TitleNumber Theory and Trigonometry (Code09050201)
B.Sc. (Hons) Mathematics (2^{nd} semester)
S.No.  Content of the topics  Learning Objectives  Teaching Guidelines  Methodology  Time (Hours) 
1 
· Divisibility, G.C.D., L.C.M.
· Primes and Fundamental theorem of Arithmetic, · Linear congruence, · Fermat’s Theorem, · Wilson’s theorem and its converse, · Linear Diophanatine equation in two variables 
Student will be able to know about the Divisibility linear congruence 
Lecture should be effective so that student will be able to grasp the topics easily 
Assignment/ Seminars/ Class tests/ Presentations 
15 
2 
· Complete residue system
· Reduced residue system modulo m, · Quadratic residue, Euler’s ø function · Generalization of Fermat’s Theorem, · Chinese remainder Theorem Legendre symbols, · Lemma of Gauss; Gauss reciprocity law. · Greatest integer function · The number of divisors and sum of divisor of a natural number n. · Moebius function and Moebius inverse formula. 
Student will be able to know about the Complete residue system 
Lecture should be effective so that student will be able to grasp the topics easily 
Assignment/ Seminars/ Class tests/ Presentations 
15 
3 
· De Moivre’s Theorem and its applications
· Expansion of Trigonometric functions, · Direct circular and hyperbolic functions and their properties, · Inverse circular and hyperbolic functions and their properties, · Logarithm of a complex quantity · Gregory series, Summation of Trigonometric series. 
Student will be able to know about the Trigonometric functions 
Lecture should be effective so that student will be able to grasp the topics easily 
Assignment/ Seminars/ Class tests/ Presentations 
15 
4 
· Inverse circular and hyperbolic functions and their properties,
· Logarithm of a complex quantity · Gregory series, Summation of Trigonometric series. .

Student will be able to know about the Inverse circular and hyperbolic functions 
Lecture should be effective so that student will be able to grasp the topics easily 
Assignment/ Seminars/ Class tests/ Presentations 
Books Recommended:
 L. Loney : Plane Trigonometry Part –II, Macmillan and company, London.
 S. Verma and K.S. Sukla : Text Book on Trigonometry, Pothishala Pvt. Ltd. Allahabad
 Ivan Ninen and H.S. Zuckerman. An Introduction to the Theory of Numbers.
 John B. Fraleigh. A First course in Abstract Algebra. 7^{th}, Pearson, 2002.
 Artin, Abstract Algebra, 2^{nd} Ed., Pearson, 2011.
 David M .Burton, Elementary Number Theory, 6^{th}, Tata McGraw–Hill, Indian reprint 2007.
 Neville Robinns, Beginning Number theory, 2^{nd} , Narosa Publishing House Pvt. Ltd. Delhi 2007.
 Joseph A Gallian, Contemporary Abstract Algebra, 4^{th}, Narosa Publishing House , 1999.