A primer for undergraduate research : from groups and tiles to frames and vaccines /: from groups and tiles to frames and vaccines. (2018)

• Record Type: Book
• Further Information: Note: Aaron Wootton, Valerie Peterson, Christopher Lee, editors.
• Editors: Wootton, Aaron; Peterson, Valerie; Lee, Christopher
• 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 Poincaré 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 Σ; 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 Almostâ#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
• Publisher Details: Cham, Switzerland : Birkhäuser
• Publication Date: 2018
• Extent: 1 online resource, illustrations
• Subjects: 516.35; Mathematics; Intersection theory (Mathematics); Presentations of groups (Mathematics); Graph theory; MATHEMATICS / Geometry / General; Graph theory; Intersection theory (Mathematics); Presentations of groups (Mathematics); Mathematics -- Algebra -- Abstract; Mathematics -- Number Theory; Mathematics -- Geometry -- Analytic; Mathematics -- Applied; Mathematics -- Algebra -- Linear; Groups & group theory; Number theory; Algebraic geometry; Applied mathematics; Algebra; Group theory; Number theory; Discrete groups; Physiology_xMathematics; Matrix theory; Mathematics -- Discrete Mathematics; Discrete mathematics; Electronic books
• Languages: English
• ISBNs: 9783319660653; 3319660659
• Related ISBNs: 9783319660646; 3319660640
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed February 15, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.