Polyteknisk Boghandel

Combining a selection of topics with previews of their applications in computer science, this text limits its coverage to those topics students will actually utilize.

1. Fundamentals
1.
1 Sets and Subsets
1.
2 Operations on Sets
1.
3 Sequences
1.
4 Properties of Integers
1.
5 Matrices
1.
6 Mathematical Structures
2. Logic
2.
1 Propositions and Logical Operations
2.
2 Conditional Statements
2.
3 Methods of Proof
2.
4 Mathematical Induction
2.
5 Mathematical Statements
2.
6 Logic and Problem Solving
3. Counting
3.
1 Permutations
3.
2 Combinations
3.
3 Pigeonhole Principle
3.
4 Elements of Probability
3.
5 Recurrence Relations 112
4. Relations and Digraphs
4.
1 Product Sets and Partitions
4.
2 Relations and Digraphs
4.
3 Paths in Relations and Digraphs
4.
4 Properties of Relations
4.
5 Equivalence Relations
4.
6 Data Structures for Relations and Digraphs
4.
7 Operations on Relations
4.
8 Transitive Closure and Warshall's Algorithm
5. Functions
5.
1 Functions
5.
2 Functions for Computer Science
5.
3 Growth of Functions
5.
4 Permutation Functions
6. Order Relations and Structures
6.
1 Partially Ordered Sets
6.
2 Extremal Elements of Partially Ordered Sets
6.
3 Lattices
6.
4 Finite Boolean Algebras
6.
5 Functions on Boolean Algebras
6.
6 Circuit Design
7. Trees
7.
1 Trees
7.
2 Labeled Trees
7.
3 Tree Searching
7.
4 Undirected Trees
7.
5 Minimal Spanning Trees
8. Topics in Graph Theory
8.
1 Graphs
8.
2 Euler Paths and Circuits
8.
3 Hamiltonian Paths and Circuits
8.
4 Transport Networks
8.
5 Matching Problems
8.
6 Coloring Graphs
9. Semigroups and Groups
9.
1 Binary Operations Revisited
9.
2 Semigroups
9.
3 Products and Quotients of Semigroups
9.
4 Groups
9.
5 Products and Quotients of Groups
9.
6 Other Mathematical Structures
10. Languages and Finite-State Machines
10.
1 Languages
10.
2 Representations of Special Grammars and Languages
10.
3 Finite-State Machines
10.
4 Monoids, Machines, and Languages
10.
5 Machines and Regular Languages
10.
6 Simplification of Machines
11. Groups and Coding
11.
1 Coding of Binary Information and Error Detection
11.
2 Decoding and Error Correction
11.
3 Public Key Cryptology
Appendix A: Algorithms and Pseudocode
Appendix B: Additional Experiments in Discrete Mathematics
Appendix C: Coding Exercises