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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.
Mathematics research opportunities for undergraduate students have
grown significantly in recent years, but accessible research topics
for first- and second-year students with minimal experience beyond
high school mathematics are still hard to find. To address this
need, this volume provides beginning students with specific
research projects and the tools required to tackle them. Most of
these projects are accessible to students who have not yet taken
Calculus, but students who know some Calculus will find plenty to
do here as well. Chapters are self-contained, presenting projects
students can pursue, along with essential background material and
suggestions for further reading. Suggested prerequisites are noted
at the beginning of each chapter. Some topics covered include:
games on graphs modeling of biological systems mosaics and virtual
knots mathematics for sustainable humanity mathematical
epidemiology Mathematics Research for the Beginning Student, Volume
1 will appeal to undergraduate students at two- and four-year
colleges who are interested in pursuing mathematics research
projects. Faculty members interested in serving as advisors to
these students will find ideas and guidance as well. This volume
will also be of interest to advanced high school students
interested in exploring mathematics research for the first time. A
separate volume with research projects for students who have
already studied calculus is also available.
This highly readable book aims to ease the many challenges of
starting undergraduate research. It accomplishes this by presenting
a diverse series of self-contained, accessible articles which
include specific open problems and prepare the reader to tackle
them with ample background material and references. Each article
also contains a carefully selected bibliography for further
reading. The content spans the breadth of mathematics, including
many topics that are not normally addressed by the undergraduate
curriculum (such as matroid theory, mathematical biology, and
operations research), yet have few enough prerequisites that the
interested student can start exploring them under the guidance of a
faculty member. Whether trying to start an undergraduate thesis,
embarking on a summer REU, or preparing for graduate school, this
book is appropriate for a variety of students and the faculty who
guide them.
This highly readable book aims to ease the many challenges of
starting undergraduate research. It accomplishes this by presenting
a diverse series of self-contained, accessible articles which
include specific open problems and prepare the reader to tackle
them with ample background material and references. Each article
also contains a carefully selected bibliography for further
reading. The content spans the breadth of mathematics, including
many topics that are not normally addressed by the undergraduate
curriculum (such as matroid theory, mathematical biology, and
operations research), yet have few enough prerequisites that the
interested student can start exploring them under the guidance of a
faculty member. Whether trying to start an undergraduate thesis,
embarking on a summer REU, or preparing for graduate school, this
book is appropriate for a variety of students and the faculty who
guide them.
Mathematics research opportunities for undergraduate students have
grown significantly in recent years, but accessible research topics
for first- and second-year students are still hard to find. To
address this need, this volume provides beginning students who have
already had some exposure to calculus with specific research
projects and the tools required to tackle them. Chapters are
self-contained, presenting projects students can pursue, along with
essential background material and suggestions for further reading.
In addition to calculus, some of the later chapters require
prerequisites such as linear algebra and statistics. Suggested
prerequisites are noted at the beginning of each chapter. Some
topics covered include: lattice walks in the plane statistical
modeling of survival data building blocks and geometry modeling of
weather and climate change mathematics of risk and insurance
Mathematics Research for the Beginning Student, Volume 2 will
appeal to undergraduate students at two- and four-year colleges who
are interested in pursuing mathematics research projects. Faculty
members interested in serving as advisors to these students will
find ideas and guidance as well. This volume will also be of
interest to advanced high school students interested in exploring
mathematics research for the first time. A separate volume with
research projects for students who have not yet studied calculus is
also available.
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.
Automorphism groups of Riemann surfaces have been widely studied
for almost 150 years. This area has persisted in part because it
has close ties to many other topics of interest such as number
theory, graph theory, mapping class groups, and geometric and
computational group theory. In recent years there has been a major
revival in this area due in part to great advances in computer
algebra systems and progress in finite group theory. This volume
provides a concise but thorough introduction for newcomers to the
area while at the same time highlighting new developments for
established researchers. The volume starts with two expository
articles. The first of these articles gives a historical
perspective of the field with an emphasis on highly symmetric
surfaces, such as Hurwitz surfaces. The second expository article
focuses on the future of the field, outlining some of the more
popular topics in recent years and providing 78 open research
problems across all topics. The remaining articles showcase new
developments in the area and have specifically been chosen to cover
a variety of topics to illustrate the range of diversity within the
field.
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