Test Bank for Discrete Mathematics and Its Applications 8th Edition by Kenneth H. Rosen
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- 117
- File size
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- Course
- Mathematics
- Category
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About this ebook
The Test Bank for 8th Edition of Discrete Mathematics and Its Applications by Kenneth H. Rosen covers 13 core chapters that bridge theoretical mathematical reasoning with computer science applications. [1, 2, 3, 4, 5]
1. The Foundations: Logic and Proofs
- Propositional logic and truth tables
- Propositional equivalences
- Predicates and quantifiers
- Nested quantifiers
- Rules of inference
- Introduction to proofs and proof methods (direct, indirect, contradiction) [1]
2. Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
- Sets and set operations
- Functions (one-to-one, onto)
- Sequences and summations
- Cardinality of sets (countable vs. uncountable)
- Matrix arithmetic and boolean matrices [1, 2]
3. Algorithms
- Algorithms and pseudocode
- Growth of functions (Big-O, Big-Omega, Big-Theta notation)
- Complexity of algorithms
- Useful algorithms (searching and sorting) [1, 2, 3, 4]
4. Number Theory and Cryptography
- Divisibility and modular arithmetic
- Integer representations and algorithms
- Primes and Greatest Common Divisors (GCD)
- Congruences and applications
- Cryptography (classical and public-key cryptography like RSA)
5. Induction and Recursion
- Mathematical induction
- Strong induction and well-ordering
- Recursive definitions and structural induction
- Recursive algorithms [1]
6. Counting
- Basics of counting (product and sum rules)
- The Pigeonhole Principle
- Permutations and combinations
- Binomial coefficients and identities
- Generalized permutations and combinations
7. Discrete Probability
- Introduction to discrete probability
- Probability theory (conditional probability and independence)
- Bayes' Theorem
- Expected value and variance
8. Advanced Counting Techniques
- Applications of recurrence relations
- Solving linear recurrence relations
- Divide-and-conquer algorithms and recurrence relations
- Generating functions
- Inclusion-Exclusion and its applications [1]
9. Relations
- Relations and their properties
- n-ary relations and their applications
- Representing relations (matrices and digraphs)
- Closures of relations
- Equivalence relations
- Partial orderings [1]
10. Graphs
- Graphs and graph models
- Graph terminology and special types of graphs
- Representing graphs and graph isomorphism
- Connectivity (paths, circuits, and connectedness)
- Euler and Hamilton paths
- Shortest-path algorithms
- Planar graphs and graph coloring [1]
11. Trees
- Introduction to trees
- Applications of trees (decision trees, Huffman coding)
- Tree traversal
- Spanning trees
- Minimum spanning trees [1]
12. Boolean Algebra
- Boolean functions and expressions
- Representing Boolean functions
- Logic gates
- Minimization of circuits (Karnaugh maps) []
13. Modeling Computation
- Languages and grammars
- Finite-state machines with and without output
- Language recognition (Deterministic and Non-deterministic Finite Automata)
- Turing machines [1]
Appendices (Online & Supplementary)
The text also features supplementary appendices covering: [1]
- Axioms for the Real Numbers and the Positive Integers
- Exponential and Logarithmic Functions
- Pseudocode Guidelines [1]
File included
Test-Bank-for-Discrete-Mathematics-and-Its-Applications-8th-Edition-by-Kenneth-Rosen.pdf
1.55 MB
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