 Chapter 1.1: Statements, Symbolic Representation, and Tautologies
 Chapter 1.2: Propositional Logic
 Chapter 1.3: Quantifiers, Predicates, and Validity
 Chapter 1.4: Predicate Logic
 Chapter 1.5: Logic Programming
 Chapter 1.6: Logic Programming
 Chapter 2.1: Proof Techniques
 Chapter 2.2: Induction
 Chapter 2.3: More on Proof of Correctness
 Chapter 2.4: Number Theory
 Chapter 3.1: Recursive Definitions
 Chapter 3.2: Recurrence Relations
 Chapter 3.3: Analysis of Algorithms
 Chapter 4.1: Sets
 Chapter 4.2: Counting
 Chapter 4.3: Principle of Inclusion and Exclusion; Pigeonhole Principle
 Chapter 4.4: Permutations and Combinations
 Chapter 5.1: Relations
 Chapter 5.2: Topological Sorting
 Chapter 5.3: Relations and Databases
 Chapter 5.4: Functions
 Chapter 5.5: Order of Magnitude
 Chapter 5.6: The Mighty Mod Function
 Chapter 5.7: Matrices
 Chapter 6.1: Graphs and Their Representations
 Chapter 6.2: Trees and Their Representations
 Chapter 6.3: Decision Trees
 Chapter 6.4: Huffman Codes
 Chapter 7.1: Directed Graphs and Binary Relations; Warshalls Algorithm
 Chapter 7.2: Euler Path and Hamiltonian Circuit
 Chapter 7.3: Shortest Path and Minimal Spanning Tree
 Chapter 7.4: Traversal Algorithms
 Chapter 7.5: Articulation Points and Computer Networks
 Chapter 8.1: Boolean Algebra Structure
 Chapter 8.2: Logic Networks
 Chapter 8.3: Minimization
 Chapter 9.1: Algebraic Structures
 Chapter 9.2: Coding Theory
 Chapter 9.3: FiniteState Machines
 Chapter 9.4: Turing Machines
 Chapter 9.5: Formal Languages
Mathematical Structures for Computer Science 7th Edition  Solutions by Chapter
Full solutions for Mathematical Structures for Computer Science  7th Edition
ISBN: 9781429215107
Mathematical Structures for Computer Science  7th Edition  Solutions by Chapter
Get Full SolutionsThe full stepbystep solution to problem in Mathematical Structures for Computer Science were answered by , our top Math solution expert on 01/18/18, 05:04PM. Since problems from 41 chapters in Mathematical Structures for Computer Science have been answered, more than 9577 students have viewed full stepbystep answer. Mathematical Structures for Computer Science was written by and is associated to the ISBN: 9781429215107. This expansive textbook survival guide covers the following chapters: 41. This textbook survival guide was created for the textbook: Mathematical Structures for Computer Science, edition: 7.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Iterative method.
A sequence of steps intended to approach the desired solution.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).