Course Outcomes |
B.Sc. Part-I Semester-I |
DSC – 5A |
DIFFERENTIAL CALCULUS
|
1. understand De- Moivre’s Theorem and applications of De- Moivre’s Theorem
2. understand Hyperbolic functions and Inverse hyperbolic function .Properties of hyperbolic functions.
3. understand relation between hyperbolic and circular functions.
4. understand concept of Successive Differentiation and applications of Leibnitz’s Theorem.
5. understand Euler’s theorem on homogenous functions, Maxima and Minima for functions of two variables and Lagrange’s Method of undetermined multipliers. |
DSC – 6A |
CALCULUS |
1. understand concept of Mean Value Theorems and Indeterminate Forms
2. understand Taylor’s and Maclaurin’s Theorem with Lagrange’s & Cauchy’s form of remainder. Maclaurin’s series expansion.
3. understand Limits and Continuity of Real Valued Functions. ∈ - δ definition of limit of function of one variable .
4. understand Classification and Types of Discontinuities.
5. understand the concept of Differentiability at a point and Differentiability in the interval [a,b]. |
|
DSC – 5B |
DIFFERENTIAL EQUATIONS |
1. understand the concept of Differential Equations of First Order and First Degree and methods of solutions.
2. understand the concept of Differential Equations of First Order but Not of First Degree and methods of solutions.
3. understand the concept of Linear Differential Equations with Constant Coefficients.
4. understand the concept of Homogeneous Linear Differential Equations and methods of solutions.
5. understand the concept of Legendre’s Linear Equations and methods of solutions. |
DSC – 6B |
HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS |
1. understand the concept of Second Order Linear Differential Equations and methods of solutions.
2. understand the concept of Simultaneous Differential Equations and Total Differential Equations and methods of solutions.
3. understand the geometrical interpretation of Simultaneous Differential Equations and Total Differential Equations.
4. understand the concept of Partial Differential Equations and linear and non-linear Partial Differential Equations .
5. understand formation of Partial Differential Equations.
5. understand the methods of solving linear and non-linear Partial Differential Equations. |
B.Sc. Part-II Semester-III |
DSC – 5C |
Real Analysis–I |
1. understand types of functions and how to identify them.
2. use mathematical induction to prove various properties.
3. understand the basic ideas of Real Analysis.
4. prove order properties of real numbers, completeness property and the Archimedean property. |
DSC – 6C |
Algebra–I |
1. understand properties of matrices.
2. solve System of linear homogeneous equations and linear non-homogeneous equations.
3. find Eigen values and Eigen vectors.
4. construct permutation group and relate it to other groups.
5. classify the various types of groups and subgroups. |
B.Sc. Part-II Semester-IV
|
DSC – 5D |
Real Analysis–II |
1. understand sequence and subsequence.
2. prove The Bolzano-Weierstrass Theorem.
3. derive Cauchy Convergence Criterion.
4. find convergence of series.
5. apply Leibnitz Test. UNIT |
DSC – 6D |
Algebra–II |
1. prove Lagrange’s theorem.
2. derive Fermat’s theorem.
3. understand properties of normal subgroups, factor group.
4. define homomorphism and isomorphism's in group and rings.
5. derive basic properties of rings and subrings. |
B.Sc. Part-III Semester-V
|
DSE – E9 |
Mathematical Analysis |
1. understand the integration of bounded function on a closed and bounded interval
2. understand some of the families and properties of Riemann integrable functions
3. understand the applications of the fundamental theorems of integration
4. understand extension of Riemann integral to the improper integrals when either the interval of integration is infinite or the integrand has infinite limits at a finite number of points on the interval of integration
5. understand the expansion of functions in Fourier series and half range Fourier series |
DSE – E10 |
Abstract Algebra |
1. understand Basic concepts of group and rings with examples
2. Identify whether the given set with the compositions form Ring, Integral domain or field.
3. Understand the difference between the concepts Group and Ring.
4. Apply fundamental theorem, Isomorphism theorems of groups to prove these theorems for Ring.
5. Understand the concepts of polynomial rings, unique factorization domain. |
DSE – E11 |
Optimization Techniques |
1. provide student basic knowledge of a range of operation research models and techniques, which can be applied to a variety of industrial and real life applications.
