Discrete Mathematics Roadmap

The core theoretical foundation for Computer Science and its applications in information technology.

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Phase Main Topic Content & Learning Activities Objectives & Deliverables
1. Overview General Introduction
  • Role in Computer Science.
  • Practical applications.
  • Understand the importance and scope of Discrete Mathematics.
2. Reasoning Mathematical Logic and Propositions
  • Propositions and logical operators.
  • Laws of logic, truth tables.
  • Theorems, proofs (by contradiction, by induction).
  • Master the foundation of all reasoning and proofs.
3. Relations Sets and Relations
  • Set concepts, operations.
  • Relations, properties of relations.
  • Equivalence relations, order relations.
  • Learn to group objects and define relationships.
4. Mappings Functions and Mappings
  • Definition, domain, range.
  • Injective, surjective, bijective functions.
  • Composite functions, inverse functions.
  • Study the rules of correspondence between sets.
5. Computer Logic Boolean Algebra
  • Structure of Boolean algebra.
  • Representing and simplifying logical expressions.
  • Application in digital circuit design.
  • Explore the mathematical system of logic and its application in computers.
6. Arithmetic Discrete Arithmetic
  • Divisibility, prime numbers, GCD.
  • Euclidean algorithm.
  • Remainders, congruence, and applications (RSA cryptography).
  • Study the properties of integers and their application in cryptography.
7. Counting Combinatorics and Discrete Probability
  • Counting rules: sum, product.
  • Permutations, arrangements, combinations.
  • Discrete probability.
  • Learn counting techniques and analyze the likelihood of events.
8. Recursion Recurrence Relations and Generating Functions
  • Definition of recurrence relations.
  • Methods for solving linear recurrence relations.
  • Generating functions.
  • Model problems with self-repeating properties.
9. Networks Graph Theory
  • Graph concepts, paths, cycles.
  • Trees, spanning trees, binary trees.
  • Eulerian and Hamiltonian paths.
  • Foundation for modeling networks and relationships.
10. Theory Relational Algebra and Formal Languages
  • Formal languages, grammars.
  • Regular expressions.
  • Applications: finite automata, compilers.
  • Theoretical basis for databases and compilers.
11. Practice Applications in IT
  • Databases (sets, relations).
  • Cryptography (discrete arithmetic).
  • Search and AI (logic, graphs).
  • Summarize and connect learned knowledge with practical fields.