Department of Mathematics
Head of Department 
Dr. Lalita Dhurve Ph.D.,M.Sc. 
Faculties 
1. Shri. Prajendra Raghuwanshi(Guest faculty) M.Sc. 2. Miss. Pooja Bhute (JBS) M.Sc. 
Cources 
B.Sc./M.Sc. 
Cources
Eligibility Criteria for B.Sc. / M.Sc.
 Eligibility Criteria for B.Sc.12^{th} in Maths Group
 Eligibility Criteria for M.Sc. Graduate with Maths one subject
B.Sc. I Year (Mathematics)
Course Name

Course Outcomes

Major –I Paper
Algebra , , Vector Analysis &
Geometry 110163

Knowledge gained:
 Concept of rank and nullity of matrix and some theorems about Normal forms
 Certain relation between Eigen values and Eigen vectors
 Concept of gradient, divergent and curl
 Basic concept of product of four vectors and reciprocal vectors
 Vector differentiation
 Vector integration
 Gauss’s, Stoke’s and green’s theorem
 Tracing of conics, confocal conics
 Polar equation of conic
 The cone, the cylinder, the central conicoids, the paraboloid
Skills Gained:
 Solving problems using the powerful concept of application of matrices.
 Ability to understand vector differentiation and vector integration
 Gain practical knowledge of tracing of conics
 Ability to understand problem solving and gain knowledge of grad,
divergent and curl
Competency developed:
 Vector integration and its application developed practical knowledge of area of curve
in daily life
Ability to handle daily life problems with the help of cone and cylinder etc.

MajorII/Minor/ Open Elective – Calculus & Differential Equations 110164/110165/110166

Knowledge gained:
 Successive differentiation.
 Leibnitz theorem, Taylor series
 Asymptotes, curvature
 Concavity and convexity, points of inflexion
 Tracing of curves
 Integration of Transcendental functions
 Definite integral
 Quadrature and rectification
 Differential equations of first order and higher degree
 Linear differential equations
 Method of variation of parameters Skills gained:
 Generalization of Concept like successive differentiation
 Understand practical knowledge of curve tracing
 Find the area of curves to understand the practical knowledge of definite integrals

B.Sc. IInd Year (Mathematics)
Major –I PaperI Abstract Algebra & Linear Algebra 210332

Knowledge gained:
 Recognize the algebraic structures as a group and classify them as ableian, cyclic and permutation groups etc.
 Link the fundamental concepts of groups and symmetrical figures.
 Analyze the subgroups of cyclic groups.
 Explain the significance of the notion of cossets, normal subgroups and quotient groups.
 The fundamental concept of rings, fields, sub rings, integral domains and the corresponding orphisms.
 Analyze whether a fini9te set of vectors in a vector space is linearly independent.
 Understand the linear transformations, rank and nullity,matrics of a linear transformations algebra of transformations and change of basic.
 Compute the characteristic polynomial, Eigen values, Eigen vectors and Eigen spaces as well as the geometric and the algebraic multiplicities of an Eigen value and apply the basis diagonalization result.
Skills gained :
 Linear algebra helps you understand geometric concepts such as planes, in higher dimensions, and perform mathematical operations on them.
 The idea of groups used in abstract algebra has helped students in finding out areas and volumes of complex structures.
Competency developed:
 Determining whether a transformation from one vector space V into another vector space W is linear.
 Determining the general rule for a linear transformation, given its behavior on a basis of the domain space.
 Finding the standard matrix of a linear transformation.
 Proving that the kernel and the range of a general linear transformation are subspaces of the corresponding.

Major II / minor /open elective Advanced Calculus & Partial Differential Equations 210332

Knowledge gained:
 Convergence of sequences, absolute and conditional convergence
 Continuity and differentiability
 Concept of limit and continuity of functions of two variables
 Partial differentiation
 Change of variables, Taylor’s theorem, Jacobians
 Maxima and minima of functions of two variables.
 Beta and gamma functions
 Taylor’s theorem for functions of two variables.
 Euler’s theorem on homogeneous functions.
Skills gained:
 Efficiency in handling various type of series for convergent or divergent nature
 Ability to understand the continuity and differentiability
 Idea about partial differentiation
Competency developed:
 Ability to solve maxima and minima for function of two variables.
 Ability to deal with homogeneous and nonhomogeneous partial differential equation constant coefficients.
 Lagrange’s solution and standard forms
 Ability to use heat flow problems and transmission of signals.

