About This Course

In this course, students are facilitated to explore many topics of elementary number theory, their history and applications. Through learning the core concepts in number theory, students are directed to develop their proof-writing skills step by step. The course covers topics: numbers, rational and irrational; mathematical induction, divisibility and primes, the Euclidean algorithm, linear Diophantine equations, the fundamental theorem of arithmetic, modular arithmetic, and modular number systems. Some historical figures who had contributed to the development of number theory, are presented to enable the students to grasp the historical development of number theory.

Upon successful completion of this course, students are expected to be able to 

1. read, interpret, and use the vocabulary, symbolism, and basic definitions used in number theory, including divisibility, greatest common divisors, Diophantine equations, congruencies, primes, and perfect numbers
2. describe the fundamental principles including the laws and theorems arising from the concepts covered in this course, including the division algorithm, the Euclidean algorithm, the fundamental theorem of arithmetic, properties of congruencies
3. use the facts, formulas, and techniques learned in this course to prove theorems and solve problems; also, compute greatest common divisors; determine the number and sum of positive divisors; solve linear Diophantine equations; solve linear and other congruencies
4. investigate and discover mathematical ideas, and communicate them to peers and the lecturer