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Course, academic year 2023/2024
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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
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Additional information: http://kam.mff.cuni.cz/~klazar/UTC17.html
Guarantor: doc. RNDr. Martin Klazar, Dr.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > Discrete Mathematics
Mathematics > Discrete Mathematics
Annotation -
1. Diophantine approximations. 2. Geometry of numbers. 3. Congruences and residues. 4. Prime numbers. 5. Integer partitions. 6. Diophantine equations.
Last update: T_KAM (07.05.2001)
Aim of the course -

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

Last update: T_KAM (25.04.2008)
Course completion requirements -

Oral exam, in person or in distant mode.

Last update: Klazar Martin, doc. RNDr., Dr. (22.09.2020)
Literature -

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

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

Last update: Klazar Martin, doc. RNDr., Dr. (12.10.2017)
Requirements to the exam -

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

Last update: Klazar Martin, doc. RNDr., Dr. (11.06.2019)
Syllabus -

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).

Last update: T_KAM (20.04.2007)
 
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