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Lie Groups
This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called 'Putting the pieces together' in which all definitions and results are collected for reference and further reading is suggested.
Difference Sets
Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of f
Fifty Years of Women in Mathematics
The Association for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Fu...
Mathematics Education
Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, ther...
The Six Pillars of Calculus: Biology Edition
The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning—to focus on when and why to use the tools of calculus, not just on how to apply formulas. Modeling and differential equations are front and center. Solut...
Quantum Computation and Information
This book is a collection of papers given by invited speakers at the first AMS Special Session on Quantum Computation and Information held at the January 2000 Annual Meeting of the AMS in Washington, DC. The papers in this volume give readers a broad introduction to the many mathematical research challenges posed by the new and emerging field of quantum computation and quantum information. Of particular interest is a long paper by Lomonaco and Kauffman discussing mathematical and computational aspects of the so-called hidden subgroup algorithm. This book is intended to help readers recognize that, as a result of this new field of quantum information science, mathematical research opportuniti...
Groups, Difference Sets, and the Monster
This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic
Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and th...
Project Impact - Disseminating Innovation in Undergraduate Education
Contains abstracts of innovative projects designed to improve undergraduate education in science, mathematics, engineering, and technology. Descriptions are organized by discipline and include projects in: astronomy, biology, chemistry, computer science, engineering, geological sciences, mathematics, physics, and social sciences, as well as a selection of interdisciplinary projects. Each abstract includes a description of the project, published and other instructional materials, additional products of the project, and information on the principal investigator and participating institutions.
