msu math syllabus

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B. Sc. (Mathematics) Syllabus
Department of Mathematics
Faculty of Science
The Maharaja Sayajirao University of Baroda
Vadodara 390002

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Sr.
No.
Course
Code
Course Title Credit
Semester – I (Principal & Subsidiary)
1 MAT1101 Matrices 2
2 MAT1102 Algebra and Number Theory 3
3 MAT1103 Calculus 3
Semester – II (Principal & Subsidiary)
1 MAT1201 Differential Equations 2
2 MAT1202 Abstract Algebra-I 3
3 MAT1203 Geometry 3
Semester – III (Principal)
1 MAT1301C07 Linear Algebra 4
2 MAT1302C08 Advanced Calculus 4
Semester – IV (Principal)
1 MAT1401C09 Elementary Analysis 4
2 MAT1402C10 Integral Calculus and Differential Equations 4
Semester – V (Principal)
1 MAT1501C11 Abstract Algebra-II 4
2 MAT1502C12 Analysis-I 4
3 MAT1503C13 Analysis-II 4
4 MAT1504C14 Numerical Analysis and Computer Programming-I 4
5 MAT1505C15 Linear Programming 4
Elective Courses
6 MAT1506E17 Applications of Mathematics in Finance 2
7 MAT1507E18 Operations Research: Inventory Control 2
8 MAT1508E19 Statics 2
9 MAT1509E20 Boolean Algebra 2
Core Foundation
10 MAT1510F01 Graph Theory 2
11 MAT1511F01 Problem Solving Techniques in Mathematics 2
Semester – VI (Principal)
1 MAT1601C16 Abstract Algebra-III 4
2 MAT1602C17 Analysis-III 4
3 MAT1603C18 Analysis-IV 4
4 MAT1604C19
Numerical Analysis and Computer Programming-
II
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5 MAT1605C20 Differential Equations 4
Optional Papers
6 MAT1606E21 Cryptography 4
7 MAT1607E22 Mathematical Modeling 4
8 MAT1608E23 Mathematics of Insurance 4
9 MAT1609E24 Mechanics 4
10 MAT1610E25
Operations Research : Game and Queueing
Theory
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Semester – III (Subsidiary)
1 MAT1303S07 Linear Algebra, Sequence and Series 4
2 MAT1304S08 Advanced Calculus 4
Semester – IV (Subsidiary)
1 MAT1403S09 Linear Programming and Numerical Analysis 4
2 MAT1404S10 Integral Calculus and Differential Equations 4

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Sr.
No.
Course
Code
Course Title Credit
Semester – I (Elective)
1 MAT1104 Matrices 2
2 MAT1105 Differential and Integral Calculus 2
Semester – II (Elective)
1 MAT1204 Differential Equations and Its Applications 2
2 MAT1205 Geometry 2
Semester – III (Elective)
1 MAT1305E05 Algebra 2
Semester – IV (Elective)
1 MAT1405E11 Numerical Analysis 2
Sr.
No.
Course
Code
Course Title Credit
Semester – III, IV (Elective (Open) Mathematics)
1 MAT1007E06 Boolean Algebra and its Applications 2
2 MAT1008E07 Discrete Mathematics and its Applications 2
3 MAT1009E08 Graph Theory 2
4 MAT1010E09 Linear Programming 2
5 MAT1011E10 Number Theory 2
Sr.
No.
Course
Code
Course Title Credit
Semester – I, II, III, IV (Foundation)
1 MAT1004F01 Algebra 2
2 MAT1005F01 Calculus 2
3 MAT1006F01 Matrices 2
Semester – III, IV (Foundation)
4 MTF04 Coding Theory 2
5 MTF05 Mathematical Biology 2

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B. Sc. Semester – I (Principal & Subsidiary):
B. Sc. Semester-I (Principal & Subsidiary Mathematics)
Course-MAT1101: Matrices
(2 Credits)
To be effective from June 2012
Unit-1: Special types of matrices and their properties, Elementary operations and
Elementary matrices, Rank of a matrix, rank of product of matrices, Invariance of
rank under elementary operations, Row reduced echelon form of a matrix,
Homogeneous and Non-homogeneous linear equations.
Unit-2: Eigen values and Eigen vectors of a matrix, Orthogonality of eigen vectors
associated with distinct eigen values, Properties of eigen vectors of a real
symmetric matrix, Diagonalization of a symmetric matrix, application to reductions
of quadrics to principal axes, Cayley-Hamilton theorem (without proof).
REFERENCE BOOKS:
1. C. W. Curtis Linear Algebra, Springer, 1987.
2. J. N. Kapur and M. K. Singal, Matrices, R. Chand & Co., 1996.
3. V. Krishnamurthy, V. P. Mainra & J. L. Arora, An Introduction to Linear Algebra, East-
West Press,2001.
4. Serge Lang, Introduction to Linear Algebra, Springer, 1986.
5. Shanti Narayan and P. K. Mittal, A text book of Matrices, S. Chand & Co., 2005.
6. I. K. Rana, An Introduction to Linear Algebra, Ane Books Pvt. Ltd, 2010.
Course-MAT1102: Algebra and Number Theory
(3 Credits)
Unit-1: De Moivre’s theorem ( Proof for rational index) and its applications, nth
roots of a
complex number, Statement of fundamental theorem of algebra, Multiple
roots and test for multiplicity, Relation between roots and coefficients,
Imaginary roots of an equation with real coefficients, Descarte’s rule of sign,
solution of cubic equations (Cardan’s Method), biquadratic equations.
Unit-2: Division algorithm, gcd, lcm, primes, Fundamental theorem of arithmetic, Euclid’s
Lemma, Congruences: Definitions and elementary properties. Results about linear
congruence equations, Chinese Remainder theorem, Euler phi-function, examples,
divisibility tests.
REFERENCE BOOKS:
1. David Burton, Elementary Number Theory, Tata Mc Graw Hill Publishers, 2006.
2. S. D. Telang, Number Theory, Tata Mc Graw Hill Publishers, 2004.
3. J. V. Uspensky, Theory of Equations, Mc Graw Hill Publishers, 1948.
Course-MAT1103: Calculus
(3 Credits)
Unit-1: Successive differentiation, Leibnitz’s theorem, Lagrange’s and Cauchy’s mean
value theorems and their geometrical interpretations, Increasing-decreasing
functions, Indeterminate forms, L. Hospital’s rules (proof for 0/0 case only),
Taylor’s and Maclaurin’s theorems (Lagrange’s form of remainder), Taylor’s
polynomial and approximation, Power series expansion of xsin , xcos , )exp(x for

