for undergraduates in mathematics by R. Gillman and Z. Szaniszlo Wabash Summer Institute in Algebra (WSIA) by M. Axtell, J. D. Phillips, and W. Turner THe SMALL program at Williams College by C. E. Silva and F. Morgan Industrial mathematics and statistics research for undergraduates at WPI by A. C. Heinricher and S. L. Weekes Descriptions of summer enrichment programs: Twelve years of summer program for women in mathematics-What works and why? by M. M. Gupta Research experience for undergraduates in numerical analysis and scientific computing: An international program by G. Fairweather and B. M. Moskal Articles: The Long-Term Undergraduate Research (LURE) model by S. S. Adams, J. A. Davis, N. Eugene, K. Hoke, S. Narayan, and K. Smith Research with students from underrepresented groups by R. Ashley, A. Ayela-Uwangue, F. Cabrera, C. Callesano, and D. A. Narayan Research classes at Gettysburg College by B. Bajnok Research in industrial projects for students: A unique undergraduate experience by S. Beggs What students say about their REU experience by F. Connolly and J. A. Gallian Diversity issues in undergraduate research by R. Cortez, D. Davenport, H
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.
"When you are a young mathematician, graduate school marks the first step toward a career in mathematics. During this period, you will make important decisions which will affect the rest of your career. This book is a detailed guide to help you navigate graduate school and the years that follow. -- Publisher description.
The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world—and you don’t need to be a mathematician to enjoy the pieces collected here. These essays—from leading names and fresh new voices—delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today’s hottest mathematical debates. Here, Viktor Blåsjö gives a brief history of “lockdown mathematics”; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of “dark data”—information that is missing or ignored. And there is much, much more.
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
Undergraduate research (UR) is widely believed to enhance the learning experience of students in science, technology, engineering, and mathematics programs. This is the first comprehensive, practical, research-based book on undergraduate research. It addresses how the benefits to UR participants arise; compares the benefits of UR with other types of educational activities or experience; the long-term value of UR; and more. Intended to assist both existing and new UR practitioners with program design and evaluation needs, the book will also be useful to the wider community of academics, policy-makers, and funders of UR programs.
