Subjects(version: 916)
Introduction to Number Theory - NMAI040
Title: Úvod do teorie čísel Department of Applied Mathematics (32-KAM) Faculty of Mathematics and Physics from 2017 winter 3 winter s.:2/0, Ex [HT] unlimited unlimited no taught Czech, English full-time http://kam.mff.cuni.cz/~klazar/UTC17.html
Guarantor: doc. RNDr. Martin Klazar, Dr. Informatika Mgr. - Diskrétní modely a algoritmy Informatics > Discrete MathematicsMathematics > Discrete Mathematics
 Annotation - ---CzechEnglish
Last update: T_KAM (07.05.2001)
1. Diophantine approximations. 2. Geometry of numbers. 3. Congruences and residues. 4. Prime numbers. 5. Integer partitions. 6. Diophantine equations.
 Aim of the course - ---CzechEnglish
Last update: T_KAM (25.04.2008)

Students learn fundamentals of elementary number theory and master its basic techniques.

 Course completion requirements - ---CzechEnglish
Last update: doc. RNDr. Martin Klazar, Dr. (22.09.2020)

Oral exam, in person or in distant mode.

 Literature - ---CzechEnglish
Last update: doc. RNDr. Martin Klazar, Dr. (12.10.2017)

G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers

lecture notes http://kam.mff.cuni.cz/~klazar/ln_utc.pdf

 Requirements to the exam - ---CzechEnglish
Last update: doc. RNDr. Martin Klazar, Dr. (11.06.2019)

Student gets at the exam one questio. Exam is oral but student can prepare for

cca 45 minutes some notes which she or he then explains to the examinator. This fully determines his/her grade.

Exam questions: 1) - 6) according to the sylabus

 Syllabus - ---CzechEnglish
Last update: T_KAM (20.04.2007)

1. Diophantine approximations (approximating real numbers by fractions).

2. Geometry of numbers (lattice points, Minkowski's theorem on convex body). 3. Congruences and residues (quadratic residues). 4. Prime numbers (estimates of Chebyshev and Mertens). 5. Integer partitions (Euler's pentagonal identity). 6. Diophantine equations (Pell equation, FLT for

n=4 and for polynomials).

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