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Title-Number Theory and Trigonometry (Code-09050201)

B.Sc. (Hons) Mathematics (2nd 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. 7th, Pearson, 2002.
  • Artin, Abstract Algebra, 2nd Ed., Pearson, 2011.
  • David M .Burton, Elementary Number Theory, 6th, Tata McGraw–Hill, Indian reprint 2007.
  • Neville Robinns, Beginning Number theory, 2nd  , Narosa Publishing House Pvt. Ltd. Delhi 2007.
  • Joseph A Gallian, Contemporary Abstract Algebra, 4th, Narosa Publishing House , 1999.
Admissions Open 2019-20