So che Discrete Mathematics è un argomento piuttosto ampio che viene utilizzato in una serie di campi, ma mi chiedevo solo quali sono alcuni degli argomenti che ci si aspetterebbe che uno studente medio di informatica sappia?
Ecco la gamma di argomenti dal sommario di un libro intitolato "Discrete Mathematics and its Applications 6th edition" di Kenneth H Rosen:
1 The Foundations: Logic and Proofs
1.1 Propositional Logic
1.2 Propositional Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
1.5 Rules of Inference
1.6 Introduction to Proofs
1.7 Proof Methods and Strategy
2 Basic Structures: Sets, Functions, Sequences and Sums
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
3 The Fundamentals: Algorithms, the Integers, and Matrices
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
3.7 Applications of Number Theory
3.8 Matrices
4 Induction and Recursion
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
4.5 Program Correctness
5 Counting
5.1 The Basics of Counting
5.2 The Pigeonhole Principle
5.3 Permutations and Combinations
5.4 Binomial Coefficients
5.5 Generalized Permutations and Combinations
5.6 Generating Permutations and Combinations
6 Discrete Probability
6.1 An Introduction to Discrete Probability
6.2 Probability Theory
6.3 Bayes Theorem
6.4 Expected Value and Variance
7 Advanced Counting Techniques
7.1 Recurrence Relations
7.2 Solving Linear Recurrence Relations
7.3 Divide-and-Conquer Algorithms and Recurrence Relations
7.4 Generating Functions
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
8 Relations
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
8.6 Partial Orderings
9 Graphs
9.1 Graphs and Graph Models
9.2 Graph Terminology and Special Types of Graphs
9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
9.5 Euler and Hamilton Paths
9.6 Shortest-Path Problems
9.7 Planar Graphs
9.8 Graph Coloring
10 Trees
10.1 Introduction to Trees
10.2 Applications of Trees
10.3 Tree Traversal
10.4 Spanning Trees
10.5 Minimum Spanning Trees
11 Boolean Algebra
11.1Boolean Functions
11.2 Representing Boolean Functions
11.3 Logic Gates
11.4 Minimization of Circuits
12 Modeling Computation
12.1 Languages and Grammars
12.2 Finite-State Machines with Output
12.3 Finite-State Machines with No Output
12.4 Language Recognition
12.5 Turing Machines
Appendixes
A.1 Axioms for the Real Numbers and the Positive Integers
A.2 Exponential and Logarithmic Functions
A.3 Pseudocode