Mathematics Research for the Beginning Student, Volume 2: Accessible Projects for Students After Calculus

The book "Mathematics Research for the Beginning Student, Volume 2" provides undergraduate students with specific research projects and the tools required to tackle them. It covers topics such as lattice walks, statistical modeling, and risk and insurance, and is suitable for students at two- and four-year colleges and advanced high school students.

Format: Hardback
Length: 308 pages
Publication date: 12 September 2022
Publisher: Birkhauser Verlag AG

Mathematics research opportunities for undergraduate students have experienced a significant surge in recent years, yet accessible research topics specifically tailored for first- and second-year students remain challenging to identify. To address this gap, this comprehensive volume is designed to provide novice students with a solid foundation in calculus and equip them with engaging research projects that can be pursued independently. Each chapter in the book is self-contained, presenting projects that students can engage with, along with essential background information and recommendations for further reading. While some chapters assume prerequisites such as linear algebra and statistics, these are clearly indicated at the beginning of each chapter. The topics covered in this volume are diverse and encompass a wide range of mathematical concepts. Some of the key topics include:
Lattice walks in the plane: This chapter explores the mathematical properties of lattice walks, which are patterns formed by moving along a grid or a network. It discusses topics such as the enumeration of lattice walks, their properties, and their applications in various fields, including physics and computer science.
Statistical modeling of survival data: This chapter focuses on the analysis of survival data, which is commonly used in medical research and other fields to study the probability of a certain event occurring. It introduces statistical models and methods for modeling survival data, including Cox proportional hazards models, log-rank tests, and Bayesian inference.
Building blocks and geometry: This chapter explores the fundamental concepts of geometry, including points, lines, planes, and shapes. It discusses topics such as Euclidean geometry, algebraic geometry, and topology, and their applications in fields such as computer graphics, engineering, and mathematics education.
Modeling of weather and climate change: This chapter focuses on the mathematical modeling of weather and climate systems. It introduces concepts such as differential equations, partial differential equations, and stochastic differential equations, and their applications in studying climate change, weather patterns, and other atmospheric phenomena.
Mathematics of risk and insurance: This chapter explores the mathematical principles underlying risk and insurance. It discusses topics such as probability theory, stochastic processes, and actuarial science, and their applications in risk management, insurance underwriting, and financial modeling.
Mathematics Research for the Beginning Student, Volume 2, is aimed at undergraduate students enrolled in two- and four-year colleges who have a keen interest in pursuing mathematics research projects. It serves as a valuable resource for faculty members who wish to advise these students and provide guidance on their research endeavors. Additionally, advanced high school students who are exploring the field of mathematics research for the first time will also find this volume to be an insightful introduction. A separate volume dedicated to research projects for students who have not yet studied calculus is also available to cater to a broader range of mathematical backgrounds.

Weight: 681g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031085635
Edition number: 1st ed. 2022