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Rx∈ and of m
x)1( + , )1log( x+ for 1|| <x (Assuming the validity of
expansions).
Unit-2: Asymptotes, Curvature and radius of curvature for Cartesian curves, Curve
tracing for )(xfy = only, Reduction formulas for ∫
2
0
sin
π
xdxm
, ∫
2
0
cos
π
xdxm
,
∫
2
0
cossin
π
xdxx nm
( Nnm ∈, ), Arc length, Surface area.
REFERENCE BOOKS:
1. Louis Leithold, The Calculus with Analytic Geometry, Harper-Collins Publishers, 1981.
2. Shanti Narayan, Differential Calculus, S. Chand & Co. Ltd,1996
3. Shanti Narayan, Integral Calculus, S. Chand & Co. Ltd, 1999.
4. V. M. Shah, Introductory Calculus, Acharya Book Depot,1980
5. G. B. Thomas Jr. and R. L. Finney, Calculus and Analytic Geometry, Addison-Wesley
Publications, 1999.
B. Sc. Semester – II (Principal & Subsidiary):
B. Sc. Semester-II (Principal & Subsidiary Mathematics)
Course-MAT1201: Differential Equations
(2 Credits)
To be effective from December 2012
Unit-1: Differential equations of first order and first degree: Geometric interpretation of first
order equations, Isoclines, Homogeneous differential equations, Equations
reducible to homogeneous form, linear differential equations, Bernoulli’s equation,
Exact differential equations, Integrating factors, Applications of first order
equations: mixture problem, orthogonal trajectories.
Unit-2: Linear differential equations of higher order, Linear independence, Fundamental
theorem (without proof), Differential operators, Homogeneous and non-
homogeneous linear differential equations with constant coefficients, Inverse
operators, Operational methods for solving linear differential equations, Euler
form of linear differential equations with variable coefficients.
REFERENCE BOOKS:
1. Zafar Ahsan, Differential Equations and their Applications, Prentice Hall of India, 2004.
2. Wilfred Kaplan, Elements of Differential Equations, Addison-Wesley Publishing Co.,
1964.
3. Shanti Narayan, Integral Calculus, S. Chand & Co. Ltd., 1999.
Course-MAT1202: Abstract Algebra-I
(3 Credits)
Unit-1: Equivalence relation and equivalence class, congruence modulo n, Definition and
examples of groups, Elementary properties of a group, finite groups and their
tables, Subgroups, centralizers and normalizers, subgroups generated by a set,
Cyclic groups, order of an element.
Unit-2: Cosets, Lagrange’s theorem, Fermat’s Theorem, Euler’s Theorem, Permutation
group, symmetries of equilateral triangle, rectangle, circle, square, transposition

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and cycles, Even and Odd permutations, Alternating Groups An, Homomorphisms
and Isomorphisms, Cayley’s theorem.
REFERENCE BOOKS:
1. Michael Artin, Algebra, Prentice Hall of India, 1994.
2. G. Birkhoff and S. Maclane, A Survey of Modern Algebra, University Press, 2003.
3. J. B. Fraleigh, A First Course in Abstract algebra, Pearson Education, Inc., 2006.
4. Joseph A. Gallien, Contemporary Abstract Algebra, Narosa Publishing House, 1998.
5. N. S. Gopalakrishnan, University Algebra, New Age International Pvt. Ltd., 2004.
6. I. N. Herstein, Topics in Algebra, Vikas Publishing house Pvt. Ltd.,2004
7. I. H. Sheth, Abstract Algebra, Prentice Hall of India, 2009.
Course-MAT1203: Geometry
(3 Credits)
Unit-1: Polar co-ordinate system, Relations between polar and Cartesian coordinates,
Graphs of polar equations, Aids in graphing polar equations, Polar equations of
Lines, Circles and Conics, Equation of a Sphere, Intersection of a sphere and a
line, Section of a sphere by a plane, Intersection of two spheres, Sphere
through a given circle, Tangent plane to a sphere.
Unit-2: Cone with a given vertex and given guiding curve, Cone with vertex origin and
homogeneous equation in x , y and z , Right circular cones, Cylinders with
generators parallel to a given line and intersecting a conic, Right circular cylinders,
Central conicoids. Identification and properties of standard quadrics namely
Ellipsoids, Hyperboloids of one sheet, Hyperboloids of two sheets, Elliptic
paraboloids and Hyperbolic paraboloids. Spherical and Cylindrical coordinates of
space points and their relation with Cartesian coordinates.
REFERENCE BOOKS:
1. P. Balasubramanyam, K. G. Subramaniam and G.R. Venkatraman, Coordinate
Geometry of Two and Three Dimension, Tata Mc Graw Hill Publ. Co., 1994
2. Gordon Fuller and Robert M. Parker, Analytic Geometry and Calculus, East-West Press
Pvt. Ltd., 1967.
3. Shanti Narayan, Analytic Solid Geometry, S. Chand & Co. Ltd., 1988.
B. Sc. Semester – III (Principal):
B. Sc. Semester-III (Principal Mathematics)
Course-MAT1301C07: Linear Algebra
(4 Credits)
Unit-1: Definition of a field and examples, Vector spaces over a field and elementary
consequences of its axioms, Subspaces, Linear span, Quotient spaces, Internal
and external direct sum of vector spaces,Linear dependence and Independence.
Properties of linearly independent vectors, Basis and its existence, Dimension of a
vector space.
Unit-2: Inner product spaces, Schwarz inequality, Orthogonal complement and
Orthonormal sets, Gram Schmidt orthogonalization process and examples. Linear
transformations, Range and Kernel of a linear map, Rank-Nullity theorem, the
space of linear transformations, composition of linear transformations, matrix
associated with a linear map and linear map associated with a matrix.

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REFERENCE BOOKS:
1. C. W. Curtis, Linear Algebra, Springer, 1984.
2. I. N. Herstein, Topics in Algebra, Vikas Publishing House Pvt. Ltd, 2004.
West Press,2001.
4. Serge Lang, Introduction to Linear Algebra, Springer, 1986.
5. I. K. Rana, An Introduction to Linear Algebra, Ane Books Pvt. Ltd, 2010.
B. Sc. Semester-III (Principal Mathematics)
Course-MAT1302C08: Advanced Calculus
(4 Credits)
Unit-1: Domain and range of a function of several variables, Limit, Continuity and Partial
derivatives, Equality of mixed partial derivatives of order two, Differentiability, Mean
value theorem, Total differentials, Approximation, Chain rule.
Unit-2: Euler’s theorem on homogeneous function and its converse, Implicit differentiation,
Jacobian formulas, Taylor’s theorem, Maxima-Minima, Lagrange’s method of
undetermined multiplier, Tangent plane and normal line to a surface, Tangent line
to a space curve, Envelopes of plane curves and of family of surfaces,
Directional derivatives, Gradient, Curl, Divergence.
REFERENCE BOOKS:
1. Tom Apostol, Calculus (Volume II), Wiley Eastern Ltd, 1980.
2. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc, 1983.
4. Shanti Narayan, Differential Calculus, S. Chand & Co. Ltd, 1996.
Publishers, 1999.
6. David V. Widder, Advanced Calculus, Prentice-Hall of India, 1989.
B. Sc. Semester – IV (Principal):
B. Sc. Semester-IV (Principal Mathematics)
Course- MAT1401C09: Elementary Analysis
(4 Credits)
Unit-1: Sequences, bounded and unbounded sequences, convergent sequences, algebra
of convergent sequences, convergence of monotonic real sequences, Cauchy
criterion for convergence of real sequences, convergence and divergence of infinite
series, series of positive terms, comparison test, integral test, alternating series,
absolute convergence, ratio test and root test (statements only of test and their
applications).
Unit-2: Field of complex numbers, graphical representation of subsets of C , geometrical
significance of complex functions β+z , zα , z , z ,
z
1
, )Re(z , )Im(z , z and
βα +z . Limit, continuity and differentiability of functions of complex variable.
Elementary functions of complex variable: exponential, trigonometric, hyperbolic,
logarithmic, inverse trigonometric.
REFERENCE BOOKS:
1. R. V. Churchill and J. W Brown, Complex variable and applications, Mc Graw Hill
Publishing Company, 2009.

