BRABU BSc Math Part-3 Syllabus (Honors Paper-5, 6, 7, 8)

BRABU BSc Math Part-3 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-5, Honors Paper-6, Honors Paper-7 and Honors Paper-8 Syllabus. These Papers are used to study in 3rd 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-3 Syllabus Details-

University Name	Babasaheb Bhimrao Ambedkar Bihar University
Notice About	BSc Mathematics Part-3 Syllabus
Paper Type	Honors Paper-5, Paper-6, Paper-7, Paper-8
Academic Year	3rd Year

BRABU BSc Math (Honors Paper-V) Syllabus

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

Group-A

Function of two variables, Limit, repeated limits, Moore, Osgood Theorem, Continuity and differentiability of function of two variable, Young’s and Schwarz condition of equality of fxy and fyx, Implicit function theorem, Taylor’s theorem, Maxima, Minima of Functions of two variables, Lagrange’s method of undermined multipliers.( Three Questions)

Group-B

Definition and existence of Riemann integral of bounded function, Darboux Condition of integrability, Riemann Integrability of continuous functions and monotonic function, Riemann integral of function with finite number of limit points, Riemann integral as the limit of a sum, the fundamental theorem of integral calculus, Mean Value theorem.(Two Questions)

Improper integral, convergence of an improper integral, comparison tests, Dirichlet’s test, Beta and Gamma functions, their properties and relationship, differentiation under integral sign.(One Questions)

Double and triple integrals, changes of order of integration, Line, surface and volume integrals Green’s Gauss’s and stokes theorem.(One Questions)

Group-C

Weierstrass Sequence and series of functions and their pointwise convergence, Uniform convergence of sequence and series of functions, Wire strass M-test, uniform convergence and continuity, Dini’s test, Abel’s test, Dirichlet’s Test, Uniform convergence and integration, Uniform convergence and differentiation.(Two Question)

Infinite product and its convergence and their mutual relations, Double series, Sum by rows, Sum by columns, Pringsheim’s Theorem, Elementary notions of metric spaces and topological spaces.

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BRABU BSc Math (Honors Paper-VI) 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 and rest question are each of 16 marks.

Group- A (Group Theory)

Centre, Normalizer, Conjugacy, class equation, auto morphisms, inner auto morphisms, Commutator and commutator sub group, Direct Product of two groups, Solvable groups, Finite Groups.(Three Questions)

Group-B: (Ring)

Division ring, Polynomial ring, Imbedding of a ring without unity in a ring with unity, Imbedding of a ring and integral domain in a field, Characteristics of a field, Field of quotients, Polynomials over commutative ring, Euclidean domains, Principal ideal domains, Unique Factorization domains.

Group-C: (Linear Algebra)

Vector spaces, Subspaces, Bases and dimension, Linear Transformation, Algebra of linear transformation, Matrix and linear transformation, Rank and nullity of a linear transformation, Direct sum of sub-spaces, characteristics value, characteristics vector, Cayley Hamilton theorem.(Four Questions)

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BRABU BSc Math (Honors Paper-VII) Syllabus

Twelve question 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 and rest questions are each of 16 marks.

Group- A ((Mechanics)

Motion in a resisting medium, motion of a body about a fixed point, Angular velocity relation between angular velocity and linear velocity of a point of the body general motion of a body. (One Questions)

Moment of inertia, Definitions and standards results, Moment ellipsoid and perpendicular axis theorem, Principal axis of inertia (existence of principal axis of inertia at point), Determination of principal axis of inertia, Equimomental systems. (One Questions)

Angular momentum and Kinetic energy of a rigid body rotating about a fixed point, Kinetic energy of a rigid body in a general motion.

Principle of linear momentum, Angular momentum and energy for a rigid body, D’Alembert’s principle and general equations of motion of a rigid body, Motion about a fixed axis, Compound pendulum. (Two
Questions)

Group-B:

(Attraction and Potential)

Attraction and potential, Attraction and potential of rod, Rectangular and circular dies, Spherical shells, sphere (Laplace’s and Poisson equations), Theorem of equipotential surface. Two Questions)

Hydrostatics

Pressure at a point, Thrust on a Plane surface, Centre of pressure, Equilibrium of floating bodies. (Two Questions)

Group-C: (Differential Equations)

Second order equations with variable coefficients, Solution of second order differential equations with variable coefficients, Method of variation of parameters, Total Differential equation in three independent variables, Simultaneous differential equations, Lagrange’s Linear partial differential equations, standard forms, Charpits method, Partial differential equations of higher order with constant coefficients, Monge’s method. (Three Questions) Ten question to be set in each optional paper and five questions to be answered.

