Welcome to Week 5 of Analysis of Algorithms. The lectures for this week address two familiar and fundamental combinatorial structures and the use of analytic combinatorics to study them, including coverage of several applications. ---------- Lecture 6: Trees. The quintessential recursive structure, trees of various sorts are ubiquitous in scientific enquiry, and they arise explicitly in countless computing applications. You can find broad coverage in the textbook, but the lecture focuses on the use of analytic combinatorics to enumerate various types of trees and study parameters Lecture 7: Permutations. The study of sorting algorithms is the study of properties of permutations. We introduce analytic-combinatoric approaches to studying permutations in the context of this relationship. ---------- Your assignment for this week, due at 11:59PM on Thursday, February 24, 2022 is to write up and submit solutions to Exercises 6.6, 5.16, 7.26, and 7.29 in "Analysis of Algorithms" (second edition). For the first two problems, use analytic combinatorics to derive ~-approximations, which considerably simplifies the calculations. A problem similar to 5.16 is worked out in Chapter 5 on the booksite. Also, as usual, submit a potential exam question on the week's material. Submit files named “AofA5-Q1.pdf" “AofA5-Q2.pdf" "AofA5-Q3.pdf" “AofA5-Q4.pdf" “AofA5-QQ.pdf" via codePost. RS