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2. S. R. Ghorpade and B. V. Limaye, A Course in Calculus and Real Analysis, Springer,
2006.
B. Sc. Semester-IV (Principal Mathematics)
Course-MAT1402C10: Integral Calculus and Differential Equations
(4 Credits)
Unit-1: Iterated integrals and double integral, Change of order, Evaluation by using
transformations, Applications to area and volume, Line integrals, Green’s
theorem (proof for special regions), Path independence of line integrals, Surface
integrals, Stoke’s theorem and its applications, Triple integrals, Gauss’ theorem
and its applications.
Unit-2: Differential equations of the first order but not of the first degree which are solvable
for p , x and y . Clairaut’s equation, singular solutions, system of linear differential
equations with constant coefficients and their applications to mixture problems,
simultaneous differential equations of the first order and first degree, Methods of
solutions of
R
dz
Q
dy
P
dx
== , Paffian differential equations, solution of Paffian
differential equations in three variables.
REFERENCE BOOKS:
1. Zafar Ahsan, Differential Equations and their applications, Prentice-Hall of India, 2004.
2. T. Amarnath, An elementary course in partial differential equations, Narosa Publ. Co,
2000.
3. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc, 1983.
Publishers, 1999.
B. Sc. Semester – V (Principal):
B. Sc. Semester-V (Principal Mathematics)
Course-MAT1501C11: Abstract Algebra-II
(4 Credits)
Unit-1: Isomorphic groups, a counting principle, Normal subgroups and quotient groups,
Fundamental theorem of homomorphism, Isomorphism theorems, Definition and
examples of automorphisms, Inner automorphisms, Automorphism and inner
automorphism groups, Automorphism group of finite and infinite cyclic groups,
Application of quotient groups to automorphism groups, Cauchy’s and Sylow’s
theorem for abelian groups.
Unit-2: Conjugacy relation, Cauchy’s and Sylow’s theorem for non-abelian groups,
discussion of Sylow subgroups, External and internal direct product of a finite
number of groups, Fundamental theorem on finite abelian groups, discussion of
number of non-isomorphic finite abelian groups.
REFERENCE BOOKS:
1. Michael Artin, Algebra, Pearson Education, 2010.
3. J. B. Fraleigh, A First Course in Abstract algebra, Pearson Education Inc, 2006.
5. N. S. Gopalakrishnan, University Algebra, New Age International Pvt. Ltd, 2004.

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6. I. N. Herstein, Topics in Algebra, Vikas Publishing house Pvt. Ltd., 2004.
7. C. Musili, Introduction to Rings and Modules, Narosa Publishing House, 1994.
8. I. H. Sheth, Abstract Algebra, Prentice-Hall of India, 2009.
Course- MAT1502C12: Analysis-I
(4 Credits)
Unit-1: Order relation and ordered set, lub and glb of an ordered set, Properties of lub and
glb, gaps in the rational number system, least upper bound property, Ordered field
and their properties, Existence theorem of an ordered field R (to be assumed
without proof), Archimedean property of R , Dense property of Q in R , Existence
of th
n root of positive reals, Extended real number systems, C is not an
ordered field, Dictionary order, Unions, intersections and Cartesian products of
arbitrary families of sets, Set mappings f and 1−
f of a function f and their
properties, Finite sets, Countable sets and uncountable sets, Well ordering
theorem for N , Well ordered sets.
Unit-2: Definition and various examples of metric spaces, Neighbourhood of a point,
Limit point, Interior point, Isolated point, Open sets and closed sets, Perfect sets,
Dense sets, Closure of a set, Compact sets in a metric space and their
properties, Compactness of k -cell, Heine-Borel theorem, Weierstrass theorem,
Perfect sets in k
R , Cantor set, Connected sets in a metric space, Separable metric
space.
REFERENCE BOOKS:
1. Tom M. Apostol, Mathematical Analysis, Narosa Publishing House, 1980.
2006.
3. Richard Goldberg, Methods of Real Analysis, Oxford and IBH Publishing Co. Pvt. Ltd,
1970.
4. S. C. Malik, Mathematical Anaylsis, Wiley Eastern Ltd, 1992.
5. J. R. Munkres, Topology-A First Course, Prentice-Hall of India, 2000.
6. I. K. Rana, Numbers to Analysis, World Scientific,1998
7. Walter Rudin, Principles of Mathematical Analysis, Mc Graw Hill book Co, 1976.
Course-MAT1503C13: Analysis-II
(4 Credits)
Unit-1: Upper and lower limit of a sequence, some special sequences, convergence and
divergence of a series, comparison test, series of non-negative terms, Cauchy’s
condensation test, number e, root and ratio test, summation by parts, Leibnitz’s
test, addition and multiplication of series, Rearrangements, Riemann’s theorem.
(Proofs of test using upper limit)
Unit-2: Power series and its convergence, Abel’s theorem, Exponential, Logarithmic and
Trigonometric functions, Algebraic completeness of complex field. Trigonometric
Fourier series and examples, Dirichlet Kernel and convergence of Fourier series,
Localization theorem, Fejer Kernel and summability of Fourier series, Orthonormal
system and Fourier series, Bessel’s inequality and Parseval’s theorem.
REFERENCE BOOKS:

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2006.
1970.
Course-MAT1504C14: Numerical Analysis and Computer Programming-I
(4 Credits)
Unit-1: Notions of round off, truncation and other errors, Solution of an equation in one
variable by Bisection method, Regula Falsi method, Newton–Raphson’s method
and General iteration method, Convergence and order of convergence for
these methods. Graeffe’s root squaring method. Solution of linear system of
equations by Gauss elimination method, Crout's method, Gauss–Seidel iterative
method. Solution of nonlinear system of equations by Newton–Raphson’s method.
Numerical solution of ordinary differential equation by Picard's method, Taylor
series method and Runge–Kutta method.
Unit-2: Definition of preliminary language constructs. Simple and formatted input/output
functions. Various operators and Precedence of operators. Simple programs.
Library functions, Header files. Statements and blocks. Control statements: if-else,
switch, break, continue, goto. Loops: for, while, do-while and programs using loop
statements. Ternary operator. Arrays. Structures, Unions. Macros and
preprocessors.
Practical: Relevant computer laboratory practical of writing and running the
programs in the above topics using C++ will be given.
REFERENCE BOOKS:
1. P. C. Biswal, Numerical Analysis, Prentice-Hall of India, 2008.
2. F. B. Hildebrand, Introduction to Numerical Analysis, Tata Mc Graw Hill Publishers,
1979.
3. E. V. Krishnamurthy and S. K. Sen, Computer-based Numerical Algorithm, East-West
Press, 1976.
4. Robert Lafore, Object Oriented Programming with C++, Galgotia Publications Pvt. Ltd,
2009.
5. Stanley B. Lippman and Josee Lajoie, C++ primer, AWAL International Student Edition,
2005.
6. S. S. Sastry, Introductory methods of Numerical Analysis, Prentice-Hall of India, 2006.
7. H. C. Saxena, Finite differences and Numerical Analysis, S. Chand and Co, 2005.
8. J. N. Sharma, Numerical Methods for Engineers and Scientists, Narosa Publishing
House, 2008.
Course-MAT1505C15: Linear Programming
(4 Credits)
Unit-1: General discussions of Linear programming problems and formulation, Graphical
method of solving two variable problem, convex sets, General Linear Programming
Problem, Slack and Surplus variables, L.P.P. in a standard form, Properties of a
solution, Generating extreme point solutions, Development of minimum feasible
solution, Simplex method.
Unit-2: Artificial basis technique, Revised Simplex method, Duality theory for the
unsymmetric and symmetric dual problems, Transportation problem, Methods for
finding initial basic feasible solution: North-west corner rule, Matrix minima method,

