MATHEMATICS HONOURS part-III

TILKA MANGHI BHAGALPUR UNIVERSITY AND MUNGER UNIVERSITY           MATHEMATICS( HONOURS)   part-III 

                    
                   

B.sc part-I math honours patern

       Honspaper                   Sub paper                 Eng/Hind

                                                                          💯/marks

        200/marks                    200/marks     

        Paper-I-100                   Physics                          Chemistry

        Paper-II-100                 75-theory                      75-theory

                                               25-practical                  25-practical

B.sc part-II math honours patern

Honspaper       Sub paper      Eng/Hind

                                                    💯/marks

200/marks        200/marks     

Paper-I-100       Phy           Chem

Paper-II-100    75-theory   75-theory

                         25-practical  25-practical

B.Sc part-III honours patern

Paper   paper   paper   paper     GK&GS

  (V)      (VI)       (VII)      (VIII)   

      💯 marks all papers

Mathematics honour's part -3

                       Paper-V

Total number of question 12.answer any 6 questions selecting at least one from each group. Question number 1 will be objective and compulsory.

                  GROUP-A

REAL ANALYSIS-

Riemann  integral, integrability of continuous and monotonic function. The fundamental theorem of integral calculus, mean value theorem of integral calculus:-

Improper integrais and their convergence, comparison tests,Abel's and Dirichlet's derivability and integrability of an integral of a function of a parameter:-

Series of arbitrary terms, convergence, divergence and oscillation, Abel's and Dirichlet's test. Multiplication of series :-

Partial derivation and differentiability of real valued functions of two variables, Schwarz and Young's theorem:-

Fourier series,Fouries expansion of piecewise monotinic functions:-

     GROUP-B

COMPLEX ANALYSIS:-

Complex numbers as ordered pairs, geometric representation of complex numbers, Sereographic projection, equation of a line through two given points Z1 and Z2 equation of circle:-

Continuity and differentiability of complex functions, Analytic function,Cauchy's kiemann equations,Hermonic functions:-

Elementary functions, Mapping by elementary functions, Mobius transformations, Fixed points, Cross ratio, Inverse points and critical mappings, Conformal mappings:

GROUP-C

METRIC SPACES:-

Definition and examples of metric space, Neighborhoods, Limit points, Interior

points,

Open and closed sets,Closures and interior, boundary points, Sub-space of matric space, Cauchy sequences,completeness  .

Cantor's intersection theorem ,Conraction principle,construction of real numbers as the completion of the incomplete metric space of retiooals,Reat numbers as a complete ordered field.

Dense subsets, Baire category's theorem ,Separable, second Countable and first countable spaces,Continuous functions, Extension theorem,Uniform continuity, Isometry and homomorphism,Equivaleot Matrix, completeness,sequential compactness.

Totally bounded spaces ,Finite intersection properly,continuous functions and compact set, connectedness,components,Corinuous functions and  connected sets:-