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### Title-Number Theory and Trigonometry (paper-1) (Code-09010201)

 S.N Unit Content of the topics Learning objects Teaching Guidelines Methodology Time (Hrs) 1 one 1.   Divisibility, G.C.D., L.C.M. 2.   Primes and Fundamental theorem of Arithmetic 3.   Linear congruence, 4.   Fermat’s Theorem, 5.   Wilson’s theorem and its converse, 6.   Linear Diophanatine equation in two variables 7.   Divisibility, G.C.D., L.C.M. Students will be able to   1.       Divisibility, G.C.D., L.C.M. 2.       Primes and Fundamental theorem of Arithmetic, 3.       Fermat’s Theorem, Wilson’s theorem and its converse. Lecture should be effective so that student can grasp the topics easily. 1. Lecture. 2.  Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5.  Discussion on Assignment. 6. Evaluation of Assignment. 15 2 Two 1. Complete residue system 2. Reduced residue system modulo m, 3. Quadratic residue, Euler’s ø function 4. Generalization of Fermat’s Theorem, 5. Chinese remainder Theorem Legendre symbols, Lemma of Gauss; Gauss reciprocity law. 6. Greatest integer function Students will be able to 1.       Complete residue system, Quadratic residue, Euler’s ø function. 2.       Generalization of Fermat’s Theorem. 3.       Chinese remainder Theorem, 4.       Legendre symbols, Gauss integer function,Chinese remainder theorem. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.     Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15 3 Three 1. De Moivre’s Theorem and its applications 2. Expansion of Trigonometrical functions, 3. Direct circular and hyperbolic functions and their properties, 4. Inverse circular and hyperbolic 5. functions and their properties, 6. Logarithm of a complex quantity 7. Gregory series, Summation of Trigonometric series. To make students familiar with Direct circular and hyperbolic functions and their properties, De Moivre’s Theorem and its applications. Inverse circular and hyperbolic functions and their properties, Logarithm of a complex quantity. Gregory series, Summation of Trigonometric series. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.    Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15