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000809307 019__ $$a1022778622
000809307 020__ $$a9783319660653$$q(electronic book)
000809307 020__ $$a3319660659$$q(electronic book)
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000809307 08204 $$a516.35$$223
000809307 24502 $$aA primer for undergraduate research :$$bfrom groups and tiles to frames and vaccines /$$cAaron Wootton, Valerie Peterson, Christopher Lee, editors.
000809307 264_1 $$aCham, Switzerland :$$bBirkhäuser,$$c2018.
000809307 300__ $$a1 online resource :$$billustrations.
000809307 336__ $$atext$$btxt$$2rdacontent
000809307 337__ $$acomputer$$bc$$2rdamedia
000809307 338__ $$aonline resource$$bcr$$2rdacarrier
000809307 4901_ $$aFoundations for undergraduate research in mathematics
000809307 504__ $$aIncludes bibliographical references and index.
000809307 5050_ $$aIntro; Contents; Coxeter Groups and the Davis Complex; 1 Introduction; 2 Group Presentations and Graphs; 2.1 Group Presentations; 2.1.1 A Constructive Approach; 2.2 Some Basic Graph Theory; 2.3 Cayley Graphs for Finitely Presented Groups; 3 Coxeter Groups; 3.1 The Presentation of a Coxeter Group; 3.2 Coxeter Groups and Geometry; 3.2.1 Euclidean Space and Reflections; 3.2.2 Spherical Geometry and Reflections; 3.2.3 Hyperbolic Geometry and Reflections; 3.2.4 The Poincaré Disk Model for Hyperbolic Space; 4 Group Actions on Complexes; 4.1 CW-Complexes; 4.2 Group Actions on CW-Complexes
000809307 5058_ $$a5 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
000809307 5058_ $$a2.3 Signatures2.4 Generating Vectors and Riemann's Existence Theorem; 3 Actions of the Alternating Group A4; 3.1 Signatures for A4-Actions; 4 Embeddable A4-Actions; 4.1 Necessary and Sufficient Conditions for Embeddability of A4; 5 Suggested Projects; References; Tile Invariants for Tackling Tiling Questions; 1 Prologue; 2 Tiling Basics; 3 Tile Invariants; 3.1 Coloring Invariants; 3.2 Boundary Word Invariants; 3.3 Invariants from Local Connectivity; 3.4 The Tile Counting Group; 4 Tile Invariants and Tileability; 5 Enumeration; 6 Concluding Remarks; References
000809307 5058_ $$aForbidden 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
000809307 506__ $$aAccess limited to authorized users.
000809307 588__ $$aOnline resource; title from PDF title page (viewed February 15, 2018).
000809307 650_0 $$aIntersection theory (Mathematics)
000809307 650_0 $$aPresentations of groups (Mathematics)
000809307 650_0 $$aGraph theory.
000809307 7001_ $$aWootton, Aaron,$$eeditor.
000809307 7001_ $$aPeterson, Valerie,$$eeditor.
000809307 7001_ $$aLee, Christopher,$$eeditor.
000809307 77608 $$cOriginal$$z3319660640$$z9783319660646$$w(OCoLC)994791721
000809307 830_0 $$aFoundations for undergraduate research in mathematics.
000809307 852__ $$bebk
000809307 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-66065-3$$zOnline Access$$91397441.1
000809307 909CO $$ooai:library.usi.edu:809307$$pGLOBAL_SET
000809307 980__ $$aEBOOK
000809307 980__ $$aBIB
000809307 982__ $$aEbook
000809307 983__ $$aOnline
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