020 MOC Mathematics

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Principles

• Set Complement

Functions

• Injective Function
• Surjective Function
• Bijective Function
• Image of Function
• Preimage of Function
• Cantor-Bernstein-Schroeder Theorem

Relations

• Equivalence Relation
  • Equivalence Class
    • All different equivalence classes are disjoint
  • Quotient Space
• Partially Ordered Set
• Totally Ordered Set
  • Zorn’s Lemma

Topics

• 021 MOC Algebra
  • 021a MOC Linear Algebra
  • 021b MOC Geometric Algebra
• 022 MOC Functional Analysis
• 023 MOC Measure Theory
  • 023a MOC Probability Theory
• 024 MOC Information Theory
• 025 MOC Lógica de Primeira Ordem
• 026 MOC Topology
• 027 MOC Calculus
• 027 MOC Category Theory
• Introduction to Umbral Calculus

References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 01
• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 02