₹275
Author: Dr. C. Muthulakshmi @ Sasikala, Dr. R. Ponraj
ISBN: 9789391549398
Copy Right Year: 2023
Pages: 286
Binding: Soft Cover
Publisher: Yes Dee Publishing
Out of stock
This book on Number Theory emphasises on the elementary topics including Binomial Theorem, Division Algorithm, Prime Numbers, Congruences and Some special congruences. Features: Many worked examples. Perfect tool for preparing for undergraduate exams. Suitable for independent study. Ideal aid for other fields such as Cryptography, Software Engineering, specifically security-based software.
| Weight | .3 kg |
|---|---|
| Dimensions | 22 × 14 × 1 cm |
Chapter 1 Number System
1.1 Introduction
1.2 Peano’s Axioms
1.3 Well Ordering Property (WOP) of Positive Integers
1.4 Triangular Numbers
1.5 Pentagonal Numbers
1.6 Catalan Numbers
1.7 Problems
1.7.1 First Principle of Finite Induction
1.7.2 Second Principle of Finite Induction
1.7.3 Problems on Binomial Coefficient
Exercises
Chapter 2 Division Algorithm
2.1 Introduction
2.1.1 Division Algorithm
2.1.2 General Version of Division Algorithm
2.2 Greatest Common Divisor
2.3 Least Common Multiple
2.3.1 The Euclidean Algorithm
2.4 The Linear Diophantine Equation
2.5 Problems on Divisibility
2.6 Problems on gcd and lcm
2.7 Problems on Linear Diophantine Equations
Exercises
Chapter 3 Prime and Composite Numbers
3.1 Introduction
3.2 Fundamental Theorem of Arithmetic
3.3 Twin Primes
3.4 Goldbach Conjecture
3.5 The Sieve of Eratosthenes
Exercises
Chapter 4 Congruences
4.1 Modulo System
4.2 Congruence Modulo n and Basic Properties
4.3 Binary and Decimal Representation of Integers
4.4 Polynomial Congruence
4.5 Tests of Divisibility
4.6 Linear Congruences
4.7 Diophantine Equations
4.8 Problems on Binary and Decimal Representations of Integers
4.8.1 Decimal Representation
Exercises
Chapter 5 Some Special Congruences
5.1 Introduction
5.2 Wilson’s Theorem
5.3 Quadratic Congruence
5.4 Generalisation of Wilson’s Theorem
5.5 Problems on Fermat’s Theorem
5.6 Problems on Wilson’s Theorem
5.7 Some Factorization Methods
5.7.1 Fermat Kraitchik Factorisation Method
5.7.2 Euler’s Factorization Method
Exercises
Bibliography
Dr. C. Muthulakshmi @ Sasikala is Associate Professor and Head, Department of Mathematics at Sri Paramakalyani College, Alwarkurichi. She has more than 25 years of teaching experience. She has published several research papers in various national/international journals. She has conducted and organized various training programmes on Recreational Mathematics and Vedic Mathematics with aid from UGC Minor Research Program.
Dr. R. Ponraj is Assistant Professor, Department of Mathematics at Sri Paramakalyani College, Alwarkurichi. He has 15 years of experience in teaching and research. He has presented papers at national and international conferences and has 170 publications in reputed national/international journals. He has served as referee for more than thirty five national and international journals and was also editor-in-chief for proceedings of the national level conference.
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