Page 74 - CatalogNEP-PS

LEARNING OUTCOMES:

This course will enable the students to:
 Get familiar with the basic number-theoretic techniques.
 Comprehend some of the open problems in number theory.
 Learn the properties and use of number-theoretic functions and special types of numbers.
 Acquire knowledge about public-key cryptosystems, particularly RSA.

THEORY (45 Hours)

UNIT – I: Divisibility and Prime Numbers (12 Hours)

The Fundamental theorem of Arithmetic‘s: Introduction, the division algorithm, divisibility, and
the greatest common divisor. Euclid‘s lemma; The Euclidean algorithm, Linear Diophantine
equations; The Fundamental theorem of Arithmetic, The sieve of Eratosthenes, Euclid theorem
and the Goldbach conjecture; The Fibonacci sequence and its nature.
UNIT – II: Theory of Congruences and Number-Theoretic Functions (21 Hours)

Congruence relation and its basic properties, Linear congruences and the Chinese remainder
theorem, System of linear congruences in two variables; Fermat's little theorem and its
generalization, Wilson's theorem, and its converse; Number-theoretic functions for sum and the
number of divisors of a positive integer, Multiplicative functions, The greatest integer function;
Euler‘s Phi-function and its properties.
UNIT – III: Public Key Encryption and Numbers of Special Form (12 Hours)

Basics of cryptography, Hill‘s cipher, Public-key cryptosystems, and RSA encryption and
decryption technique; Introduction to perfect numbers, Mersenne numbers and Fermat numbers.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

1. Burton, David M. (2011). Elementary Number Theory (7th ed.). McGraw-Hill Education
Pvt. Ltd. Indian Reprint 2017.
2. Jones, G. A., & Jones, J. Mary. (2005). Elementary Number Theory. Springer
Undergraduate Mathematics Series (SUMS). Indian Reprint.
3. Robbins, Neville (2007). Beginning Number Theory (2nd ed.). Narosa Publishing House
Pvt. Ltd. Delhi.
4. Rosen, Kenneth H. (2011). Elementary Number Theory and its Applications (6th ed.)
Pearson Education. Indian Reprint 2015.
5. Elementary Number Theory, Sharma Publication, Jalandhar.

Math.213 Combinatorics 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to:
 Introduce various techniques of permutations, combinations, and inclusion-exclusion.
 Learn basic models of generating functions and recurrence relations in their application
22. to the theory of integer partitions.

LEARNING OUTCOMES:

After completing the course, student will:

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