1381170045_768__232_lecture_4.4

# 1 limit laws and comb marni 11 but if it does have

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Unformatted text preview: Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 13 f a cu lty of science d epa r tm ent of m athema tic s Week 6 Date Sections from FS2009 Part/ References MATH 895-4 Fall 2010 Course Schedule Topic/Sections Algebraic Multiplicity 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) MATH 232 S ECTION #4.4 Notes/Speaker Symbolic methods Unlabelled structures The 21 II.1, II.2, II.3 multiplicity structures I eigenvalue of a square matrix A is its algebraic 3 Labelled of an 4 28 II.4, II.5, II.6 Labelled structures II multiplicity as a root of the characteristic polynomial det(λI − A). Combinatorial Combinatorial 5 Oct 5 III.1, III.2 Asst #1 Due parameters Parameters FS A.III 123 6 12 IV.1, IV.2 Multivariable GFs (self-study) Example: IV.4 Find Analytic Methods the eigenvalues of A = 0 4 7 and for each one, state its 7 19 IV.3, Complex Analysis FS: Part B: IV, V, VI 8 26 Singularity Analysis 001 Appendix B4 IV.5 V.1 Stanley 99: Ch. 6 9 Nov 2 Asst #2 Due Asymptotic methods Handout #1 algebraic multiplicity. (self-study) 9 VI.1 12 A.3/ C Introduction to Prob. Mariolys 18 IX.1 Limit Laws and Comb Marni 20 IX.2 Discrete Limit Laws Sophie 23 IX.3 Combinatorial instances of discrete Mariolys 25 IX.4 Continuous Limit Laws Marni 13 30 IX.5 Quasi-Powers and Gaussian limit laws Sophie 14 Dec 10 10 11 12 Sophie Random Structures and Limit Laws FS: Part C (rotating presentations) Presentations Asst #3 Due Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 14 f a cu lty of science d epa r tm ent of m athema tic s Week 7 Date Sections from FS2009 Part/ References MATH 895-4 Fall 2010 Course Schedule Topic/Sections MATH 232 S ECTION #4.4 Notes/Speaker Eigenvalues of Diagonal and Triangular Matrices 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Symbolic methods Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Complex Analysis Random Structures and Limit Laws FS: Part C (rotating presentations) Discrete Limit Laws Sophie Combinatorial instances of discrete Mariolys Continuous Limit Laws Marni Quasi-Powers and Gaussian limit laws Sophie Unlabelled structures 123 4 28 II.4, the Labelled structures II We saw onII.5, II.6 previous slide that the eigenvalues of A = 0 4 7, if we list Combinatorial Combinatorial 5 Oct 5 III.1, III.2 Asst #1 Due 001 parameters Parameters FS A.III them withIV.2 6 12 IV.1, their algebraic multiplicities are 1, 1, and 4. Multivariable GFs (self-study) 3 21 II.1, II.2, II.3 7 19 IV.3, IV.4 More generally IV.5 V.1 8 26 9 Nov 2 Labelled structures I Singularity Analysis Asymptotic methods Asst #2 Due Theorem (4.4.5) If A is triangular (diagonal, upper or lower) its eigenval9 VI.1 Sophie 10 ues 12 A.3/ C entries on the main Prob. Mariolys and the algebraic multiplicity of are the Introduction to diagonal 18 IX.1 Limit of times it an eigenvalue is the numberLaws and Comb Marni appears on the main diagonal. 11 20 IX.2 23 IX.3 25 IX.4 13 30 IX.5 14 Dec 10 12 Presentations Asst #3 Due Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 15 f a cu lty of science d epa r tm ent of m athema tic s Week 8 Date Sections from FS2009 Part/ References MATH 895-4 Fall 2010 Course Schedule Topic/Sections MATH 232 S ECTION #4.4 Notes/Speaker Eigenvalues, Determinant, and Trace 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 Combinatorial Structures FS: Part...
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