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Elementary Discrete Mathematics
Douglas Weathers
Contents
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Contents
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Front Matter
Colophon
Acknowledgements
Patch notes
I
Sets and Logic
1
Sets
Representing sets
Containment
Set operations
Exercises
2
Propositional logic
Statements and connectives
Propositional equivalence
Exercises
3
Predicate logic
Predicates and quantifiers
Predicate equivalence
Exercises
4
Proofs
Direct proofs
Indirect proofs
Biconditional proofs
Exercises
II
Recursive Structures
5
Recursion and integer representation
Introduction to recursion
Binary representation
Octal and hexadecimal numbers
Exercises
6
Sequences and sums
Sequences
Recurrence relations
Summation
Calculating sums indirectly
Exercises
7
Asymptotics
The growth of sequences
Exercises
8
Mathematical induction
Proof by induction
Induction with sums
Induction with inequalities
Exercises
III
Combinatorics
9
Learning to count
Combinatorics
Binary samples
Basic counting principles
Ordered samples
Unordered samples
Exercises
10
Combinatorial identities
Counting strings
Binomial identities
Multinomial coefficients
Exercises
11
Discrete probability
Axioms of probability
Enumerative probability
Discrete random variables
Binomial distribution
Exercises
IV
Relations
12
Boolean structures
Boolean algebras
Boolean matrices
Exercises
13
Relations and their properties
Introduction to relations
Representing relations
Properties of relations
Exercises
14
Closure and composition
Basic closures
Composition
Transitive closure
Exercises
15
Equivalence relations
Equivalence relations
Modular arithmetic
Exercises
16
Partial orders
Partial orders and their diagrams
Extreme values
Exercises
Back Matter
A
Appendix I: Sets and Logic
More about functions
Exercises
Authored in PreTeXt
Exercises
A.2
Exercises