Mathematics Research in Data Science, Machine Learning, and Cybersecurity

Accessible Research Topics for Undergraduate Students
Erscheinungsjahr 2027
ISBN: 978-3-032-45872-8
Verlag: Birkhäuser

Buch, Englisch, 532 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Foundations for Undergraduate Research in Mathematics

This edited volume introduces undergraduate students to emerging research topics in technology-focused disciplines founded in mathematics, including data science, machine learning, optimization, and cybersecurity.  Each chapter is self-contained and provides students with the required background knowledge, context, and relevant references to motivate and enable them to successfully undertake research in these areas.  A variety of accessible research projects are included that can be conducted independently or in collaboration with a mentor. Many chapters also offer challenge problems and exercises along the way to aid students in learning the material. This volume will also serve as a valuable resource to faculty mentors, graduate students, and others who are interested in supervising undergraduate research.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Quijano, Alex John

Lewis, Allison

Wootton, Aaron

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mensch-Maschine-Interaktion Informationsvisualisierung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Algebra
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik

Inhaltsverzeichnis

Preface.- Eigenvalues, Clustering, and Food Deserts.- In a World of Great Complexity, Less is More: Model Reduction Using the Active Subspace.- Dynamic Mode Decomposition for Spatiotemporal Data-Driven Discovery.- Computational Methods for Efficient Fitting of ODE Models to Time Series Data Using pomp.- What is the Best Way to Do Something? A Discreet Tour of Discrete Optimization.- Using Integer Programming to Solve Games, Puzzles, and Ciphers.- Topic Modeling via Nonnegative Matrix Factorization.- Using Machine-Learning and CFD to Understand Biomechanics of Marine Organisms.- One-Way Functions and Their Application in Public Key Cryptography.- Quantum Computing and Cryptography.

Über Autor(innen)

Alex John Quijano is an Assistant Professor of Mathematics at the University of Portland, a private Catholic university affiliated with the Congregation of the Holy Cross. He has a background in applied mathematics and data science, focusing on data visualization and statistical modeling. Experienced with supervising undergraduate theses and research projects, he has developed an understanding of guiding students through the research process, fostering their academic growth.

Allison Lewis is an Associate Professor of Mathematics at Lafayette College, an undergraduate liberal arts college that prioritizes opportunities for undergraduate students to engage in cutting-edge research.  With a background in mathematical modeling and uncertainty quantification, she has engaged numerous students in research experiences via REU programs, senior honors theses, independent studies, and summer research opportunities.

Aaron Wootton is a Professor of Mathematics at the University of Portland. His research lies in the areas of Complex Algebraic Geometry and Group Theory, with specific interests in Symmetries of Surfaces. Other interests include participation and fostering of undergraduate research in mathematics and the development of educational resources including resources in Cryptology.