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Vogel’s approximation method, Optimal solution: MODI Method, Assignment
problem: Hungarian Method. Special cases of maximization, unbalanced and
prohibited transportation and assignment problems.
REFERENCE BOOKS:
1. S. I. Gass, Linear programming, Mc Graw Hill Book Company, 1985.
2. K. V. Mittal and C. Mohan, Optimization methods in Operations Research and System
Analysis, New Age International Publications,1996.
3. Kanti Swaroop, Man Mohan and P.K. Gupta, Operations Research, Sultan Chand and
Sons, 2005.
4. Hamdy A. Taha, Operations Research: An Introduction, McMillan Publishing Company,
2007.
Course-MAT1506E17: Applications of Mathematics in Finance (Elective Paper)
(2 Credits)
Unit-1: Financial Management – An overview. Nature and scope of Financial
Management. Goals of Financial Management and main decisions of
financial management. Difference between investment, speculation and
gambling.
Unit-2: Time value of Money – Interest rate and discount rate. Present value and
future value – discrete case as well as continuous compounding case.
Annuities and its kinds.
REFERENCE BOOKS:
1. Prasanna Chandra, Investment Analysis and Portfolio Management, Tata McGraw Hill,
2008.
2. Aswath Damodaran, Corporate Finance–Theory and Practice, John Wiley and Sons,
2001.
3. C. D. Daykin. T. Petikainen and M. Pesonen, Practical Risk Theory for Actuaries,
Chapman and Hall, 1994.
4. Mark S. Dorfman, Introduction to Risk Management and Insurance, Prentice-Hall of
India, 2007.
5. A. K. Gupta and T. Varga, An Introduction to Actuarial Mathematics, Kluwer Academic
Publisher, 2002.
6. Rajesh Kothari and Bobby Dutta, Contemporary Financial Management, Macmillan India
Ltd., 2005.
7. Jim Mc Menamin, Financial Management: An Introduction, Oxford University Press,
2000.
8. Sheldon M. Ross, An elementary Introduction to Mathematical Finance, Cambridge
University Press, 2003.
Course-MAT1507E18: Operations Research: Inventory Control (Elective Paper)
(2 Credits)
Unit-1: General discussions of Operations Research (OR), origin and development of OR,
modeling in OR, general solution methods for OR models, methodology of OR and
applications of OR. Inventory: Associated costs and inventory control,
Deterministic inventory situations without and with shortages.
Unit-2: Determining buffer stocks and reorder level, Multi-item deterministic problems:
Limitation on inventory, limitation on floor space and limitation on investment,

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Probabilistic inventory Problems: Single period problems without setup cost and
with uniform and Instantaneous demand.
REFERENCE BOOKS:
1. D. T. Phillips, A. Ravindra, J. Solberg, Operation Research Principles and Practice,
John Wiley and sons,2000.
2. S. D. Sharma, Operations Research, Kedar Nath Ram Nath & Company.
3. Kanti Swaroop, Man Mohan, P.K. Gupta, Operations Research, Sultan Chand and
Sons, 2005.
4. Hamdy A. Taha, Operations Research: An Introduction, Mc Millan Publishing Company,
2007.
Course-MAT1508E19: Statics (Elective Paper)
(2 Credits)
Unit-1: Introduction, Velocity and acceleration, gradient vector, Fundamental laws of
Newtonian Mechanics, Equilibrium of a particle and system of particles, The
moment of a vector about a line, Varignon’s Theorem , Conditions of equilibrium of
a system of particles, Equipollent system of forces, Couples, Reduction of a
general plane force system, Work and potential energy, The principle of virtual
work.
Unit-2: Mass centers and center of gravity, Theorems of Pappus, Gravitation, Friction,
Flexible cable and its differential equation, The suspension bridge, The common
catenary, Cables in contact with smooth and rough curves.
REFERENCE BOOKS:
1. Sunil Dutta, Mechanics, Prentice Hall of India, 2010.
John L. Synge and Byron A. Griffith, Principles of Mechanics, Mc Graw Hill Book Company,
1970.
Course-MAT1509E20: Boolean Algebra (Elective Paper)
(2 Credits)
Unit-1: Binary relation, Properties of binary relation, Partially ordered sets, Hasse
diagram, Lattices, Chains, Principle of duality, Basic properties of algebraic
systems defined by lattices, Distributive and Complete lattice, Boolean algebra.
Unit-2: Atoms of a Boolean algebra and its properties, Uniqueness of finite Boolean
algebras, Boolean expressions and Boolean functions, Applications to logic, Gates
and digital circuits.
REFERENCE BOOKS:
1. Narsingh Deo, Graph theory with applications to Engineering and Computer Science,
Prentice-Hall of India, 1993.
2. C. L. Liu, Elements of Discrete Mathematics, McGraw Hill International Editions, 1985.
3. J. P. Trembley and R. Manohar, Discrete Mathematical Structure with applications to
Computer Science, Mc Graw Hill Book Company, 2001.

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Course-MAT1510F01: Graph Theory (Core Foundation)
(2 Credits)
Unit-1: Definition and elementary properties of graphs, Isomorphism of graphs,
Subgraphs, Walks, Paths and circuits, Connected graphs, Euler graphs,
Operations on graphs, Hamiltonian circuits, Definition and properties of tree.
Unit-2: Centers in a tree, Rooted and Binary tree, Spanning trees, Fundamental
circuits, cut set and its properties, Planar graphs and Kuratowski’s two graphs,
Representation of planar graphs.
REFERENCE BOOKS:
Course-MAT1511F01: Problem Solving Techniques in Mathematics (Core Foundation)
(2 Credits)
Unit-1: Abstract Algebra: determinants, roots of equations and congruencies, groups,
rings, fields.
Analysis: limit, continuity (with uniform continuity), and differentiability of a real-
valued function of one real variable (or more real variables), mean-value theorems
for derivatives and integrals, problems of finding extrema, higher order derivatives,
Riemann integral, sequences and series of numbers and functions, Taylor’s series,
nth roots of a complex number, analytic function of a complex variable, contour
integral, residue.
Unit-2: Linear Algebra: Vector spaces, linear transformations, matrices.
Geometry: lines, circles, conics, triangles, quadrilaterals, polygons in the plane;
polyhydra, planes, spheres, cones, cylinders, conicoids in the space; convex
regions in the plane and the space.
REFERENCE BOOKS:
1. I. N. Herstein, Topics in Algebra, Vikas Publishing House Pvt. Ltd., 2004.
3. Richard Goldberg, Methods of Real Analysis, Oxford and IBH Publishing Co. Pvt. Ltd.,
1970.
West Press, 2001.
6. Hema Vasavada, Analytic Geometry of Two and Three Dimensions, Second Edition,
Published by Hema Vasavada, Near New Tank, Nana Bazar, Vallabh Vidyanagar,
1998.
7. P. Balasubramanyam, K. G. Subramanyam and G. R. Venkatraman, Coordinate
Geometry of Two and Three Dimension, Tata Mc Graw Hill Publ. Co., 1994.

