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Section 1 Key

  • KT = Keller and Trotter
  • L = Levin
  • G = Guichard
  • DL = Doerr and Levasseur
  • B = Beezer

Created: April 1, 2019

Section 2 Topics and Texts

Topic KT L G DL B
Basic Counting
Introduction 1 0.1 1.1
(Binary) Strings 2.1 1.2 1.4
Addition Principle 1.1 1.2 2.3
Multiplication Principle 1.1 1.2 2.1
Permutations 2.2 1.3 1.2 2.2
Combinations 2.3 1.2 1.2 2.4.1
Ordered Set Partitions 2.7 1.5
Ordered Integer Partitions 1.5 1.5
Binomial Coefficients 2.5, 2.6 1.2 1.3 2.4.2
Multinomial Coefficients 2.7
Advanced Counting
Inclusion-Exclusion 7 1.6 2
Set Partitions 1.8
Recurrence Relations 9 2 3.4 8
Generating Functions 8 5.1 3 8.5
Graph Theory
Graph Theory Basics 5.1 4.1 4.4, 5.1 9.1
Eulerian, Hamiltonian 5.3 4.4 5.2, 5.3 9.4
Trees 5.5 10
Planarity 5.5 4.2 5.10 9.6
Coloring 5.4 4.3 5.4, 5.8, 5.10 9.6

Section 3 Suggested Exercises

Topic Exercises
Basic Counting
Introduction Discern Floor 4 tile patterns
Addition, Multiplication Principles L.1.1.1, L.1.1.2, L.1.1.3, L.1.1.4, L.1.1.11, L.1.1.13
G.1.2.3, G.1.2.5
DL.2.3.10, DL.2.1.2, DL.2.1.3, DL.2.1.5
Permutations and Combinations KT.2.9, 1–14
L.1.3, 1–14
G.1.2, 1–7
DL.2.4, 1–4, 7–11, 13, 14, 16, 18
Ordered Set Partitions KT.2.9, 31, 32
Ordered Integer Partitions L1.5, 1-4, 7-9, 11
Binomial, Multinomial Coefficients KT.2.9, 20, 21, 29, 30
L.1.2, 8, 9, 13
G.1.3, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15–18
Advanced Counting
Inclusion-Exclusion KT.7.7, 1–21
L.1.6, 1–11
G.2.1, 2
Recurrence Relations KT.9.9, 2, 3, 4, 11, 13
L.2.4, 1–12
G.3.4, 1–9
DL.8.3, 1–9, 16
Generating Functions KT.8.8, 2, 3, 4–19
KT.9.9, 15, 16, 17
L.5.1, 1, 2, 5, 8, 9, 10, 13, 14, 15
G.3.1, 4, 5, 6, 7, 9
DL.8.5, 1–6, 9, 10
Graph Theory
Graph Theory Basics KT.5, 1–5, 7
L.4.1, 1–6, 8
G.5.1, 1–12
Eulerian, Hamiltonian KT.5, 8–12
L.4.4, 1–11
G.5.2, 1–4
G.5.3, 1–3
DL.9.4, 1–6
Trees KT.5, 6, 36, 37–42
G.5.5, 1–6
DL.10.1, 1–5
Planarity KT.5, 29–32
L.4.2, 1–10
DL.9.6, 1, 2, 7, 9, 12
Coloring KT.5, 13–17
L.4.1, 6, 7
L.4.3, 1–11
G.5.4, 2, 3
G.5.8, 1–4
G.5.10, 1
DL.9.6, 3, 4, 5, 6, 11, 13, 14
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