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