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B. Sc. Semester – VI (Principal):
B. Sc. Semester-VI (Principal Mathematics)
Course-MAT1601C16: Abstract Algebra-III
(4 Credits)
Unit-1: Definition and examples of a ring, Integral domains, Division rings and Fields, Ring
homomorphism and isomorphism, Ideals and Quotient rings, Maximal ideals and
Fields, Field of quotient of an integral domain, Euclidean ring, gcd, units and prime
elements in an Euclidean ring, Unique factorization theorem.
Unit-2: The ring of Gaussian integers, Polynomial ring ][xF and its properties,
Polynomials over the rational field, Primitive polynomials, The Eisenstein criterion,
Polynomial ring over commutative rings, Unique factorization domains.
REFERENCE BOOKS:
1. Michael Artin, Algebra, Prentice-Hall of India, 1994.
3. J. B. Fraleigh, A First Course in Abstract algebra, Pearson Education, Inc., 2006.
5. N. S. Gopalakrishnan, University Algebra, New Age International Pvt. Ltd, 2004.
6. I. N. Herstein, Topics in Algebra, Vikas Publishing house Pvt. Ltd., 2004.
7. C. Musili, Introduction to Rings and Modules, Narosa Publishing House, 1994.
Course-MAT1602C17: Analysis-III
(4 Credits)
Unit-1: Convergent sequences in a metric space and their properties, Subsequences
and Cauchy sequences in a metric space, Complete metric spaces, Limit of
functions and continuous functions in metric spaces, Continuity and
compactness, Uniformly continuous functions, Continuity and connectedness,
Intermediate value theorem.
Unit-2: Discontinuities, Monotonic functions and types of discontinuities, Fixed point and
contraction principle, Local maximum and Local Minimum, Generalized mean
value theorem, Continuity of derivatives, The metric space ],[ baC and its
completeness, Equicontinuous families, Totally boundedness and Arzela’s
theorem.
REFERENCE BOOKS:
2006.
1964.
3. S. C. Malik, Mathematical Anaylsis, Wiley Eastern Ltd., 1992.
4. J. R. Munkres, Topology-A First Course, Prentice-Hall of India, 2000.
5. I. K. Rana, Numbers to Analysis, World Scientific.1998.
6. Walter Rudin, Principles of Mathematical Analysis, Mc Graw Hill book Co., 1976.

15
Course-MAT1603C18: Analysis-IV
(4 Credits)
Unit-1: Riemann integral, Definition and existence of Riemann – Stieltje’s integral, its
properties, The integral as a limit of a sum, Change of variable, Integration and
differentiation, Fundamental theorem of Calculus, Integration by parts, First and
Second Mean-Value theorems, Integral of vector-valued functions, Functions of
bounded variation.
Unit-2: Rectifiable curves, Convergence of improper integrals, Gamma and Beta functions,
Relation between them, Stirling’s formula, Pointwise convergence of sequences
and series of function, Discussion of main problem, Uniform convergence, Uniform
convergence and continuity, Uniform convergence and integration, Uniform
convergence and differentiation.
REFERENCE BOOKS:
2006.
1964.
4. Walter Rudin, Principles of Mathematical Analysis, Mc Graw Hill book Co., 1976.
Course-MAT1604C19: Numerical Analysis and Computer Programming-II
(4 Credits)
Unit-1: Ordinary differences, Newton’s forward and backward interpolation formulas.
Divided differences, Newton’s divided difference interpolation and Lagrange’s
interpolation formulas, Central difference, Gauss’s and Stirling’s central difference
interpolation, Error analysis of interpolation, Numerical differentiation by Newton’s
Forward, Backward and Stirling’s formula. General quadrature and derivation of
Trapezoidal, Simpson’s and Weddle’s rules. Error analysis in Quadrature.
Unit-2: Functions. Functions with reference variables. Programs for numerical methods
using functions. Default arguments signature of function, Functions and arrays,
Functions and structures, Pointers and addresses, Pointers and arrays, Pointers
and functions, Function overloading and operator overloading, Scope of
variables, External, Local, Static and register variables, Conditional compilation
directives, Typedef statement.
Practical: Relevant computer laboratory practical of writing and running the
programs in the above topics using C++ will be given.
Following Numerical Method programs will be discussed:
Bisection Method, Regula Falsi Method, Newton Raphson Method, Lagrange’s
Interpolation Method, Trapezodial Rule, Programs for Maclaurin’s series expansion
for xsin , xcos and )exp(x .
REFERENCE BOOKS:
1988.
3. E. V. Krishnamurthy and S. K. Sen, Computer-based Numerical Algorithm, East-West
Press, 1976.
4. Robert Lafore, Object Oriented Programming with C++, Galgotia Publications Pvt. Ltd.,
2006.

16
5. Stanley B. Lippman and Josee Lajoie, C++ primer, AWAL International Student Edition,
2005.
7. H. C. Saxena, Finite differences and Numerical Analysis, S. Chand and Co., 2005.
8. J. N. Sharma, Numerical Methods for Engineers and Scientists, Narosa Publishing
House, 2008.
Course-MAT1605C20: Differential Equations
(4 Credits)
Unit-1: The Laplace transform, property of Laplace transform, inverse Laplace transform,
the convolution, solution of linear differential equation and system of linear
differential equation using Laplace transform, Linear equations with variable
coefficients, initial value problem for the homogeneous equation, solution of
homogeneous equation, the Wronskian and linear independence, reduction of
order of a homogeneous equation, the non-homogeneous equation.
Unit-2: Partial differential equation of first order, origin of the first order partial differential
equation, classification of first order partial differential equation, classification of
integrals, Linear partial differential equations of first order, integral surface
passing through a given curve, surface orthogonal to a given system of surfaces,
non-linear partial differential equation of the first order, the Cauchy problem, the
method of the characteristics, compatible system of first order equations, Charpits
method, special types of first order equations.
REFERENCE BOOKS:
1. T. Amarnath, An Elementary Course in Partial Differential Equations, Narosa Publishing
House, 2000.
2. E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice-Hall of
India, 1989.
3. S. L. Ross, Differential Equations, John Weily and Sons, 1984.
4. Ian Sneddon, Elements of Partial Differential Equations, Mc Graw Hill International,
1972.
5. D. Somasundaram, Ordinary Differential Equations–A First Course, Narosa Publishing
House, 2009.
Course-MAT1606E21: Cryptography (Optional Paper)
(4 Credits)
Unit-1: Introduction and Basic Number Theoretic Ciphers, Secure Communications, Shift
Ciphers, Substitution Ciphers, Block Ciphers, Some Modern Ciphers, Hill
cryptosystem, public key encryption, RSA encryption and decryption, primality
testing, integer factorization and digital signatures.
Unit-2: Diffie Hellman key exchange, the knapsack cryptosystem, the ElGamal
cryptosystem, elliptic curves, elliptic curve cryptography through examples, Elliptic
Curves, Elliptic Curve Cryptosystems.
REFERENCE BOOKS:
1. David Burton, Elementary Number Theory, Tata McGraw Hill Publishers, 2006.
2. Neal Koblitz, A Course in Number Theory and Cryptography, Springer, 1994.
3. Thomas Koshy, Elementary Number Theory with Applications, Academic Press, 2007.

