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Appendix A Selected Hints

0 Introduction and Preliminaries

0 Introduction and Preliminaries
0.2 Mathematical Statements

Exercises

0.3 Sets

Exercises

0.4 Functions

Exercises

1 Counting

1 Counting
1.1 Additive and Multiplicative Principles

Exercises

1.2 Binomial Coefficients

Exercises

1.3 Combinations and Permutations

Exercises

1.4 Combinatorial Proofs

Exercises

1.6 Advanced Counting Using PIE

Exercises

1.7 Chapter Summary

Chapter Review

2 Sequences

2 Sequences
2.1 Describing Sequences

Exercises

2.4 Solving Recurrence Relations

Exercises

2.5 Induction

Exercises

2.6 Chapter Summary

Chapter Review

3 Symbolic Logic and Proofs

3 Symbolic Logic and Proofs
3.1 Propositional Logic

Exercises

3.2 Proofs

Exercises

4 Graph Theory

4 Graph Theory
4.1 Definitions

Exercises

4.2 Trees

Exercises

4.3 Planar Graphs

Exercises

4.4 Coloring

Exercises

4.5 Euler Paths and Circuits

Exercises

4.7 Chapter Summary

Chapter Review

5 Additional Topics

5 Additional Topics
5.1 Generating Functions

Exercises

5.2 Introduction to Number Theory

Exercises