Discription

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers & integer-valued functions. There are two subfields of number theory. One is Analytical Number Theory and other is Algebraic number theory. The focus of the course is on study of the fundamental properties of integers & develops ability to prove basic theorems.

Learning Outcomes

After successful completion of the course, student is able to

1. effectively express the concepts and results of Number Theory. 
2. construct mathematical proofs of statements and find counterexamples to false statements
3. explore multiple representations of topics including graphical, symbolic, numerical, oral, and written. Encourage students to make connections among the various representations to gain a richer, more flexible understanding of each concept.
4. use mathematical concepts in problem-solving through integration of new material and modeling.

Contents

1. Divisibility
2. The function [x]
3. Greatest common divisor
4. Euclid’s theorem, Eculidean Algorithm
5. Fundamental theorem of Arthimatic
6. Linear and nonlinear Diophantine equations
7. Congruences,Residue classes
8. Linear congruences and congruences with prime moduli
9. The chinese remainder theorem
10. Fermat's numbers, Fermat's little theorem
11.  Wilson's theorem
12. Euler's theorem and Euler's function
13. Euler's function for composite moduli, Mobious function
14. Primitive roots 
15. Universal exponents
16. Quadratic Residues
17. Legendre symbol
18. Law of quadratic reciprocity,
19. The Jacobi symbol
20. Equations & Fermat’s conjecture for n = 2, n = 4

Recommended Books

1. Rosen, K.H. (2011). Elementary number theory & its applications. (6th ed.). Boston: Addison-Wesley.
2. Apostal, T.M. (2010). Introduction to analytic number theory (3rd ed.). New York: Springer.

Suggested Books

1. Leveque, W. J. (2002). Topics in number theory, Volumes I & II. New York: Dover Books.
2. Burton, D. M. (2007). Elementary number theory. New York: McGraw-Hill.

Assessment Criteria

       Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

       Mid-Term Exam:   30

       Final-Term Exam: 50

Key Dates and Time of Class Meeting

Monday         09:30 AM -11:00 AM (Reg)     12:30 PM-02:00 PM (SS)                                                                         08:00 AM-09:30 AM (EX-PPP New-1) 

Tuesday                                                                                                           03:30 PM-05:00 PM (EX-PPP New)      08:00 AM-09:30 AM (EX-PPP New-1) 

Thursday                                                                                                          12:30 AM-02:00 PM (EX-PPP New)     

Friday            08:00 AM -09:30 AM (Reg)    11:00 PM-12:30 PM (SS)

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                           December 14, 2020 to December 18, 2020

Final Term Examination                                                         February 08, 2021 to February 12, 2021 

Declaration of Result                                                             February 19, 2021