17
Course-MAT1607E22: Mathematical Modeling (Optional Paper)
(4 Credits)
Unit-1: Introduction: motivation and classification of mathematical models, population
models: Malthusian and logistic model, Smith’s model, Gompertz growth model,
difference equation for logistic model, logistic model for a non-isolated population,
derivation of logistic model with time delay, a simple prey-predator model.
Unit-2: Optimal exploitation models: logistic models with constant harvesting rate, growth
of predetor-prey populations with harvesting, growth of population in competitions
under harvesting, optimization problem in harvesting of fishes, optimal utilization of
forests, epidemic models: deterministic models without removal, deterministic
model with removal, control of an epidemic.
REFERENCE BOOKS:
1. Martin Braun, Differential Equations and their Applications, Springer, 1993.
2. J. N. Kapur, Mathematical Models in Biology and Medicine, Affiliated East-West Press,
1985.
3. J. N. Kapur, Mathematical Modeling, Wiley Eastern Pvt. Ltd., 1988.
Course-MAT1608E23: Mathematics of Insurance (Optional Paper)
(4 Credits)
Unit-1: Insurance Fundamentals – Insurance defined. Meaning of loss. Chances of loss,
peril, hazard and proximate cause in insurance, Costs and benefits of insurance to
the society and branches of insurance – life insurance and various types of general
insurance. Insurable loss exposures – features of loss that is ideal for insurance.
Mortality and survival Time, Actuarial Functions of Mortality and Mortality Tables.
Unit-2: Stochastic cash flows, Pure Endowments, Life Insurances, Endowments, Life
Annuities. Determination of claims for General insurance – Using Poisson
Distribution and Negative Binomial Distribution. Determination of the amount of
Claims in General Insurance – Compound aggregate claim model and its
properties, and claims of reinsurance.
REFERENCE BOOKS:
1. Aswath Damodaran, Corporate Finance–Theory and Practice, John Wiley and Sons,
2001.
2. C. D. Daykin. T. Petikainen and M. Pesonen, Practical Risk Theory for Actuaries,
Chapman and Hall, 1994.
3. Mark S. Dorfman, Introduction to Risk Management and Insurance, Prentice Hall of
India, 2006.
4. A. K. Gupta and T. Varga, An Introduction to Actuarial Mathematics, Kluwer Academic
Publisher, 2002.
5. Rajesh Kothari and Bobby Dutta, Contemporary Financial Management, Macmillan India
Ltd., 2005.
6. Jim Mc Menamin, Financial Management: An Introduction, Oxford University Press,
2000.
7. Sheldon M. Ross, An elementary Introduction to Mathematical Finance, Cambridge
University Press, 2003.

18
Course-MAT1609E24: Mechanics (Optional Paper)
(4 Credits)
Unit-1: The ingredients of Mechanics, Frames of reference, Velocity and acceleration
gradient vector, Fundamental laws of Newtonian Mechanics, Newtonian frame of
reference. Tangential and normal components of velocity and acceleration, radial
and transverse components of velocity and acceleration, The Hodograph, Motion of
a particle and a system of particles, Principle of energy, D’ Alembert’s principle,
Frames of reference with uniform translational velocity and acceleration, Frames of
reference relating with constant angular velocity.
Unit-2: Projectiles without resistance, the simple pendulum, The harmonic oscillators,
Effect of a disturbing force, Damped oscillations, Forced oscillations, General
motion under a central force: Cartesian equations and the law of direct distance,
Differential equation of the orbit of a particle moving under an attractive central
force, Apsides and Apsidal angles, determination of a orbit, Kepler’s laws, The two
body problem. Moment of inertia: theorem of parallel axes, Theorem of
perpendicular axes, Kinetic energy and angular momentum, Konig’s theorem, Rigid
body rotating about a fixed axis, The compound pendulum, Cylinder rolling down
an inclined plane.
REFERENCE BOOKS:
1. Sunil Dutta, Mechanics, Prentice Hall of India, 2010.
2. John L. Synge and Byron A. Griffith, Principles of Mechanics, Mc Graw Hill Book
Company, 1970.
Course-MAT1610E25: Operations Research: Game and Queueing Theory (Optional Paper)
(4 Credits)
Unit-1: Game Theory: Competitive Games, two person zero sum games, maximin and
minimax criterion (based on pure strategies), Saddle points and the value of the
game. Games without Saddle point : Mixed strategy solution of 22× games,
Fundamental theorem of rectangular games, Expectation function of nm×
rectangular games and the minimax - maximin theorem for it, Graphical Solution of
n×2 and 2×m games. Dominance properties in games, Algebraic method of
solving a game, Symmetric games, Games and linear programming.
Unit-2: Queueing Theory: Queueing system and its elements, Operating characteristics of
queueing systems. The Poisson queueing system: queueing systems with single
service channel with finite/infinite capacity and its characteristics. Queueing system
with more than one parallel service channels with finite/infinite capacity and its
characteristics.
REFERENCE BOOKS:
1. D. T. Phillips, A. Ravindra, J. Solberg, Operation Research Principles and Practice,
John Wiley and sons,2000.
2. S. D. Sharma, Operations Research, Kedar Nath Ram Nath & Company.
3. Kanti Swaroop, Man Mohan, P.K. Gupta, Operations Research, Sultan Chand and
Sons, 2005.
4. Hamdy A. Taha, Operations Research: An Introduction, Mc Millan Publishing Company,
2007.

19
B. Sc. Semester – III (Subsidiary):
B. Sc. Semester-III (Subsidiary Mathematics)
Course-MAT1303S07: Linear Algebra, Sequence and Series
(4 Credits)
Effective from June 2013
Unit-1: Vector spaces (Real/Complex) and elementary consequences of its axioms,
Subspaces, Linear span, Intersection and Direct sum of subspace, Linear
dependence and Independence. Bases and dimension, Inner product in Cn
,
Length of a vector and Angle between two vectors, Schwarz inequality,
Orthogonality and Gram-Schmidt orthogonalization process, Orthonormal basis.
Unit-2: Linear transformations, range and kernel of a linear map, Rank-Nullity Theorem.
Convergence of monotone real sequences, Cauchy criterion, Convergence and
Divergence of infinite Series, Series of positive terms, Comparison tests, Integral
test, Alternating series, Absolute convergence, Ratio test and Root test.
REFERENCE BOOKS:
2. Kenneth Hoffman and Ray Kunze, Linear Algebra, Prentice-Hall of India, 2e, 2009.
West Press, 2001.
4. Louis Leithold, The Calculus with Analytic Geometry, Harper-Collins Publishers,6/e,
1981.
B. Sc. Semester-III (Subsidiary Mathematics)
Course-MAT1304S08: Advanced Calculus
(4 Credits)
Effective from June 2013
Unit-1: Domain and range of a function of severable variables, Limit, Continuity and Partial
derivatives, Equality of mixed partial derivatives of order two (without proof),
Differentiability, Total differentials, Approximation, Chain rule (without proof),
Euler’s theorem on homogeneous function.
Unit-2: Jacobian formulas, Implicit differentiation, Taylor’s theorem, Maxima-Minima,
Lagrange’s method of undetermined multipliers, Gradient, Curl and Divergence.
Directional derivatives. Tangent plane and normal line to a surface, Tangent line
to a space curve, Envelopes of plane curves and of family of surfaces, Power
series, Binomial series and Fourier series.
REFERENCE BOOKS:
2. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc., 1983.
4. Shanti Narayan, Differential Calculus, S. Chand & Co. Ltd., 2005.
Publishers, 1999.

