Bsc final year mathematics syllabus 2021 download pdf

Hello friends, there is often confusion in the minds of the students regarding the syllabus and students are wondering what will be asked in the exam. To overcome this dilemma, we are constantly trying to provide you the syllabus of different subjects and classes in a simple and effective way. Today we have provided the syllabus of B.Sc Final Year Mathematics subject. So let's see.

Table of content (toc)

Bsc final year mathematics Paper 1st Linear Algebra And Numerical Analysis syllabus

Unit -1 : Definition and example of vector space, subspace, sum of subspaces and direct.  Sum, linear extension, linear dependence, independence and their basic properties, basis, of basis.  Existence theorem, extension theorem, immutability of the number of elements in a basis, dimension, finite dimensional vector spaces, existence of a complement subspace of a subspace of finite dimensional vector space, dimension of the sum of subspaces, division space and its dimension.

Unit -2 : Linear transforms and their matrix representations, algebra of linear transformations, Species.  Emptiness Theorem, Transformation of Base, Dual Space, Binary Space and Natural Isomerism, Linear Transformation of Adjoint, Eigen Values ​​and Eigen Vectors of Linear Transforms, Diagonalization, Quadratic, Quadratic and Hermitian Homogeneous.

Unit - 3 : Intrinsic multiplication space - Cauchy-Swarz inequality, Orbital vector, Ordinal complement, Normal orthogonal set and base, Bessel's inequality for finite dimensional spaces, Gram Schmidt perpendicularity process.

Unit 4: Solutions of Equations- Bi-division Method, Sequent Method, Regula False Method, Newton's Method Roots of Polynomial Equations of Second Order.  Interpolation Lagrange Interpolation, Interpolation Formula Using Divided Difference Difference, Numerical Quantification, Newton Coates Formula, Gauss Quadrant Formula.

Unit 5: Linear Equations, Direct Methods of Solving System of Linear Equations: (Gauss Elimination, L-U Decomposition, Cholesky Decomposition), Iterative Methods (Jacobi Method, Gauss-Sidel Method), Simple Differential Equations: Euler Method, Single Step Method, Rung Kutta Method , Multistep Method, Milne-Simpson Method, Methods based on Numerical Integration and Methods Based on Numerical Differential.

Note :- Use of Scientific Calculator is allowed in the examination of this question paper.

Linear Algebra And Numerical Analysis Text Books : 

1. K. B. Datta- Matrix and Linear Algebra , Pretice hall of India Pvt . Ltd. New Delhi , 2000 . 

2. S. S. Sastry- Introductory Methods of Numerical Analysis , PHI Learning Pvt . Ltd.

Linear Algebra And Numerical Analysis Reference Books 

1. K. Hoffiman and R. Kunze - Linear Algebra , 2nd Edition , Prentice Hall Englewood Cliffs New Jersey , 1971 . 

2. S. K. jain , A Gunawardena & P. B. Bhattacharya- Basic Linear Algebra with MATLAB Key College Publishing ( Springer - Verlag ) 2001 

3. S. Kumarsaran- Linear Algebra , A Bermetric Approac Prentice - Hall of India , 200 

4. Balaguruswamy- Numerical Methods , Tata Mc Graw Hill Publication , New Yark .

Bsc final year mathematics Paper 2st Real and Complex Analysis syllabus

Unit.1 - Riemann Integral, Key Integration, Fundamental Theorem of Integration, Mean Theorem of Integrations, Partial Derivatives and Differentiability of Real Value Functions of Two Variables, Schwarz and Young's Theorem, Ambiguous Function Theorem.

Unit 2. Improper integrals and their convergence, comparison tests, Abel and Dirichle's test, Fulani integrals as operating functions, continuums, integrals, differentiability and integrability of a Pachel's function, Fourier series of half and complete intervals.

