Semester Wise Syllabus of Kumaun University B.Sc. Mathematics from 2016

KUMAUN UNIVERSITY NAINITAL

Department of Mathematics

B. Sc. Mathematics

The Course of Mathematics in Kumaun University: Mathematics is the study of universal patterns and structures and is the quantitative language of the world. Students with a good background in fundamental mathematics have many options in terms of career possibilities and are high in demand after postgraduate study in almost every quantitative field like actuarial sciences, environmental sciences, finance, economics, etc.

This course gives students, the understanding of the notion of mathematics with basic ideas of pure mathematics (including analysis, linear algebra, geometry and group and ring theory). A broad understanding of and practice in using, basic tools of applied mathematics (including differential equations, mechanics, numerical analysis, probability and statistics).


Currently Kumaun University's Department of Mathematics running Four Courses :

• B.Sc. Semester Mode (For students admitted after 2016-17)
• B.A. Semester Mode (For students admitted after 2016-17)
• B.Sc. Regular Mode (For students admitted before 2016-17)
• B.A. Regular Mode (For students admitted before 2016-17)

Semester system course structure: 

1.  The course work shall be divided into six semesters with three papers in each semester. 
2.  Each paper in a semester will be of 80 marks out of which 60 marks for theory and  20 marks are allotted for internal assessment (written test or assignments or both)
3.   Each theory paper shall consists of Three Section

• Section (A): 20% of total marks (objective, one word answer, fill in the blanks, true- false; all parts will be compulsory)
• Section (B): 40% of total marks (short answer)
• Section (C): 40% of total marks (long answer).  

4.  Question paper shall cover the whole syllabus. 
5.  The duration of theory examination shall be 03 hrs. 

B.A./B. Sc. Mathematics

Course Structure (Semester System) 

B.Sc. I Semester  
Elementary Algebra  and Trigonometry                                                                                 
Differential  Calculus            
Geometry and  Vector Analysis


B.Sc. II Semester 
Group Theory          
Integral Calculus
Analytical Geometry

B.Sc. III Semester 
Advanced  Algebra       
Differential  Equations
Mechanics  


B.Sc. IV Semester 
Vector spaces and Matrices 
Real Analysis        
Mathematical Methods

B.Sc. V Semester
Linear Algebra
Complex Analysis        
Functions of several variables  and Partial Differential Equations


B.Sc. VI Semester
Numerical Methods
Mathematical Statistics
Operations  Research

PDF of Kumaun University UG [B.Sc. and B.A.] Semester Syllabus of Mathematics from 2016 onwards

For Previous Year Papers of B.Sc./B.A. Mathematics Visit this Link


B.Sc. Mathematics Syllabus of Kumaun University, B.A. Maths syllabus of KU, Semester wise syllabus of Mathematics of Kumaun University.

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Syllabus of Maths for post graduation in Kumaun University

The Department of Mathematics was established in 1973 (under university status) and has units in both the Campuses. The department of mathematics of Kumaun University at DSB Campus came into existence in 1951 under the leadership of Dr. A.N. Singh, a renowned scholar of Hindu Mathematics and the Department of Mathematics at SSJ Campus, Almora came into Existence in the year 1962. Both these departments are one of the biggest in the respective campuses in terms of strength of the students.

MATHEMATICS

Syllabus of Maths for M.Sc. in Kumaun University

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M.A. and M.Sc. I semester Compulsory maths papers

 

M.A. and M.Sc. II semester Compulsory maths papers

M.A. and M.Sc. III semester Compulsory maths papers 

 

M.A. and M.Sc. IV semester Compulsory maths papers

Syllabus of Maths for PG Course in Kumaun University, Maths Syllabus for Kumaun University PG Course, Syllabus of Maths for all Semester in KU.

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Syllabus of Mathematics for B.A. and B.Sc.III year

Click to download PDF of Proposed Syllabus for B. Sc. Semester program implemented from Session 2016-17 of Kumaun University for Mathematics



Paper-I : Linear Algebra and Linear Programming
M.M:50

Note: There shall be three sections A, B and C in this paper. Questions within all the three sections
shall carry equal marks. Section A will be compulsory and objective in nature having ten Questions. Marks allotted to this section shall be 10. Questions in section B will be short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at least one question from both parts (viz. Linear Algebra and Linear Programming). Questions in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of four questions. The number of questions for framing of question paper shall be 80% from Linear Algebra, 20% from Linear Programming . The question paper be framed proportionately from the whole syllabus.


