MAS/320

Number Theory

Coursework:		1	2	3	4	5			results
Hints:		1	2	3	4	5

		prime problems
		Sample examination paper

Coursework regulation:

• To be admitted to the final exam, you must submit all courseworks. Requests for exemptions must be supported by a statement from your advisor.
• Each coursework must be submitted in the course's box and it must display the student's number and name.
• The coursework marks will be posted on this site, the marked scripts will be returned in class.
• Model solutions -when given- will be given only in class.
• Any query must be submitted in writing to the lecturer, along with the script, within one week of the marked script being returned.

Final examination:

Duration:

3 hrs.

Rubric:

You should attempt all questions. Marks awarded are shown next to the questions.
Calculators are permitted, but any programming, plotting or algebraic facility may not be used.

Grade boundaries:

Standard QMW Maths.

Key objectives:

To pass the exam, you must be able to explain and exemplify all concepts listed below,
and be fluent at computations.
• SIMPLE CONTINUED FRACTIONS:
  expansion into SCF; convergents; accuracy of approximation.
  
  
• QUADRATIC IRRATIONALS:
  reduced quadratic irrationals and their SCFs;
  compute SCF given a quadratic irrational, and vice-versa;
  Legendre's algorithm for sum of squares; solve x^2-Dy^2=N.
  
  
• QUADRATIC FORMS
  discriminant; (in)definite forms; reduced forms; unimodular transformations; equivalent forms; class number;
  decide whether two forms are equivalent; compute all reduced forms of a given discriminant; compute the class number.
  
  
• MODULAR ARITHMETIC
  Euler's phi-function; additive and multiplicative orders; primitive roots; quadratic residues; Legendre's symbol; quadratic reciprocity.