# Number Theory

Vrije Universiteit Amsterdam

## Course Description

• ### Course Name

Number Theory

• ### Host University

Vrije Universiteit Amsterdam

• ### Location

Amsterdam, The Netherlands

Mathematics

• ### Language Level

Taught In English

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

6
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4
• ### Overview

COURSE OBJECTIVE
- The student is able to perform basic number theoretic calculations (including congruence arithmetic, primes, continued fractions algorithm, arithmetic functions, Jacobi symbols, constructions of rational points on conic sections and cubic curves from other rational points) to solve concrete problems.
- The student knows some central applications, open problems, and related directions in number theory (including factorization, cryptography, abc-conjecture, Mason-Stothers theorem) and can analyze their consequences for specific situations.
- The student knows fundamental number theoretic concepts and theorems (including primitive roots, quadratic reciprocity, Diophantine
equations, some algebraic number theory, continued fractions) and can solve problems/create proofs about and with those in explicit
situations.

COURSE CONTENT
The following subjects will be treated:

- integers, primes, prime distribution
- congruences, primitive roots
- primality tests, factorization
- public key cryptography
- Diophantine equations, abc-conjecture
- algebraic numbers, algebraic integers
- continued fractions

Next to a theoretical approach, practical/algorithmic aspects will also
be covered. The mathematics software system "SageMath" will be used to
illustrate some explicit number theoretic calculations.

TEACHING METHODS
Lectures and exercise sessions

TYPE OF ASSESSMENT
Homework assignments (25%) and a final written exam (75%)

ENTRY REQUIREMENTS
Basic knowledge of groups, rings, and fields is essential.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.

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