B.Sc. III Year (Mathematics)
Course Name

Course Outcomes

PaperI Linear Algebra and
Numerical Analysis 310332

Knowledge gained:
 Concept of vector spaces, basis, finite dimensional, vector spaces
 Linear transformations and their representation as matrices
 Eigen values and Eigenvectors of a linear transformation and Diagonalization
 Inner product, solution of equations
 Interpolation
 Numerical Quadrature
 Linear Equations, ordinary Differential Equation Skill gained:
 Solving problems using the powerful concept of vector spaces
 Solving problems of linear transformations and their representation as matrices


 Ability to understand interpolation in practical way Competency gained:
 Understanding of vector spaces and inner product
 Applying the concept of interpolation and Quadrature in daily life problems such engineering
 Understanding linear equations and ordinary differential equations

PaperII Real and
Complex Analysis 310333

Knowledge gained:
 Concept of Riemann integral and some theorems
 Partial derivatives, Differentiability of real valued function of two variables
 Concept of improper integrals and their convergence
 Generalization of concepts like continuity and differentiability
 Metric spaces
 Concept of continuous functions, compact sets, connectedness
 Concept of analytic function, CauchyRiemann equation
Skill gained:
 Idea about Riemann integration and some theorem like mean value theorem


 Ability to understand Matrix spaces, limit points, open and closed sets, Cauchy sequences
 Geometric representation of complex numbers, idea about analytic function
Competency developed:
 Ability to understand real number system and the relation between number line
one to one correspondence of a function

PaperIII
Discrete Mathematics (Optional) 310346

Knowledge gained:
 Binary relations, equivalence relation, partial order relation
 Graph, multi graph and weighted graph
 Path and circuits
 Shortest paths, Eulerian paths and circuits
Trees and their properties.
 Cutest and its properties,
 Planar graphs kuratowskis two graphs
Skill gained:
 Efficiency in handling with discrete structures
 Efficiency in set theory and binary relations
Efficiency in notations of matching, ordering, planarity
Competency gained:
 Application to real life problems such as network theory
 Developed efficiency with planar graph
 Ability to apply combinatorial intuitions in network theory
 Ability to use graphs as unifying theme for various combinational problems
 Ability to deal with notations

M.Sc. I Semester (Mathematics)
Course Code

Course Name

Course Outcomes

212100

Real AnalysisI

Knowledge Gained:
 Definition and existence of Riemamm stieltjes integral
 Integration and differentiation of vector valued function
 Point wise and uniform convergence of sequence and series, cauchy criterion, weirtars Mtest.
 Uniqueness theorem for power series abels and taubers theorems
 Function of several variables
 Inverse function theorem
 Implicit function theorem
 Stoke’s theorem
Skills gained:
• Viewing C [0, 1], i.e., the space of continuous functions on [0, 1] as a metric space.
• The notion of convergence in c [0, 1] and related theorems.
• Differentiability of functions in several variables and their relation to partial derivatives.
• Realizing the differentials in terms of geometric properties.
Competency developed:
• Ability to handle convergence of series and sequence of functions.
• Ability to differentiate functions in Rn.
• Apply Implicit and inverse function theorem, moving towards calculus on manifolds.

212101

TopologyI

Knowledge Gained:
 Definition and examples of topological spaces
 Closed sets, closure , dense subsets neighborhoods
 Accumulation points and derived sets
 Kuratowski closure operator and Neighbourhood systems
 Connected space
 Path connectedness
 Linear continuum
 Topologist’s sine curve
 Axioms T1 ,T2, T3, spaces
 Metric topology
Skills Gained:`
 Solving problems using powerful concept of groups, Sylows gro commutator groups
 Ability to understand the Galois groups theory, extended field the Invariants etc.
Competency developed:
 Applying the concept of groups and fields in real life problem thinking logically.
 Implies facility in working with matrices, a concept that find a la number of applicants in real life including graphs and networks.

