Discrete Mathematics Roadmap
Step by step guide to becoming an Android developer.
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1General Introduction
Understand the importance and scope of applications of Discrete Mathematics.
Role in Computer Science
Practical Applications
2Mathematical Logic and Propositions
The foundation of all reasoning and proofs in mathematics and computer science.
Propositions and logical operations
Logical laws, truth tables
Theorems, proofs (contradiction, induction)
3Sets and Relations
Learn how to group objects and define relationships between them.
Set concepts, operations on sets
Relations, properties of relations
Equivalence relations, order relations
4Functions and Mappings
Study the rules of correspondence between sets.
Definition, domain, range
1-1, onto, bijective functions
Composite functions, inverse functions
5Boolean Algebra
Explore the mathematical system of logic and its application in computers.
Boolean algebra structure
Representation and minimization of logic expressions
Application in digital circuit design
6Discrete Arithmetic
Study the properties of integers and their application in cryptography.
Divisibility, prime numbers, GCD
Euclidean algorithm
Residues, congruence and its applications (RSA cryptography)
7Combinatorics and Discrete Probability
Learn counting techniques and analyze the likelihood of events.
Counting rules: sum, product
Permutations, arrangements, combinations
Discrete probability
8Recurrence Relations and Generating Functions
Model problems that have recursive properties.
Definition of recurrence relations
Methods for solving linear recurrence relations
Generating functions
9Graph Theory
The foundation for modeling networks and relationships.
Graph concepts, paths, cycles
Trees, spanning trees, binary trees
Eulerian, Hamiltonian algorithms
10Relational Algebra and Formal Languages
The theoretical basis for databases and compilers.
Formal languages, Grammars
Regular expression
Applications: finite automata, compilers
11Applications in IT
Summarize and connect the learned knowledge with practical fields.
Databases (sets, relations)
Cryptography (discrete arithmetic)
Search and AI (logic, graphs)