Linear Algebra Vector spaces: Vector space, sub spaces, Linear combinations, linear spans, Sums and direct sums, Linear dependence, Bases and dimensions, Dimensions and subspaces, Coordinates and change of bases.

Linear Transformations: Linear ransformations, rank and nullity, Operations with linear transformations, Linear operators, Algebra of linear operators, Invertible linear operators, Matrix of linear transformation, Matrices and linear transformation, Matrix of linear operator, Change of basis, similarity.

Linear Functional: Linear functional, Dual space and dual basis, Double dual space, Annihilators, Transpose of linear transformation, Bilinear, Quadratic and Hermitian forms, quadratic form.

Linear programming
Programming, Graphical Linear method, Simplex method, the dual of a linear programming problem.                                    


Paper-II : Analysis
 M.M.: 50 


Real Analysis Continuity of functions, Properties of continuous functions, Types of discontinuities, Uniform continuity, Differentiability, Taylor's theorem with various forms of remainders, Riemann integral-definition and properties, Condition of integrability, Convergence and uniform convergence of improper integrals.
Point wise convergence, Uniform convergence, Test of uniform convergence, Convergence and uniform convergence of sequences and series of functions.


Complex Analysis
Functions of complex variable, Harmonic functions, Cauchy and Riemann equations, Analytic functions, Complex integration, Cauchy's theorem, Cauchy's integral formula, Taylor's series, Laurent's series, Liovelle’s theorem, Poles and singularities, Residues, Residue theorem and its applications in the evaluation of integrals.




Paper III:This paper shall consist of any one of the four options
M.M.: 50


               a)  Numerical Analysis
               b)  Mathematical Statistics
               c)   Spherical Trigonometry and Astronomy
               d)  Principal of Computer Science and Information Technology

Note-(1). The choice for selecting the optional paper will be subject to the approval of the Head of
Department, depending upon availability of resources and will be as per combinations available at the respective centers.

Note-(2).candidates offering Statistics as one of the optional subjects in B.A./ B.Sc. I& II shall not be allowed to offer paper III(a) and III(b).

Note-(3).   Simple Calculators (Non-Programmable) be allowed to the examinees during examination of paper III(a).

Note-(4).Note-(3) should invariably be printed as instruction in the question paper III(a).

Note-(5). Candidates offering Computer Science and Information Technology as one of the optional subject in B.A./B.Sc I &II shall not be allowed to offer paper III(d).

                                    


Paper-III (a) : Numerical Analysis(only this is available)


Finite difference, Difference operators, Newton's interpolation formula, divided differences, Interpolation with unequal interval of arguments, Lagrange’s formula, Sterling and Bessel formula (application only).

Numerical differentiation, Numerical integration, Simpson's rule, Trapezoidal rule and their accuracy, Numerical solution of algebraic equations in two unknown quantities, Regula Falsi, Newton Raphson, Graff's root squaring method. Numerical method of matrix inversion, determination of Eigen values and Eigen vectors.

 


Paper-III (b) : Mathematical Statistics


Mathematical Statistics
Elements of the theory of probability, Addition and Multiplication theorems, Expectations, Moments, m.g.f. (definition and application to Binomial and Poisson’s distributions), Skewness, Kurtosis, Binomial, Poisson’s and normal distributions, Interpolation (Newton's and Lagrange's formula).

Simple random sampling, Association of attributes, Yule's coefficient of association, Consistency of data, Curve fitting, Correlation, Regression lines and rank correlation coefficient. Chi square test, test of significance based on "t" and "z" test.

 


 Paper-III(c) : Spherical Trigonometry and Astronomy


Spherical Trigonometry:
Fundamental formulae of spherical trigonometry, (excluding circles and areas), Solutions of right angled triangles, Latitudes and Longitudes on the surface of the earth.


Astronomy:
Celestial sphere, Diurnal motion, Twilight, Atmospheric refraction, Meridian circle, planetary motions, Time planetary phenomenon, Precession and notation.




