BRABU BSc Math Part-2 Syllabus (Honors Paper-3 & 4)

BRABU BSc Math Part-2 Syllabus: Here we are writing all the UG (BA/ BSc / BCom) Syllabus of Babasaheb Bhimrao Ambedkar Bihar University. So All those students who are studding under this BRABU Bihar University can get their All Subjects Syllabus from this Website- www.studyorigin.in

Here we are providing you BSc Mathematics Honors Paper-3 and Honors Paper-4 Syllabus. These Papers are used to study in 2nd Year of BSc Mathematics Honors Subject. Each of which Paper there are 100 Marks Examination will be held. There is no any Practical Paper is present in BSc Mathematics Subject.

BRABU BSc Math (Honors) Part-2 Syllabus Details-

University Name	Babasaheb Bhimrao Ambedkar Bihar University
Notice About	BSc Mathematics Part-2 Syllabus
Paper Type	Honors Paper-3 & Paper-4
Academic Year	2nd Year

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BRABU BSc Math (Honors Paper-III) Syllabus

Twelve questions to be set, Six to be answered selecting at least one from each group. One question will be objective and it will be compulsory. This question will carry 20 marks. Rest question are each of 16 marks. Real Analysis I & Abstract Algebra

Group-A: Real Analysis-I (Four questions)

Dedekind’s theory of real numbers ,sequence and its convergence, Cauchy’s sequence, Cauchy’s general principle for convergence, Monotonic sequence, Canter’s construction of real numbers, properties of real numbers.

Continuity and Differentiability of a function of real variable, properties of continuous and discontinuous function, Rolle’s theorems, Mean value theorem, Taylor’s, Lagrange’s and Cauchy’sform of remainders in Taylors expansion,Taylor’s and Maclarin’s series of elementary function.

Group-B: Infinite Series (Three Questions)

Infinite series and their convergence, Comparison test, Cauchy root test, Raabe’s test
Cauchy’s condensation test, Integral test, Leibnitz’s test, Gauss Test, Kummer’s Test, De
Morgan and Parrande’s test,Bertrand test, Absolute convergence and rearrangement of
series, Pringsheim’s theorem, Cauchy’s multiplication of series and its convergence.

Group-C: Algebra (Four Questions)

Binary operation notions of group, Abelian group and non-abelian group with examples, uniqueness of Identity elements and inverse element in a group, Different ways of defining group , Concept of sub-group and cycle group with examples, intersection of sub-group, Subgroup of cyclic group concepts of rings integral domain and field and their examples and general properties, Cancellation law, Divisions of Zero, A finite integral domain as a field.

Cosets, order of an element, Lagrange’s theorem, Group of residue classes, permutations group Cayley’s theorem, Homomorphism and isomorphism of Group, Normal sub-group, Kernal of a group homomorphism, Isomorphism theorem for cyclic group, Factors group, Fundamental theorem of homomorphism of group, Ring of residue classes, Ring of matrices, subring ideals, ring homomorphism and ring, Isomorphism, Kernal of a Homomorphism, Quotient rings, Fundamental theorem of homomorphism of rings.

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BRABU BSc Math (Honors Paper-III) Syllabus

Twelve question to be set, Six to be answer selecting at least one from each group, one question will be objective and it will be compulsory. This question will carry 20 marks and rest question are each of 16 marks.

Group-A: Vector Calculus (Two Questions)

Products of Three and four vectors Differentiation of vectors functions, Differentiation of product of two vectors, Gradient Divergence and curl of a vector function and deduction, Moments of a localized vector about a point work done by a force, Scalar moment of a vector about a directed line.

Group-B: Differential Equations (Three Questions)

Formation and solution of differential equation, Differential equation of the first order, Separation of Variables, Homogeneous form, Linear equation of first order, Clairaut’s from, Geometrical application of first order, differential equation, Linear differential equation of second order with constant coefficients, C.F. and P.I. Orthogonal Traiectories.

Group-C: Statics (Via-Vector) (Three Questions)

Reduction of a force system to a force and a couple, equation of the resultant Principle of virtual work in two dimension, stable equilibrium, Energy test for stability, Catenary Poinsot’s central axis pitch, Null lines.

Group-D: Dynamics

S.H.M. Simple Pendulum, Elastics String and springs, Hook’s Law (One Questions) Components of velocities and acceleration, Cartesian, radial and transverse, tangential and normal, Projectile motion in non-resisted medium (One questions). Motion of a particle under central force, Differential equation of central orbit in polar and pedal forms Newton’s law of gravitation and planetary orbit, Kepter’s laws.

BRABU BSc Math Honors Part-1 Syllabus Marks Distribution:

BSc Math Theory Paper-III	Full Marks: 100
BSc Math Theory Paper-IV	Full Marks: 100
Exam Time for Theory Paper-III	3 Hours
Exam Time for Theory Paper-IV	3 Hours

BRABU BSc Math (Honors Paper-III) Syllabus Image-

BRABU BSc Math (Honors Paper-IV) Syllabus Image-

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