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Home > MATH > MATH_BOOKS

Mathematics

Mathematics Faculty Books

 
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  • Thinking Algebraically: An Introduction to Abstract Algebra by Thomas Q. Sibley

    Thinking Algebraically: An Introduction to Abstract Algebra

    Thomas Q. Sibley

    Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings\-first and groups\-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout.\n\nThe book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester\- or year\-long algebra course.

  • Thinking Geometrically: A Survey of Geometries by Thomas Q. Sibley

    Thinking Geometrically: A Survey of Geometries

    Thomas Q. Sibley

    Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas.

    Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics.

    The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

  • The Continued Adventures of the Parrot by Gary Brown

    The Continued Adventures of the Parrot

    Gary Brown

    Fritz, better known as the Parrot, solves cases using mathematical reasoning and metaphors from modern game theory. In The Case of the Missing Heroine, Fritz is enticed by a seductive voice to find two characters that appear in a recurring dream. All he is given is an old photo and a client that has a missing childhood. In the process of his investigation he encounters the stories of three famous heroines and a possible connection to the characters in the dream. He tries to build game theoretical models using ideas from Heisenberg and Von Neumann that give some sort of measure of randomness and information. In the end, is he successful in finding a quantitative method for determining the truth from a collection of four similar stories?

  • How to Mentor Undergraduate Researchers by Louise Temple, Thomas Q. Sibley, and Amy J. Orr

    How to Mentor Undergraduate Researchers

    Louise Temple, Thomas Q. Sibley, and Amy J. Orr

  • The Adventures of the Parrot by Gary Brown

    The Adventures of the Parrot

    Gary Brown

    Fritz, better known as the Parrot, solves cases using mathematical reasoning and metaphors from modern game theory.

  • The Foundations of Mathematics by Thomas Q. Sibley

    The Foundations of Mathematics

    Thomas Q. Sibley

    Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems.

  • The Geometric Viewpoint : A Survey of Geometries by Thomas Q. Sibley

    The Geometric Viewpoint : A Survey of Geometries

    Thomas Q. Sibley

  • Instructor's Resource Guide Including Solutions and Projects for the Geometer's Sketchpad to Accompany The Geometric Viewpoint : A Survey of Geometries, Sibley by Thomas Q. Sibley and Dan Bennett

    Instructor's Resource Guide Including Solutions and Projects for the Geometer's Sketchpad to Accompany The Geometric Viewpoint : A Survey of Geometries, Sibley

    Thomas Q. Sibley and Dan Bennett

 
 
 

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