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MAT 213 Number Theory

NCE2 levelSciences23 topics

MAT 213 covers 23 topics. StudyPath paces them into daily study sessions that finish before your exam date, with practice questions and worked answers for each one.

Study MAT 213 on StudyPath

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Course outline

The topics this course covers, in teaching order.

  1. Process of counting, Piano’s Axons using ordered pairs
  2. Fundamental operations in Mathematical Structures
  3. Group – Group properties
  4. Further properties of Integers
  5. Well ordering principle
  6. Mathematical Induction
  7. Laws of tracheotomy
  8. Divisibility (Basic definitions, divisions, primes god)
  9. Basic theorems on god
  10. Relatively prime integers (unique factorization)
  11. The fundamental theorem of arithmetic (proof may be required)
  12. Congruences
  13. Basic definitions and examples
  14. Properties of Congruence (reflexive symmetric and transitive: the equivalence relation)
  15. Residue classes
  16. Linear Congruences
  17. Basic theorems and solutions of linear Congruences
  18. Proofs of the main theorem may be required
  19. Fermat’s theorem and applications, the proof of Fermat’s theorem may be required
  20. Euler function and number (proof not required)
  21. Application to linear Congruences
  22. Fundamental operation in mathematical structures
  23. Group properties.

A sample from this course

One topic, as StudyPath teaches it.

Process of counting, Piano’s Axons using ordered pairs

This topic introduces the basic process of counting from first principles and shows how Peano’s axioms provide a logical foundation for the natural numbers. You also need to understand how ordered pairs are used to represent numerical relationships and constructions, because exam questions often test definitions, successor ideas, and how ordered pairs preserve position.

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