212102

Complex analysisI

Knowledge Gained:
 Concept of analytic function and power series and some theorems
 Concept of Cauchy Riemann equation, singularities
 Cauchy’s theorem, Cauchy integral formula and its applications
 Cauchy residue theorem, mobius transformations
 Concept of complex integration
 Concept of conformal mapping and its theorems
 Generalization of concept of continuity and differentiability
Skills Gained:
 Understanding of Conformal and Isogonal mappings
 Development of functions into power series, classifying power seri
 Applications to counting Zeros and Poles
Competency developed:
 Ability to handle competitive exams like I.E.S. , I.A.S., I.R.S. etc.
 Ability to handle NET, GATE, SLET exams
 Ability to gain the concept of limit and continuity
 Ability to understand complex integration and some theor

212099

Advanced Abstract algebraI

Knowledge Gained:
 Concept of nilpotent group, modules,
 Cauchy theorem, sylows theorems
 Series of groups
 Solvable groups
 Finite field
Skills Gained:
 Solving problems using powerful concept of groups, Slows group commutator groups
 Ability to understand the Galois groups theory, extended field the Invariants etc.
Competency developed:
 Applying the concept of groups and fields in real life problem thinking logically.

 Implies facility in working with matrices, a concept that find a la number of applicants in real life including graphs and networks.

212103

Advanced Discrete MathematicsI

Knowledge Gained:
 Binary relations, equivalence relation, partial order relation
 Graph, multi graph and weighted graph
 Path and circuits
 Shortest paths, Eulerian paths and circuits
Trees and their properties.
 Cutest and its properties,
 Planar graphs kuratowski’s two graphs
Skills Gained:
 Efficiency in handling with discrete structures
 Efficiency in set theory and binary relations
Efficiency in notations of matching, ordering, planarity
Competency developed:
 Application to real life problems such as network theory
 Developed efficiency with planar graph
 Ability to apply combinatorial intuitions in network theory
 Ability to use graphs as unifying theme for various combinational problems
 Ability to deal with notations



 Limit and continuity of functions on metric spaces
 Compactness and connectedness of metric spaces
 Definition and existence of Riemann – stieltjes integral
 Integration and differentiation of vector valued function
 Point wise and uniform convergence of sequences and series, Cauchy criterion, weirtars M test
 Measurable sets and its properties borel sets
 Lebesgue integral of bounded function
 Integration of nonnegative function
Skills Gained:
 Calculation of different matrices spend examining the compactness
 Calculation of limit of a function on metric spaces and examining continuity
 Computation of RS integral
 Application of different test of convergence for sequences and se
 Computation of measures of sets
Competency developed:
 Concepts gained are helpful in the exams NET, JRF and UPSC
 Understanding the concept of metric as a distance function
 Enhancing the topological properties of metric spaces completeness, compactness and connectedness
 Understanding the concept of RS integral and measure theory.




M.Sc. II Semester (Mathematics)
Course Code

Course Name

Course Outcomes

220334

Lebesgue Measure

Knowledge gained:
 Students acquired basic knowledge of measure and integration theory.
 Analyze measurable sets and Lebesgue measure.
 Describe the Borel sets and Measureable functions.
 The student will be able to describe the structure of measurable functions.

220335

TopologyII

Knowledge Gained:
 Topological spaces with their bases and topological properties.
 Axioms T1 ,T2, T3, spaces
 Continuous function and countability axioms
 Connectedness, path connectedness and components
 Compactness with local and sequential compactness
 Separation axioms and product topology
 All above properties with respect to product spaces
 The definitions of standard terms in topology.
 Some important concepts like continuity, compactness, connectedness, projection mapping etc
 Using new ideas in mathematics and also help them in communicating the subject with other subjects.

220336

Complex analysisII

Knowledge gained:
 Weierstrass factorization theorem.
 Riemanan zeta function Riemans functional equation.
 Runge’s theorem, mittagelefflers theorem.
 Power series method of analytic continuation.
 Schwartz reflection principle.
 Borel’s theorem, Dirichlet problem Green’s functions.
 Students will learn more about everywhere differentiable function and they will learn how it helps them to decide analyticity.

220333

Advanced Abstract algebraII

Knowledge gained:
 The students will be able to define the concept of module over a ring and will be able to give examples of this kind of algebraic structures.
 The students will be able to define the concept of Linear transforms, algebra of linear transformations & linear operators, Nilpotent transformations, Jordan blocks and forms.
 The students will be able to give detail proof and work with the concepts of Schurz lemma.
 The students will be able to apply the basic concept of modules, including uniform and primary modules.
 The students will be able to define and work the concepts of homomorphism.
 The students will be able to apply the basic concept of field theory, including field extensions and finite fields.

