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Viser: Discrete Mathematics - An Open Introduction
Discrete Mathematics
An Open Introduction
Oscar Levin
(2025)
Sprog: Engelsk
CRC Press LLC
2.362,00 kr.
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Detaljer om varen
- 4. Udgave
- Hardback: 480 sider
- Udgiver: CRC Press LLC (Marts 2025)
- ISBN: 9781032965529
Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the "bridge" course for math majors.
Features
- Uses problem-oriented and inquiry-based methods to teach the concepts.
- Suitable for undergraduates in mathematics and computer science.
New to the 4th edition
- Large scale restructuring.
- Contains more than 750 exercises and examples.
- New sections on probability, relations, and discrete structures and their proofs.
0. Introduction and Preliminaries.
0.1. What is Discrete Mathematics?.
0.2. Discrete Structures.
1. Logic and Proofs.
1.1. Mathematical Statements.
1.2. Implications.
1.3. Rules of Logic.
1.4. Proofs.
1.5. Proofs about Discrete Structures.
1.6.
Chapter Summary.
2. Graph Theory.
2.1. Problems and Definitions.
2.2. Trees.
2.3. Planar Graphs.
2.4. Euler Trails and Circuits.
2.5. Coloring.
2.6. Relations and Graphs.
2.7. Matching in Bipartite Graphs.
2.8.
Chapter Summary.
3. Counting.
3.1. Pascal's Arithmetical Triangle.
3.2. Combining Outcomes.
3.3. Non-Disjoint Outcomes.
3.4. Combinations and Permutations.
3.5. Counting Multisets.
3.6. Combinatorial Proofs.
3.7. Applications to Probability.
3.8. Advanced Counting Using PIE.
3.9.
Chapter Summary.
4. Sequences.
4.1. Describing Sequences.
4.2. Rate of Growth.
4.3. Polynomial Sequences.
4.4. Exponential Sequences.
4.5. Proof by Induction.
4.6. Strong Induction.
4.7.
Chapter Summary.
5. Discrete Structures Revisited
.
5.1. Sets.
5.2. Functions.
6. Additional Topics.
6.1. Generating Functions.
6.2. Introduction to Number Theory.
0.1. What is Discrete Mathematics?.
0.2. Discrete Structures.
1. Logic and Proofs.
1.1. Mathematical Statements.
1.2. Implications.
1.3. Rules of Logic.
1.4. Proofs.
1.5. Proofs about Discrete Structures.
1.6.
Chapter Summary.
2. Graph Theory.
2.1. Problems and Definitions.
2.2. Trees.
2.3. Planar Graphs.
2.4. Euler Trails and Circuits.
2.5. Coloring.
2.6. Relations and Graphs.
2.7. Matching in Bipartite Graphs.
2.8.
Chapter Summary.
3. Counting.
3.1. Pascal's Arithmetical Triangle.
3.2. Combining Outcomes.
3.3. Non-Disjoint Outcomes.
3.4. Combinations and Permutations.
3.5. Counting Multisets.
3.6. Combinatorial Proofs.
3.7. Applications to Probability.
3.8. Advanced Counting Using PIE.
3.9.
Chapter Summary.
4. Sequences.
4.1. Describing Sequences.
4.2. Rate of Growth.
4.3. Polynomial Sequences.
4.4. Exponential Sequences.
4.5. Proof by Induction.
4.6. Strong Induction.
4.7.
Chapter Summary.
5. Discrete Structures Revisited
.
5.1. Sets.
5.2. Functions.
6. Additional Topics.
6.1. Generating Functions.
6.2. Introduction to Number Theory.
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