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Title- Number Theory and Trigonometry (Code-09050201) | B.Sc. (Hons) Mathematics | 2nd semester

Title- Number Theory and Trigonometry (Code-09050201)

B.Sc. (Hons) Mathematics – 2nd semester

S.No. Topic Domain Hours as per UGC
 

 

 

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

 

 

 

Must know

 

 

 

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.

 

 

 

 

Must know

 

 

 

 

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.

 

 

 

Must know

 

 

 

 

15

 

 

4

·         Inverse circular and hyperbolic functions and their properties,

·         Logarithm of a complex quantity

·         Gregory series, Summation of Trigonometric series.

.

 

 

 

Nice to know

 

 

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.
Admission 2017