Math 108 serves as an introduction to combinatorics, with a focus on graph theory and enumerative combinatorics. The syllabus can be found here , and a more detailed breakdown of the schedule and homework can be found at the Course Schedule page.

Math 108 Homework 6 Solutions Problem 13G. Show that (13.12) leads to B(n) = 1 e P 1 k=0 kn k!. PAnswer: We actually just use (13.13) and (13.11). We get from (13.11) that B(n) = n k=1 S(n;k), but note that for k = 0 and k > n 1 that S(n;k) = 0, so we also have B(n) = P 1 k=0 S(n;k). Next, we plug in the formula from (13.13), and obtain B(n ...

Math 108 Homework 1 Solutions Problem 1B Suppose that G is a simple graph on 10 vertices that is not connected. Prove that G has at most 36 eges. Can equality occur? Proof. Let v be one of the vertices of G. Let A be the connected component of G containing v, and let B be the remainder of G, so that B = GnA. Let a be the number

Math 108, Intoduction to Combinatorics and its Applications: Syllabus Classroom: 380-380Y Class Time: MWF 11:00-11:50 Instructor: Robert J. Lemke Oliver Email: [email protected]

Math 108 Homework 4 Solutions Problem 10A How many positive integers less than 1000 have no factor between 1 and 10? Proof. Let p i be the ith prime number, so that p 1 = 2, p 2 = 3, etc. Let E i = fn 2 Z j1 n 1000 and p i divides ngfor 1 i 4. Noting that the intersection \m k=1 E i k = fn 2Z j1 n 1000 and Q m k=1 p i

Math 108 Winter 2015: Home: Course Schedule: Syllabus: This schedule is only tentative, and may be adjusted as necessary. The homework is due on Wednesday at the beginning of lecture. Date Reading assignment Written assignment; Week 1 (Jan. 5 - Jan. 9) Introduction to graphs and trees, §1,2 :

Oct 25, 2024 · ENGR108 covers the basics of vectors and matrices, solving linear equations, least-squares methods, and many applications. We'll cover the mathematics, but the focus will be on using matrix methods in applications such as tomography, image processing, data fitting, time series prediction, finance, and many others.

Math 108: Final Review Format: The exam will be three hours in McCullough 115, from 8:30-11:30 AM on Friday, March 20. It is closed notes. A large chunk of the exam will be computational (e.g., in how many ways can I distribute nidentical balls into mdistinct boxes?) and applications of theorems and de nitions (e.g., inclusion-exclusion).

Math 108 Homework 5 Solutions Problem 10H Prove that for 0 k n, Xk i=0 k i D n i = Xn k j=0 ( 1)j n k j (n j)!: Answer: Here we note that D n i represents the number of derangements of n i objects. I claim that both sides of this equation represent the number of permutations ˙

MATH 108. Introduction to Combinatorics and Its Applications. Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or 103 or equivalent. GER:DB-Math. 3 units, Spr (Kahle, M) MATH 109.