220337

Advanced Discrete MathematicsII

Knowledge gained:
 Understand the basic principles of sets and operations in sets.
 Demonstrate different traversal methods for trees and graphs.
 Write model problems in mathematical science using trees and graphs.
 Finite state machines and their transition table and diagrams
 Equivalence of finite state machines, finite automatea.
 Moore and mealy machines
 Grammars and languages phraseStructure Grammars.
 The reverse polish notation.

M.Sc. III Semester (Mathematics)
Course Cod

Course Name

Course Outcomes

320337

Functional AnalysisI

Knowledge Gained:
 Properties of finite dimensional normed space with concept and dealing with examples.
 Concept of uniform boundedness principles and its applications.
 Inner product space and their elementary properties.
 Hahn Banach theorem for normed linear spaces.
 Study of orthonormal sets, Bessel’s inequality.
 Concept of Cantor’s intersectionit theorem

320338

Advanced Functional AnalysisI

Knowledge Gained:
 Concept of normed space, Gateaux derivative, fretchet derivative.
 Concept of fixed point theorem and their applications, Banach contraction principle and its generalization.
 Application of Banach contraction principle.
 Definitions and examples of topological vector space , covex and their properties, Minkowski’s functional, subsace.
 Product space and quotient space of a topological vector space.

320341

Algebric TopologyI

Knowledge gained:
• Concept of structure of homology groups, connected simplex.
• Concept of chain map, simplicial map, examples.
• Concept of homology group of ndimensional sphere.
• Concept of Geometrically independent set, k simplex. Face of a simplex, triangulation of sphere, Mobius band. Torusn Klein bottle.

320344

Machenics –I

Knowledge gained:
 Concept of holonomic and nonholonomic systems.
 Constraint and its classifications.
 Possible and virtual displacement.
 Larange’s equation of first kind.
 Concept of uniqueness of solution
 Hamilton’s variables, Hamilton’s canonical equations.
 Shortest distance, minimum surface of revolution.
 Isopreimetric problems.

320350

Integral TransformI

Knowledge gained:
 Basic concept of Laplace transform, inverse Laplace transform
Application of Laplace transform to solution of differential equation and integral equations with convolution type kernel
 Application of L.T. to the solution of initial –boundary valuel problem, solution of heat equation, wave equation
 Concept of Fourier transform, inverse Fourier transform
Application of F.T. to the solution of initial boundary value problem, solution of heat equation, diffusion equation, w equations
 Skills for solving various types of differential equations, , initial values problems.
 Skills for solving various real life problems related to physical science mathematical sciences, engineering etc.

M.Sc. IV Semester (Mathematics)
Course Cod

Course Name

Course Outcomes

420346

Applied Functional Analysis

Knowledge Gained:
 Hilbet space obtained from Hilbert space and tensor product of Hilbert space , convex set and projections.
 Weak convergence, weak compactness properties.
 Minkowski functional support plane through a boundary point, support mapping.
 Linear operators and their adjoints, bounded and unbounded operators.
 Spectral theory of opertaors.

420347

Advanced Functional AnalysisII

Knowledge Gained:
 Finite dimensional topological vector space, locally convex topological vector space.
 Normable and metrizable topological vector spaces.
 Frechet space, uniform boundedness principle, open mapping theorem
 Banach alaoglu theorem.
 Points and external sets krein miliman’s theorem.

420350

Algebric TopologyII

Knowledge Gained:
 The fundamental group and its properties.
 Introduction homotopy definitions and examples.
 Simply connected space.
 Path lifting and homotopy lifting property.
 Covering pojections.
 Applications of homotopy lifting theorem.
 The monodromy theorem.

420353

MachenicsII

Knowledge Gained:
 Fundamental lemma of calculus of variations.
 Euler’s equations for one dependent function and its generalization.
 Conditional extremum under geometry constraints.
 Hemilton – Jacobi equation, Jacobi theorem.
 Poisson brackets invariance of Lagrange brackets.

0
420359

Integral TransformII

Knowledge Gained:
 To apply the Fourier transform methods for solving functions.
 Applications of Laplace transform to boundary value problems.
 Electric circuits problems, related to application of Electric circuits.
 Applications to beams.
 Wave equations.
 Fourier cosine and sine transform.
