MATH111, Numbers and Relations

Undergraduate course, Lancaster University, Department of Mathematics & Statistics, 2018

My role: Graduate Teaching Assistant

Main topics:

  • Logic: truth tables, methods of proof (direct, contraposition, contradiction), simple examples of mathematical proofs.

  • Number theory: division with remainder; highest common factors and the Euclidean algorithm; lowest common multiples; prime numbers; the Fundamental Theorem of Arithmetic and the existence of infinitely many prime numbers; applications of prime factorization.

  • Congruences: definition; solving congruences; the Chinese Remainder Theorem.

  • Relations: equivalence relations; the sum and product of two congruence classes; constructions of number systems.

  • Polynomials: the division algorithm; highest common factors and the Euclidean algorithm.