20
B. Sc. Semester – IV (Subsidiary):
B. Sc. Semester-IV (Subsidiary Mathematics)
Course-MAT1403S09: Linear Programming and Numerical Analysis
(4 Credits)
Effective from December 2013
Unit-1: General discussions of Linear programming problems and their illustrations, Linear
inequalities, Graphical method of solving two variable problem, convex sets,
Problem of Linear Programming, Slack and Surplus variables, L.P.P. in a standard
form, Properties of a solution, Simplex method and its computational procedure,
Artificial basis technique, Transportation problem, Assignment problem.
Unit-2: Forward and backward differences, Newton’s forward and backward interpolation
formulas, Lagrange’s interpolation formula with error analysis, Gauss’s and
Stirling’s central difference interpolation formulas, Solution of equations in one
variable by Bisection method, Regula Falsi method, Newton-Raphson’s method.
Solution of system of linear equations by Gauss elimination method, Gauss-Seidel
iterative method, Numerical differentiation by Newton’s forward and backward
formulas and by Stirling’s formula, General quadrature formula, Trapezoidal rule,
Simpson’s rule with error analysis, Numerical solution of differential equations by
fourth order Runge-Kutta method.
REFERENCE BOOKS:
1987.
4. K. V. Mittal and C. Mohan, Optimization methods in Operations Research and System
Analysis, New Age International Publications, 2004.
5. G. Shankar Rao, Numerical Analysis, New Age International Pvt. Ltd, 2006.
7. Ralp G. Stanton, Numerical methods for science and Engineering, Prentice-Hall of India,
1967.
Sons, 2005.
2007.
B. Sc. Semester-IV (Subsidiary Mathematics)
Course-MAT1404S10: Integral Calculus and Differential Equations
(4 Credits)
Effective from December 2013
Unit-1: Iterated integrals and double integral, Change of order, Evaluation by using
transformations, Applications to area and volume, Line integrals, Path
independence of line integrals, Green’s theorem (proof for special regions). Triple
integrals, Surface integrals, Stokes’s theorem (without proof) and its applications,
Gauss’ theorem (without proof) and its applications, Beta and Gamma functions.
Unit-2: Differential equations of the first order but not of the first degree which are solvable
for p , x and y . Clairaut’s equation, singular solutions, system of linear differential
equations with constant coefficients and their applications to mixture problems,
simultaneous differential equations of the first order and first degree, Methods of

21
solutions of
R
dz
Q
dy
P
dx
== , Paffian differential equations, solution of Paffian
differential equations in three variables.
REFERENCE BOOKS:
1. Zafar Ahsan, Differential Equations and their applications, Prentice-Hall of India, 2004.
2. T. Amarnath, An Elementary Course in Partial Differential Equations, Narosa Publ. Co.,
1997.
3. Tom Apostol, Calculus (Volume II), Wiley Eastern Ltd., 1980.
4. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc., 1983.
6. Shanti Narayan, Differential Calculus, S. Chand & Co. Ltd., 2005.
Publishers, 1999.
B. Sc. Semester – I (Elective):
B. Sc. Semester-I (Elective Mathematics)
Course-MAT1104: Matrices
(2 Credits)
Unit-1: Special types of matrices and their properties, Elementary operations and
Elementary matrices, Rank of a matrix, rank of product of matrices, Invariance of
Unit-2: Eigen values and Eigen vectors of a matrix, Orthogonality of eigen vectors
associated with distinct eigen values, Properties of eigen vectors of a real
symmetric matrix, Diagonalization of a symmetric matrix, application to reductions
of quadrics to principal axes, Cayley-Hamilton theorem (without proof).
REFERENCE BOOKS:
West Press,2001.
B. Sc. Semester-I (Elective Mathematics)
Course-MAT1105: Differential and Integral Calculus
(2 Credits)
Unit-1: Successive differentiation and Standard forms, Leibnitz’s theorem (without proof),
Rolle’s Theorem (without proof), Lagrange’s and Cauchy’s mean value theorems
(without proof) and their geometrical interpretations, Increasing-decreasing
functions.
Unit-2: Taylor’s and Maclaurin’s theorems (without proof), Power series expansion of
xsin , xcos , )exp(x for Rx∈ and of m
x)1( + , )1log( x+ for 1|| <x (Assuming

22
the validity of expansions)Reduction formulas for ∫
2
0
sin
π
xdxm
, ∫
2
0
cos
π
xdxm
,
∫
2
0
cossin
π
xdxx nm
( Nnm ∈, ), Arc length, Surface area.
REFERENCE BOOKS:
Publications, 1999.
B. Sc. Semester – II (Elective):
B. Sc. Semester-II (Elective Mathematics)
Course-MAT1204: Differential Equations and Its Applications
(2 Credits)
Unit-1: Differential equations of first order and first degree: Exact equations, Linear
equations, Bernoulli’s equation, Applications of First order equations: Growth and
Decay, Half-life, Age of Fossil, Compound interest, Mixture problem, One
dimensional heat flow, Electric circuits, Applications in Economics.
Unit-2: Linear differential equations of higher order. Homogeneous equations, Differential
operators, Method of solving homogeneous equations, Non-homogeneous
equations, Inverse operators, Method of solving non-homogeneous equations,
Method of variation of parameters, Euler’s equations. Applications of higher order
equations: Simple pendulum, Damped and Forced motions, Microeconomic market
models, Price and supply model.
REFERENCE BOOKS:
1. Zafar Ahsan, Differential Equations and Their Applications, Prentice Hall of India, 2004.
2. Dennis G.Zill and Michael R. Cullen, Differential Equations (with Boundary-Value
Problems), Brooks/Cole Publishing Company, 2005.
B. Sc. Semester-II (Elective Mathematics)
Course-MAT1205: Geometry
(2 Credits)
Unit-1: Polar co-ordinate system in two dimensions, Relations between polar and
Cartesian coordinates, Graphs of polar equations, Aids in graphing polar equations,
Sketching of limacons, lemniscates, rose curves and spirals, Polar equations of
Lines, Circles and Conics and sketching them.
Unit-2: Equation of a Sphere, Section of a sphere by a plane, Intersection of two
spheres, Sphere through a given circle, Intersection of a sphere and a line,
Tangent plane to a sphere, Right circular cones, Right circular cylinders.
REFERENCE BOOKS:
1. P. Balasubramanyam, K. G. Subramaniam and G.R. Venkatraman, Coordinate
Geometry of Two and Three Dimension, Tata Mc Graw Hill Publ. Co., 1994
2. Gordon Fuller, Analytic Geometry, 5th edition, Addison-Wesley, 1979.

