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Tables of Contents for Mathematics for the Analysis of Algorithms
Chapter/Section Title
Page #
Page Count
Binomial Identities
1
10
Summary of Useful Identities
1
2
Deriving the Identities
3
2
Inverse Relations
5
3
Operator Calculus
8
1
Hypergeometric Series
9
1
Identities with the Harmonic Numbers
10
1
Recurrence Relations
11
20
Linear Recurrence Relations
11
10
Finite History
12
1
Constant Coefficients
12
2
Variable Coefficients
14
3
Full History
17
1
Differencing
17
1
By Repertoire
17
4
Nonlinear Recurrence Relations
21
10
Relations with Maximum or Minimum Functions
21
4
Continued Fractions and Hidden Linear Recurrences
25
2
Doubly Exponential Sequences
27
4
Operator Methods
31
11
The Cookie Monster
31
3
Coalesced Hashing
34
4
Open Addressing: Uniform Hashing
38
1
Open Addressing: Secondary Clustering
39
3
Asymptotic Analysis
42
35
Basic Concepts
42
13
Notation
43
1
Bootstrapping
43
1
Dissecting
44
1
Limits of Limits
45
2
Summary of Useful Asymptotic Expansions
47
1
An Example from Factorization Theory
48
7
Stieltijes Intergration and Asymptotics
55
10
O-notation and Integrals
57
1
Euler's Summation Formula
58
2
An Example from Number Theory
60
5
Asymptotics from Generating Functions
65
12
Darboux's Method
65
3
Residue Calculus
68
2
The Saddle Point Method
70
7
Bibliography
77
4
Appendices
81
A. Schedule of Lectures, 1980
81
2
B. Homework Assignments
83
1
C. Midterm Exam I and Solutions
84
11
D. Final Exam I and Solutions
95
6
E. Midterm Exam II and Solutions
101
6
F. Final Exam II and Solutions
107
4
G. Midterm Exam III and Solutions
111
5
H. Final Exam III and Solutions
116
8
I. A Qualifying Exam Problem and Solution
124
Index
12