MATH5645 is a Mathematics Level V course. See the course overview below.

Units of credit: 6

Prerequisites: no formal ones, but at least second year algebra is assumed

Exclusions: third year number theory courses MATH3740, MATH3521

Cycle of offering: not offered every year, probably offered every second year

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. (This pdf will usually be updated by the end of the first week of the session.)

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH5645, you can log into the My eLearning Vista instance of this course.

Number theory has long fascinated humankind with its elementary but difficult problems, the beauty and elegance of its theorems and the surprising connections with disciplines seemingly far-removed from it. There are famous old problems such as the Goldbach conjecture or Fermat's last Theorem and more recent mind-bogglers such as the following. Take a positive integer n; if it is even divide it by two, and if it is odd multiply it by three and add one. Continue - do you always eventually arrive at the cycle 1 4 2 1 4 2 ?

Besides such recreational problems, number theory also has important applications in computing, the design of algorithms, error correcting codes, digital signal transmission as well as in other areas of pure mathematics.

The Higher Number Theory course covers elementary number theory (primes, congruences etc) as well as a selection of topics such as Diophantine equations, rational approximations to real numbers, quadratic reciprocity, algebraic number domains, lattice packings of spheres, analytic properties of primes and their distribution and some applications.