https://math.byu.edu/wiki/api.php?action=feedcontributions&feedformat=atom&user=Wwb3 2026-07-16T13:19:49Z User contributions MediaWiki 1.26.3 https://math.byu.edu/wiki/index.php?title=Math_622:_Matrix_Theory_2&diff=1608 2010-10-31T04:51:29Z

<p>Wwb3: /* Textbooks */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 2.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> [[Math 621]]<br /> <br /> === Description ===<br /> Research topics in combinatorial matrix theory.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> As a course directed toward research in combinatorial matrix theory, the emphasis in this course will be to develop some facility in a current research topic. Topics covered in past courses include the Colin de Verdiere parameter, the minimum rank problem for graphs, and Ramanujan graphs.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Typically the course material will come from recent research papers.<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|622]]</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_622:_Matrix_Theory_2&diff=1607 2010-10-31T04:50:37Z

<p>Wwb3: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 2.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> [[Math 621]]<br /> <br /> === Description ===<br /> Research topics in combinatorial matrix theory.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> As a course directed toward research in combinatorial matrix theory, the emphasis in this course will be to develop some facility in a current research topic. Topics covered in past courses include the Colin de Verdiere parameter, the minimum rank problem for graphs, and Ramanujan graphs.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|622]]</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_622:_Matrix_Theory_2&diff=1606 2010-10-31T04:46:44Z

<p>Wwb3: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 2.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> [[Math 621]]<br /> <br /> === Description ===<br /> Research topics in combinatorial matrix theory.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|622]]</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=1605 2010-10-31T04:43:57Z

<p>Wwb3: /* Courses for which this course is prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Richard A Brualdi and Herbert J Ryser, Combinatorial Matrix Theory<br /> <br /> Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic, An Introduction to the Theory of Graph Spectra<br /> <br /> Chris Godsil and Gordon Royle, Algebraic Graph Theory<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]<br /> <br /> Math 622</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=1604 2010-10-31T04:43:33Z

<p>Wwb3: /* Textbooks */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Richard A Brualdi and Herbert J Ryser, Combinatorial Matrix Theory<br /> <br /> Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic, An Introduction to the Theory of Graph Spectra<br /> <br /> Chris Godsil and Gordon Royle, Algebraic Graph Theory<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=1603 2010-10-31T04:40:28Z

<p>Wwb3: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]</div>

Wwb3 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=1602 2010-10-31T04:29:08Z

<p>Wwb3: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will understand simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]</div>

Wwb3