Unit 3. Definition and examples of distance space, proximity, boundary points, interior points, open and closed sets, convex and interior, boundary points, subspaces of distance space, Cauchy sequence, completeness, Kentor's universal theorem, contraction principle, of complete ordered field  Real numbers in form, dense subsets, Bayer-category theorem, separation, second countable and first countable space, continuous functions, uniform continuum, properties of continuous functions on compact sets.

Unit 4 - Continuity and Differentiability of Complex Functions, Analytical Functions, Cauchy-Riemann Equations, Harmonic Functions, Cauchy Theorem and Cauchy Integration Formulas.

Unit 5. Power Series, Formulation of Analytical Functions, Taylor's Series, Laurent's Series, Singularity Singularities), Cauchy's Remainder Theorem, Contour Integration.

Real and Complex Analysis Text Books -

1. Mathematical analysis by S. C. Malik and Savita Arora , New Age Publication , Delhi . 

2. G.F. Simmons - Introduction to Topology and Modern Analysis , Mc Graw Hill , New York 1963 

3. L. V. Alhfors , complex Analysis Mc Graw Hill , New York 

4. MP  Books of Hindi Granth Academy.

Real and Complex Analysis Recommend Books -

1. Walter Rudin- Real and Comples Analysis , Mc Graw Hill , New York 

2. Ponnuswamy - Complex Analysis , Narosa Publication , New Delhi .

3. R. V. Churchill & J.W. Brown , Complex Variables and Application , 5th Edition , Mc Graw Hill , New York , 1990

Bsc final year mathematics Third Paper optional - A Statistical methods Syllabus 

Unit.1. Frequency distribution - measure of central tendency, mean, median, mode, geometric mean, harmonic mean. Divisive value, measure of deflection - range, interquartile range, mean deviation, standard deviation, moment, contrast and truncation.

Unit.2. Probability- Event, Sample space, Probability of an event, Probability sum and multiplication theorem, Baez's theorem, Continuous probability, Probability density function and its applications in finding the mean, mode, median for various continuous probability distributions, Mathematical expectation, Random  Mathematical Expectation of Addition and Multiplication of Variables, Momentary Function

Unit 3. Theoretical Distributions – Binomial, Poisson, Rectangular and Exponential Distributions, their properties and applications

Unit 4. least square method, curves of adhesion, correlation and regression, partial and multiple correlations up to three variables only).

Unit 5. Sampling-Sampling of large samples, null and alternative hypothesis, first and second type of errors, significance test based on significance level, critical area, Kai-berg, AA and numerical

Note :- Use of Simple Calculator is allowed in this question paper examination.

Bsc final year mathematics Third Paper optional - B Discrete Mathematics Syllabus 

Unit 1. Boolean functions, separable and combinatorial normal forms (canonical and dual canonical), Boole's expansion theorem.  Relations- Binary relation, Inverse relation, Connected relation, Equivalence relation, Equivalence class and its properties religion, Division of sets.

Unit 2. Partially Reduced Relations, Partly Committed Sets, Completely Committed Sets, Haisu diagrams, Maximal and Minimal Elements, First and Last Elements, Lattice – Definition and Examples, Dual Lattice, Bounded Lattice, Distributive Lattice, Complementary Lattice.

Unit 3. Graphs - Definition and Types Sub-Graphs, Motion, Paths and Circuits, Related and Unrelated Graphs, Euler Graphs, Hamiltonian Paths and Circuits, Dijkstra, Algorithms for Shortest Path in Weighted Graphs.

Unit 4. Trees and Virtues, Fixed Trees, Binary Trees, Parent Trees, Species and Emptiness of Graphs, Algorithms of Kuscal and Prime.

Unit. 5. Matrix representations of graphs – Incident and Adjacency matrices, Cutsets and their properties, Planar graphs (definition), Kuratovsky's binaries.

Text Books For Discrete Mathematics  :

1. C.L.Liu.- Elements of Discrete Mathematics , Mcgraw Hill New - York 

2. Narsingh Deo - Graph Theory , Prentice Hall . 

3. MP Books of Hindi Granth Academy.

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