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Number Theory for CS Students

This document outlines a course on number theory for computer science students. The course aims to teach basic number theory concepts with a computational focus, including prime factorization, modular arithmetic, and properties of integers. It is divided into 5 units covering topics such as divisibility, the fundamental theorem of arithmetic, congruences, Fermat's theorem, and primitive roots. The course objectives are to teach factorization, quadratic residues, the Chinese remainder theorem, and polynomial arithmetic. Upon completing the course, students should be able to apply number theory concepts and analyze related theorems and algorithms.

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Abhishek Kumar
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63 views2 pages

Number Theory for CS Students

This document outlines a course on number theory for computer science students. The course aims to teach basic number theory concepts with a computational focus, including prime factorization, modular arithmetic, and properties of integers. It is divided into 5 units covering topics such as divisibility, the fundamental theorem of arithmetic, congruences, Fermat's theorem, and primitive roots. The course objectives are to teach factorization, quadratic residues, the Chinese remainder theorem, and polynomial arithmetic. Upon completing the course, students should be able to apply number theory concepts and analyze related theorems and algorithms.

Uploaded by

Abhishek Kumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Department of Computer Science and Engineering, GITAM Deemed to be University

L T P S J C
MATH2311 NUMBER THEORY 2 0 0 0 0 2

Pre-requisite None
Co- requisite None
Preferable Engineering and Science
exposure

Course Description:
This course is designed to explain the basics and applications of number theory for the students
of Computer Science. The core courses of these branches encounter with concepts like prime
factorization, modular arithmetic, and quadratic reciprocities in number theory. The first unit
of the course provide a strong platform for such encounters and the other units focuses on
applications of number theory.

Course Educational Objectives:


1. To teach basic concepts of number theory focusing on Computational aspects.
2. To teach the concepts of factorization of integers.
3. To teach Format’s theorem and quadratic residues.
4. To explain Chines remainder theorem and Euclidean algorithm.
5. To explain polynomial arithmetic.

UNIT 1 Basic Concepts in Number Theory 5 Hours


Topics in elementary number theory, Divisibility, Greatest Common Divisor, Euclidean
Algorithm

UNIT 2 5 Hours
Fundamental theorem of Arithmetic, Congruences, Properties of congruences, Linear
congruences

UNIT 3 5 Hours
Fermat's theorem, Fermat's little theorem, Wilson’s theorem

UNIT 4 5 Hours
Chinese remainder theorem, The functions 𝜏𝜏 𝑎𝑎𝑎𝑎𝑎𝑎 𝜎𝜎, Euler Phi-function, Euler’s theorem,
Some properties of phi function

UNIT 5 5 Hours
The order of integer modulo n, Primitive roots for prime, Composite number having
primitive roots

B Tech. Computer Science and Engineering w.e.f. 2021-22 admitted batch


Department of Computer Science and Engineering, GITAM Deemed to be University

Textbooks:
1. Elementary Number Theory | 7th Edition by David Burton, Mc Graw Hill Education

References:
1. Basic Number Theory by S.B. Malik,S. Chand publishers

Course Outcomes:
Upon successful completion of this course the student should be able to
1. Apply concepts of number theory focusing on Computational aspects.
2. Analyze concepts of factorization of integers.
3. Explain Fermat’s theorem and quadratic residues.
4. Analyse Chines remainder theorem and Euclidean algorithm.
5. Analyse the concept of polynomial arithmetic.

CO-PO Mapping:

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3
CO1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
CO2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
CO3 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
CO4 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
CO5 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1

Note: 1 - Low Correlation 2 - Medium Correlation 3 - High Correlation

APPROVED IN:
BOS : 26-04-2021 ACADEMIC COUNCIL: 17-09-2021

SDG No. & Statement: 4


Ensure inclusive and equitable quality education and promote lifelong opportunities for
all.
SDG Justification:
Learning of various mathematical techniques will lead to knowledge of applications in
Engineering problems

B Tech. Computer Science and Engineering w.e.f. 2021-22 admitted batch

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