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Course, academic year 2022/2023
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Introduction to Number Theory - NMAI040
Title: Úvod do teorie čísel
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information:
Guarantor: doc. RNDr. Martin Klazar, Dr.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > Discrete Mathematics
Mathematics > Discrete Mathematics
Annotation -
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 -
Last update: T_KAM (25.04.2008)

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

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

Oral exam, in person or in distant mode.

Literature -
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

Requirements to the exam -
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 -
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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