23
3. Gordon Fuller and Robert M. Parker, Analytic Geometry and Calculus, East-West Press
Pvt. Ltd., 1967.
B. Sc. Semester – III (Elective):
B. Sc. Semester-III (Elective Mathematics)
Course-MAT1305E05: Algebra
(2 Credits)
Unit-1: Field of complex numbers, graphical representation of subsets of complex plane,
geometrical significance of complex functions β+z , zα , z , z ,
z
1
, )Re(z , )Im(z ,
z and βα +z , exponential and trigonometric functions.
Unit-2: De Moivre’s theorem and its applications, nth
roots of a complex number,
Statement of fundamental theorem of algebra, Multiple roots and test for
multiplicity, Relation between roots and coefficients, Imaginary roots of an
equation with real coefficients.
Practical using mathematical software’s for the geometrical visualization of
some of the above topics will be given.
REFERENCE BOOKS:
Publishing Company.
2. J. V. Uspensky, Theory of Equations, Mc Graw Hill Publishers.
B. Sc. Semester – IV (Elective):
B. Sc. Semester-IV (Elective Mathematics)
Course-MAT1405E11: Numerical Analysis
(2 Credits)
Unit-1: Error, absolute error, relative error, rounding-off a number. Solution of equations in
one variable by Bisection method, Regula falsi method, Newton-Raphson’s
method. Difference operators ∆ ,δ ,∇, µ , shift operator E and relations among
them. Differences of a polynomial, Newton’s forward and backward interpolation
formulae, Lagrange’s interpolation formula.
Unit-2: Gauss’s and Stirling’s central difference interpolation formulae, Solution of system
of linear equations by Gauss elimination method, Gauss – Seidel iterative method,
Numerical differentiation by Newton’s forward and backward formulae(without
derivation), General quadrature formula(without derivation), Trapezoidal rule,
Simpson’s 1/3 rule, Numerical solution of first order and first degree ordinary
differential equations by Picard's method and fourth order Runge-Kutta method.
REFERENCE BOOKS:
1. Erwin Kreysizg, Higher Engineering Mathematics, John Wiley & Sons Inc., 2007.
3. H. C. Saxena, Finite Differences and Numerical Analysis, S. Chand & Co. Ltd., 1988.

24
B. Sc. Semester – III, IV (Elective (Open) Mathematics)
B. Sc. Semester-III, IV (Elective (Open) Mathematics)
Course- MAT1007E06: Boolean Algebra and its Applications
(2 Credits)
Unit-1: Binary relation, Properties of binary relation, Partially ordered sets, Hasse
diagram, Lattices, Chains, Principle of duality, Basic properties of algebraic
systems defined by lattices, Distributive and Complete lattice, Boolean algebra.
Unit-2: Atoms of a Boolean algebra and its properties, Uniqueness of finite Boolean
algebras (without proof), Boolean expressions and Boolean functions, Applications
to logic, Gates and digital circuits.
REFERENCE BOOKS:
2. C. L. Liu, Elements of Discrete Mathematics, McGraw Hill International Editions, 1985.
Course-MAT1008E07: Discrete Mathematics and its Applications
(2 Credits)
Unit-1: Induction and Recursion: Mathematical Induction, Recursively defined sequences,
Solving recurrence relations. Principles of counting: The principle of inclusion –
exclusion, The addition and multiplication rules, The Pigeonhole principle and its
applications.
Unit-2: Permutations and Combinations, Probability theory, Repeated experiments,
counting and probability, The Euclidean Algorithm, The RSA Public-Key
Cryptosystem.
REFERENCE BOOKS:
1. E. G. Goodaire and M. M. Parmenter, Discrete Mathematics with Graph Theory,
2. R. Johnsonbaugh, Discrete Mathematics, Prentice Hall International, 1997.
3. W. D. Wallis, A Beginner’s Guide to Discrete Mathematics, Birkhauser, 2003.
Course- MAT1009E08: Graph Theory
(2 Credits)
Unit-1: Definition and elementary properties of graphs, Isomorphism of graphs,
Subgraphs Walks, Paths and circuits, Connected graphs, Euler graphs,
Operations on graphs, Hamiltonian circuits, Definition and properties of tree,
Centers in a tree, Rooted and Binary tree.
Unit-2: Spanning trees, fundamental circuits, Cut set and its properties, Planar graphs
and Kuratowski’s two graphs, Representation of planar graphs, Geometric and
combinatorial duals, Chromatic number, Chromatic polynomial, Matchings.
REFERENCE BOOKS:

25
Course- MAT1010E09: Linear Programming
(2 Credits)
Unit-1: General discussions of Linear programming problems and their illustrations,
Graphical method of solving two variable problem, Convex sets and their
properties, Feasible solution, optimum solution, Slack and Surplus variables, L.P.P.
in a standard form, Properties of a solution (without proof), Simplex method and its
computational procedure, Artificial basis technique.
Unit-2: Transportation problem, Methods for finding initial basic feasible solution: North-
west corner rule, Matrix minima method, Vogel’s approximation method, optimal
solution: MODI Method. Assignment problem: Hungarian Method.
REFERENCE BOOKS:
Sons, 2005.
2007.
Course- MAT1011E10: Number Theory
(2 Credits)
Unit-1: Division algorithm, gcd and lcm of more than two integers, The Linear Diophantine
equation, primes, Composite numbers, Fundamental theorem of arithmetic,
Euclid’s Theorem.
Unit-2: Congruences: Definitions and elementary properties. Results about linear
congruence equations, Applications of congruences: Euler’s theorem, Fermat’s
Little theorem, Wilson’s theorem (without proof), Divisibility test, Chinese
Remainder theorem (without proof).
REFERENCE BOOKS:
1. Donald M. Burton, Elementary Number Theory, Allyn and Bacon Inc, 2006.
2. S. D. Telang, Number Theory, Tata Mc Graw Hill Publishers, 2004.

26
B. Sc. Semester – I, II, III, IV (Foundation)
B. Sc. Semester-I, II, III, IV (Foundation Mathematics)
Course- MAT1004F01: Algebra
(2 Credits)
Unit-1: Trigonometric functions and Standard formulas for trigonometric functions, Algebra
of complex numbers, graphical representation of subsets of complex plane,
geometrical significance of complex functions β+z , zα , z , z ,
z
1
, )Re(z , )Im(z ,
z and βα +z .
Unit-2: De Moivre’s theorem (without proof) and its applications, nth
roots of a complex
number, Statement of fundamental theorem of algebra, Multiple roots and
test for multiplicity, Relation between roots and coefficients, Imaginary roots
of an equation with real coefficients.
REFERENCE BOOKS:
Publishing Company.
2. J. V. Uspensky, Theory of Equations, Mc Graw Hill Publishers.
Course- MAT1005F01: Calculus
(2 Credits)
Unit-1: Concept of a limit, Continuity and derivative of elementary functions, Rules of
differentiation (without proof), Chain rule (without proof). Derivative of implicit
functions, Derivative of parametric functions, Applications of Derivatives:
Increasing decreasing functions, maxima and minima, Concavity/ convexity of a
function.
Unit-2: Standard integration formulae, Integration by the method of substitution, Integration
by parts, Integration by the method of partial fractions, Properties of definite
integrals (without proof), application to Integration : Area under a curve as a definite
integral, Volume and area of surface of revolution.
REFERENCE BOOKS:
Publications, 1999.
Course- MAT1006F01: Matrices
(2 Credits)
Unit-1: Introduction to complex numbers, Matrices, Addition and multiplication of Matrices,
Special types of matrices and their properties, Determinants of order 2, 3 and 4,
Inverse of a matrix, Cayley-Hamilton theorem (without proof).

27
Unit-2: Elementary operations and Elementary matrices, Rank of a matrix, Invariance of
REFERENCE BOOKS:
West Press, 2001.
---------------------------

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