(18 Mar 03)

MA5202 Number Theory

Modular credits: 4

Workload: 3-0-0-0-7

Pre-requisite(s): MA4203

Preclusion(s): Nil

<SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">The aim of this course is to illustrate the use of algebraic structures (e.g. groups, rings, domains<SPAN style="mso-tab-count: 2"></SPAN>,<o:p></o:p></SPAN><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><SPAN style="mso-spacerun: yes"></SPAN><SPAN style="mso-spacerun: yes"> </SPAN><SPAN class=GramE>fields</SPAN>) in the understanding of the properties of algebraic numbers. <o:p></o:p></SPAN>

<SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN>

Major topics: Algebraic numbers, conjugates, algebraic integers. Discriminant, norm and trace. Integral basis. Units. Ideals. Prime factorization of ideals. Norm of an ideal. Geometry of numbers: lattices, Minkowski's convex body theorem. Class group. Minkowski's constant. Calculation of class number. Dirichlet's Unit Theorem. Fundamental units. Application to Pell's equation. Regular primes. Kummer's special case of Fermat's Last Theorem.