BRABU BSc Math (Honors Paper-VIII) Syllabus

Group- A Numerical Analysis

Finite, Central and Divided difference, interpolation, Inverse Interpolation, Numerical Differentiation, Numerical Integration, Trapezoidal, Simpson’s 1/3rd and 3/8th rules, Weddle’s rule, Gauss quandrature formula of integration, Gregory’s formula and the Euler Maclaurin’s formula. (Three Questions)

Solution of difference equation of the first order, General equations, Linear difference equations with constant coefficients, solution of ordinary differential equations- one step method : Euler’s modified method Picard’s and Runge- Kutta’s methods of solution and Milne- Simpson’s Method. (Three Questions)

Simultaneous Linear Equations: Gauss elimination, Gauss- Seidel’s, Jordan’s and relaxation methods (simple problems). (Two Questions)

Finding roots of polynomial equations: Regula falsi, Bisection, Newton- Raphson method for several variables, iterative method and its generalization, significant figure and errors of computation. (Two Questions)

Group-B

(Spherical Trigonometry and Astronomy)

Spherical triangle, Definition, Fundamental Formula ( Cosine, Sine, Sine-Cosine, Cotangent), Napier’s rule, D’Alemberts analogies, right angle triangle

(Astronomy)

Celestial sphere: Definition: Different System of Co-ordinates, Phenomenon of rising and setting of stars, Twilight. (Two Question)

Solar system, Two body problem, Equation of relative motion. (One Questions)

Area integral, Kepler’s law, Anomalies, Kepler’s Equations. (One Questions)

Stationary points phase of planet, Refraction, Simpson’s- Bradlay’s and Cassini’s formulas, Effect of refraction in the position of a body. (Two Questions)

Annual Aberration, Effect of the aberration on celestial latitude and longitude, Effect of aberration on right ascension and declination, Parallax, Effect of Parallax on latitude, longitude, right ascension and declination. (Two Questions)

Group-C: (Number Theory)

The basic representation theorem, Linear Diophantine equation, fundamental theorem of Arithmetic, Fermat’s little theorem and Wilson’s Theorem. (Two Questions)

Basic properties of Congruences, Residue System, Euler’s thorem; Chinese Remiander theorem; Multiplicative arithmetic functions, the Euler’s function ϕ (n), μ, (n) and their simple properties; Moblus Inversion formula, Perfect numbers and the function r (n). (Three Questions)

The quadratic Reciprocity law; Euler’s criterion. The legendre symbol and its properties and applications, Gauss, Lemma Gauss quadratic reciprocity law, Quandratic congruences with composite moduli.
(Three Questions)

Representation of integers as sums of squares; Sums of two squares. Thue’s lemma, Feemat’s theorem, sums of four squares and Euler’s lemma, Lagrange’s theorem. (Two Questions)

Group-D: (Probability Theory)

Event, Probability of an event, sample space, probabilities a finite sample space, Mutually exclusively events and complementary events, independent events, conditional probability. (One question)

Axoms for probability in finite sample spaces, product rule of probabilities in a sample space, Baye’ s theorem , Random variables and their probability functions. Mathematical expectation and moment of a random variable, Mean absolute deviation, variance, standard variation, Chebyshev’s theorems for a probability distribution and frequency distribution of measurements. (Three questions)

Convergence of a sequence of random variables, convergence in distributions, convergence in probability, almost sure convergence, convergence in a quadratic mean, Halley/ Bary theorem. (Three questions)

Complex valued random variables, characteristic function, Inversion theorem , continuity theorem, Distrubution and Kolomogarow ‘s inequality, weak and strong laws of large numbers. (Three questions)

BRABU BSc Math Honors Part-1 Syllabus Marks Distribution:

BSc Math Theory Paper-V	Full Marks: 100
BSc Math Theory Paper-VI	Full Marks: 100
BSc Math Theory Paper-VII	Full Marks: 100
BSc Math Theory Paper-VIII	Full Marks: 100
Exam Time for Theory Paper-5, 6, 7, 8	3 Hours

BRABU BSc Math (Honors Paper-5) Syllabus Image-

BRABU BSc Math (Honors Paper-6) Syllabus Image-

BRABU BSc Math (Honors Paper-7) Syllabus Image-

BRABU BSc Math (Honors Paper-8) Syllabus Image-

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