Paper-III (d) : Principles of Computer Science and Information Technology

Introduction to computers: Information Processing and the electronic digital computers, Information Technology, Use of computers, Computers and human beings, Generations and types of computers, Microcomputer, Input output devices, Storages devices.

Data storage and data manipulation: Storage of bits, Main memory, Coding information of storage, Storing integers, Storing functions, Communication errors, The central processing unit, Programme execution, Arithmetic/Logic instructions, Computer-Peripheral communication.

Computer Languages: Characteristics of programming languages, Machine languages, Assembly languages, High level languages, Fifth generation languages, Object oriented and visual programming.

Data communications and networks: Communications, Computers and communications, Telephone related communications, New technologies in modem, Communications protocols, Communication channels, Types of connections, Types of networks, Local area networks, Transmission models, Data encoding and decoding.






PDF of Mathematics Syllabus of B.Sc. II of Kumaun University

Source : Kumaun University

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Syllabus of Mathematics for B.A. and B.Sc.II year

Click to download PDF of Proposed Syllabus for B. Sc. Semester program implemented from Session 2016-17 of Kumaun University for Mathematics

Paper-I : Higher and Abstract Algebra
M.M:50

Note: There shall be three sections A, B and C in this paper. Questions within all the three sections shall carry equal marks. Section A will be compulsory and objective in nature having ten questions. Marks allotted to this section shall be 10. Questions in section B shall be short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at least one question from all the three parts (viz. Higher Algebra, Group Theory and Ring Theory). Questions in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of four questions. The number of questions for framing of question paper shall be 30% from Higher Algebra, 60% from Group Theory and 10% from Ring Theory. The question paper be framed proportionately from the whole syllabus.


Higher Algebra

Transformation of equations, Descarte’s rule of signs, Solution of cubic equations (Cardon’s method), Biquadratic equations, Convergence and Divergence of sequence and series.

Group Theory

Relations and binary operations on a set, Definition, Examples and simple properties of groups, Order of a group and order of an element of a group, Abelian and cyclic groups, Groups of permutations, Even and odd permutations, Symmetric group, Alternating groups.

Subgroup: Definition and simple properties (Necessary and sufficient conditions on non-empty set for being subgroups) of subgroups, Cosets of a subgroup and its properties, Quotient group of a group, Lagrange’s theorem, Corollaries of Lagrange’s theorem.

Homomorphism, Fundamental theorem of homomorphism, Kernel of homomorphism, Cayley’s theorem, Normal subgroups, Isomorphism theorems.

Ring Theory

Definition, Examples and simple results related to rings, Special rings, Integral domain, skew field and fields.

  
                         


Paper-II : Differential Equations 
M.M.:50

Differential equations of first order and first degree, Clairaut’s form, Singular solutions, Trajectories, Existence and uniqueness of the solution dy/dx= f(x,y), Initial and boundary value properties, simple applications of differential equations of first order to the problems of general interest, Linear equations with constant coefficients Simultaneous equation with constant coefficient and  of the form dx/P= dy/Q= dz/R where P, Q, R are functions of x, y,z, Homogeneous linear equations, Exact differential equations, Linear differential equations of second order with variable coefficients, Total differential equations, Solutions in series, Partial differential equations of first order, Charpit’s method, Linear partial differential equations with
constant coefficients.

                                      


Paper-III : Statics and Dynamics
M.M.:50



Statics

Centre of gravity in two and three dimensions, Strings in two dimensions (Common catenary of uniform strengths only), Virtual works, Forces in three dimensions, Central axis.


Dynamics

Kinematics, Rectilinear motions, Motion in resisting medium, Central orbits (Excluding Kepler’s Laws), Constrained motion (Circular and cycloidal motions only), Moments and products of inertia (Simple case, Theorem of parallel axis, Momental ellipsoid, Principal axes).




PDF of Mathematics Syllabus of B.Sc. II of Kumaun University

Source : Kumaun University

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Syllabus of Mathematics for B.A. and B.Sc.I year

Click to download PDF of Proposed Syllabus for B. Sc. Semester program implemented from Session 2016-17 of Kumaun University for Mathematics


Paper-1  Matrices, Trigonometry and Vector Analysis
M.M.: 50

Note:  There   shall   be   three   sections   A,B  and   C   in   this   paper.   Questions   within   all   the   three sections shall carry equal marks. Section A will be compulsory and objective in nature having
ten   questions.   Marks   allotted   to   this   section   will   be   10.   Questions   in   section   B   will   be   short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at
least one question  from all the three parts (viz.Matrices,Trigonometry and Vector Analysis). Question in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of four questions. The number of questions for framing of question paper shall  be  30%from  Matrices, 30% from   Trigonometry  and 40% from Vector Analysis. The question paper be framed proportionately from the whole syllabus.


