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Title A primer for undergraduate research : from groups and tiles to frames and vaccines / Aaron Wootton, Valerie Peterson, Christopher Lee, editors.
Imprint Cham, Switzerland : Birkhauser, 2018.

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View online
Series Foundations for undergraduate research in mathematics.
Foundations for undergraduate research in mathematics.
Subject Intersection theory (Mathematics)
Presentations of groups (Mathematics)
Graph theory.
Alt Name Wootton, Aaron,
Peterson, Valerie (Valerie J.),
Lee, Christopher, 1975-
Description 1 online resource : illustrations.
polychrome rdacc
Bibliography Note Includes bibliographical references and index.
Note Online resource; title from PDF title page (EBSCO, viewed February 15, 2018).
Contents Intro; Contents; Coxeter Groups and the Davis Complex; 1 Introduction; 2 Group Presentations and Graphs; 2.1 Group Presentations; 2.1.1 A Constructive Approach; 2.2 Some Basic Graph Theory; 2.3 Cayley Graphs for Finitely Presented Groups; 3 Coxeter Groups; 3.1 The Presentation of a Coxeter Group; 3.2 Coxeter Groups and Geometry; 3.2.1 Euclidean Space and Reflections; 3.2.2 Spherical Geometry and Reflections; 3.2.3 Hyperbolic Geometry and Reflections; 3.2.4 The PoincarA Disk Model for Hyperbolic Space; 4 Group Actions on Complexes; 4.1 CW-Complexes; 4.2 Group Actions on CW-Complexes
5 The Cellular Actions of Coxeter Groups: The Davis Complex5.1 Spherical Subsets and the Strict Fundamental Domain; 5.1.1 Spherical Subsets; 5.1.2 The Strict Fundamental Domain; 5.2 The Davis Complex; 5.3 The Mirror Cellulation of I; 5.4 The Coxeter Cellulation; 5.4.1 Euclidean Representations; 5.4.2 The Coxeter Cell of Type T; 6 Closing Remarks and Suggested Projects; References; A Tale of Two Symmetries: Embeddable and Non-embeddable Group Actions on Surfaces; 1 Introduction; 2 Determining the Existence of a Group Action; 2.1 Realizing A4 as a Group of Rotations; 2.2 Preliminary Examples
2.3 Signatures2.4 Generating Vectors and Riemann's Existence Theorem; 3 Actions of the Alternating Group A4; 3.1 Signatures for A4-Actions; 4 Embeddable A4-Actions; 4.1 Necessary and Sufficient Conditions for Embeddability of A4; 5 Suggested Projects; References; Tile Invariants for Tackling Tiling Questions; 1 Prologue; 2 Tiling Basics; 3 Tile Invariants; 3.1 Coloring Invariants; 3.2 Boundary Word Invariants; 3.3 Invariants from Local Connectivity; 3.4 The Tile Counting Group; 4 Tile Invariants and Tileability; 5 Enumeration; 6 Concluding Remarks; References
Forbidden Minors: Finding the Finite Few1 Introduction; 2 Properties with Known Kuratowski Set; 3 Strongly Almosta#x80;#x93;Planar Graphs; 4 Additional Project Ideas; References; Introduction to Competitive Graph Coloring; 1 Introduction; 1.1 Trees and Forests; 1.2 The (r, d)-Relaxed Coloring Game; 1.3 Edge Coloring and Total Coloring; 2 Classifying Forests by Game Chromatic Number; 2.1 Forests with Game Chromatic Number 2; 2.2 Smallest Tree with Game Chromatic Number 4; 3 Relaxed-Coloring Games; 4 The Clique-Relaxed Game; 5 Edge Coloring; 6 Total Coloring; 7 Conclusions and Problems to Consider
ISBN 9783319660653 (electronic bk.)
3319660659 (electronic bk.)
OCLC # 1022266224
Additional Format Print version: Primer for undergraduate research. Cham, Switzerland : Birkhauser, 2018 3319660640 9783319660646 (OCoLC)994791721.