1381170045_768__232_lecture_4.4

Iii self study combinatorial parameters analytic

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Unformatted text preview: 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 If k is a positive integer, then Ak x = 23 Example. Find 3 −6 4 3 . 1 Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 Recall that C EDRIC C HAUVE , FALL 2013 3 is an eigenvector of the matrix with eigenvalue 3. 1 9 MATH 895-4 Fall 2010 Course Schedule f a cu lty of science d epa r tm ent of m athema tic s Week 3 Date Sections from FS2009 Part/ References Topic/Sections Complex Eigenvalues 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 3 21 II.1, II.2, II.3 4 28 II.4, II.5, II.6 5 Oct 5 III.1, III.2 Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Combinatorial Parameters Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Notes/Speaker Symbolic methods Combinatorial parameters FS A.III (self-study) MATH 232 S ECTION #4.4 Complex Analysis Consider the matrix A = Unlabelled structures 1 −2 Labelled structures II 31 Labelled structures I Asst #1 Due We can calculate its characteristic polynomial 6 12 IV.1, IV.2 Multivariable GFs 7 19 8 26 9 Nov 2 IV.3, IV.4 IV.5 V.1 Singularity Analysis Asymptotic methods Asst #2 Due 11 12 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 10 IX.4 Continuous Limit Laws Marni Quasi-Powers and Gaussian limit laws Sophie Random Structures and Limit Laws FS: Part C (rotating presentations) 13 30 IX.5 Which has roots 14 Dec 10 Sophie Presentations Asst #3 Due Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 10 MATH 895-4 Fall 2010 Course Schedule f a cu lty of science d epa r tm ent of m athema tic s Week 4 Date Sections from FS2009 Part/ References Topic/Sections Factoring Polynomials 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 The21Fundamental Theorem of Algebra: If 3 II.1, II.2, II.3 Labelled structures I 4 28 II.4, II.5, II.6 5 Oct 5 III.1, III.2 Labelled structures II n −1 p(λ) =Combinatorialpn−1 λAsst #1 + · · · + p1 λ + p0 λn + Due Combinatorial parameters FS A.III (self-study) Parameters Multivariable GFs is6 a 12 IV.1, IV.2 polynomial whose coefficients p0 , p1 , . . ., pn−1 are numbers (real, imagi7 19 IV.3, IV.4 Complex Analysis Analytic Methods nary, or complex), thenVI weSingularityfactor p(λ) completely: can Analysis FS: Part B: IV, V, 8 26 9 Nov 2 IV.5 V.1 9 VI.1 12 IX.3 Asst #2 Due p(λ) = (λ Asymptotic methods r2 ) · · · (λ − rn−1 )(λ − rn ) − r1 )(λ − Sophie A.3/ C 23 10 Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Introduction to Prob. Mariolys Combinatorial instances of discrete Mariolys where r1IX.1r2 , . . ., rn are numbersand Comb Marni complex, even if the original coeffi, (possibly 18 Limit Laws 11 cients p0IX.2p1 , . . ., pn−Structures Discrete Limit Laws Sophie , Random 1 were real). 20 and Limit Laws FS: Part C (rotating presentations) 12 For example, from the previous Limit Laws slide 25 IX.4 Continuous 13 30 14 Dec 10 Quasi-Powers and Gaussian limit laws IX.5 Presentations Marni Sophie Asst #3 Due Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 11 MATH 895-4 Fall 2010 Course Schedule f a c...
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