Matrices
Symmetric, Skew-Symmetric, Hermitian and skew-Hermitian matrices, Orthogonal  and Unitary matrices, Elementary operations on matrices, Inverse of a matrix, Linear dependence of rows and columns of a matrix, Row rank, column rank and their equivalence, Rank of a matrix, Eigen     vectors,   Eigen   values   and   the  characteristics    equation    of  a  matrix,   Cayley-Hamilton theorem and its use in finding inverse of a matrix, Applications of matrices in solving system of linear(both   homogeneous   and   non-homogeneous)   equations,   Conditions   of   consistency   for   a system of linear equations.

Trigonometry
Exponential,  Logarithmic,     Circular    and   hyperbolic    functions     together   with   their
inverses,   Gregory’s   series,   Summation   of   Trigonometric   series,   Trigonometric   expansions   of
sine and cosine as infinite products(without proof).

Vector Analysis
Vector Algebra: Triple products, Reciprocal vectors, products of four vectors.
Vector  Differentiation:  Ordinary  Differentiation  of  vectors, Applications   to  mechanics  and geometry,      Differential  operators,del,  Definitions of  del,  Gradient,  Divergence,  Curl, Vector identities.
Vector integration: Line, Surface and Volume  Integrals, Simple  applications of  Gauss’s divergence theorem, Green’s theorem and Stroke’s theorem (without proof).




Paper-II  :   Calculus
M.M.: 50

Note:  There   shall   be   three   sections   A,   B   and   C   in   this   paper.   Questions   within   all   the   three sections shall carry equal marks. Section A will be compulsory and objective in nature having ten questions.   Marks   allotted   to   this   section   will   be   10.   Questions   in   section   B   will   be  short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at least one question from two parts (viz. Differential Calculus and Integral Calculus).Question in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of   four   questions.   The   number of questions for framing  of   question   paper   shall   be   60% from Differential   Calculus  and  40% from Integral    Calculus. The  question  paper  be framed proportionately from the whole syllabus.


Differential Calculus
A   brief   review   of   limit,   Continuity   and   differentiability,   Rolle’s   theorem,  Mean   value theorem and their applications, intermediate value theorem, successive differentiation, Taylor’s and Maclaurin’s series expansions, Indeterminate forms, Tangents and normals of polar curves, Derivatives of arc,  Asymptotes, Curvature, Double Points, Curve tracing, Functions of  two variables,  Partial    differentiation  and change     of    independent   variables(two  variables), jacobians(simple applications-function   of  a   function   case),   Maxima   and  Minima   of  two independent variables.



Integral Calculus

Integral as limit of a sum, Fundamental theorem of  integral calculus(statement only), Beta  and Gamma  Functions, Change of order of   integration   in   double   integrals,   Drichlet’s theorem and its Liovelle’s extension, Multiple integrals, Area(quadrature), Rectification(length of curves), Volumes and Surfaces, Differentiation and integration under the integral sign.




Paper-III : Geometry of Two and Three Dimensions
M.M. 50


Two Dimensions

A   briefreview   of    general   equation   of   second   degree,   Confocal   conics        and   Points   of
contact, Polar equation of a conic, Equation of a Chord, Tangent, Normal and polar to a conic.


Three Dimensions

System of coordinates in three dimensions, change of origin, Projections, dc’s and dr’s, Change   of   axes,   Plane,   straight   Line,   intersection   of   three   panes,   Volume   of   a   tetrahedron, Sphere,     Cylinder,    Cone     central   conicoids    with   basic   fundamental      properties,    paraboloids, General equation of second degree in three dimensions. Cylindrical,   Spherical   coordinate   systems,   their   transformations  and   their   relation   to   Cartesian coordinate systems.



PDF of Mathematics Syllabus of B.Sc. I of Kumaun University


Source : Kumaun University

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