MATM15F

Tillfällig

Number Theory

7.5

Gemensam kurs, avancerad nivå och forskarnivå

7151 (Matematikcentrum (inst LTH) / Matematik (LTH))

 -02-27

Professor Thomas Johansson

Engelska

Varje hösttermin

That the postgraduate student should learn the basic concepts of Number Theory. This is an important research field within Mathematics, but also has applications in Cryptography, Coding Theory and Computer Science.

Classical theory of modulo arithmetic, quadratic reciprocity, quadratic forms and Diophantine approximation.

be able to state and prove the Quadratic Reciprocity Law

be able to state and prove some results about when it is possible to express an integer as a sum of squares
be able to account for the basic theory of Diophantine approximation of real numbers.

be able to solve systems of linear congruences.

Föreläsningar

Seminarier

Skriftlig tentamen

Muntlig tentamen

Underkänd, godkänd

Calculus in one and several variables. Linear Algebra.

Burton, David M.: Elementary Number Theory. 2010. ISBN 9780071289191.

MATM15F

 -02-27

Professor Thomas Johansson