This course include these topics: Number systems: natural numbers, radix r representation of integers, mathematical induction. Logic: propositional logic, predicate logic. Boolean algebra; sets; recursion; relations, and functions. Combinatory: counting principles; permutation groups. Graphs: graphs; diagraphs; trees; Euler's formula and coloring of graphs. Formal machines: automata and regular expressions; register machines: turning machines.
Intended learning outcomes
Knowledge and understanding
That the student be able to prove the statements of hypothetical logic and original logic
To familiarize the student with the technical terminology of relations and functions in original logic
That the student be able to prove the expressions that are used in the infinite induction
The student will be able to prove the statements using standard arithmetic
The student will be able to explain and prove preliminary results in graph theory
The student interprets the proofs automatically using the Proof Assistant
mental skills
This course provides a mathematical foundation for further study in computer science
Develop the skills necessary to solve practical problems
Give students a basic facility with logic and proof theory, counting, and graph theory
It provides the student of computer science with the solid mathematical foundations that he needs when studying advanced materials in computer science such as (data structures) and (computer algorithms),
For the student to think in a logical mathematical way
Practical and professional skills
That the student use the data of default logic and original logic in the design of software functions
That the student characterize the relationships and functions in original logic to help design systems
That the student use standard arithmetic to understand how to write software procedures
That the student diagnoses the evidence using an evidence assistant
General and transferable skills
Thinking in a logical mathematical way
Develop the skills needed to solve practical and programmatic problems
Preparing the student with the mathematical foundations he needs to study advanced subjects