2. Formulate and apply suitable methods to solve problems.
3. Identify and select procedures for various sequencing, assignment, transportation problems.
4. Identify and select suitable methods for various games .
5. To apply linear programming and find algebraic solution to games. |
DSE – E12 |
Integral Transforms |
1. understand concept of Laplace Transform.
2. apply properties of Laplace Transform to solve differential equations.
3. understand relation between Laplace and Fourier Transform.
4. understand infinite and finite Fourier Transform.
5. apply Fourier transform to solve real life problems. |
B.Sc. Part-III Semester-VI
|
DSE – F9 |
Metric Spaces |
1. acquire the knowledge of notion of metric space, open sets and closed sets.
2. demonstrate the properties of continuous functions on metric spaces,
3. apply the notion of metric space to continuous functions on metric spaces.
4. understand the basic concepts of connectedness, completeness and
compactness of metric spaces,
5. appreciate a process of abstraction of limits and continuity to metric spaces |
DSE –F10 |
Linear Algebra |
1. understand notion of vector space, subspace, basis.
2. understand concept of linear transformation and its application to real life situation.
3. work out algebra of linear transformations.
4. appreciate connection between linear transformation and matrices.
5. work out eigen values, eigen vectors and its connection with real life situation. |
DSE – F11 |
Complex Analysis |
1. understand basic concepts of functions of complex variable.
2. understand concept of analytic functions.
3. understand concept of complex integration and basic results thereof.
4. understand concept of sequence and series of complex variable.
5. understand concept of residues to evaluate certain real integrals. |
DSE – F12 |
Discrete Mathematics |
1. understand use classical notions of logic: implications, equivalence, negation, proof by contradiction, proof by induction, and quantifiers.
2. understand to apply notions in logic in other branches of Mathematics.
3. know elementary algorithms : searching algorithms, sorting, greedy algorithms, and their complexity.
4. understand to apply concepts of graph and trees to tackle real situations.
5. understand to appreciate applications of shortest path algorithms in computer science. |
|
CC-101 |
Advanced Calculus |
1. Analyze convergence of sequences and series of functions
2. understand to check differentiability of functions of several variables
3. understand to apply inverse and implicit function theorems for functions of several variables
4. understand to use Green's theorem, Stoke’s Theorem, Gauss divergence Theorem |
CC-102 |
Linear Algebra |
1. understand basic notions in Linear Algebra and use the results in developing advanced mathematics.
2. study the properties of Vector Spaces, Linear Transformations, Algebra of Linear
3. construct Canonical forms and Bilinear forms.
4. apply knowledge of Vector space, Linear Transformations, Canonical Forms and Bilinear Transformations. |
CC-103 |
Complex Analysis |
1. understand fundamental concepts of complex analysis.
2. identify analytic functions, Conformal maps.
3. construct Taylor and Laurent series.
4. classify singularity and apply Residue Theorem to evaluate real integrals.
5. enjoy the beauty of analytic functions and related concepts. |
CC-104 |
Classical Mechanics |
1. discuss the motion of system of particles using Lagrangian and Hamiltonian approach.
2. solve extremization problems using variational calculus. 3. discuss the motion of rigid body.
4. construct Hamiltonian using Routh process. 5. use infinitesimal and finite rotations to analyze motion of rigid body. |
CC-105 |
Ordinary Differential Equations |
1. study basic notions in Differential Equations and use the results in developing advanced mathematics.
2. solve problems modeled by linear differential equations 3. use power series methods to solve differential equations about ordinary points and regular singular points.
4. construct approximate solutions using method of successive approximation.
5. establish uniqueness of solutions |
M. Sc. Part-I Semester-II |
CC- 201 |
Functional Analysis |
1. understand the fundamental topics, principles and methods of functional analysis.
2. demonstrate the knowledge of normed spaces, Banach spaces, Hilbert space.
3. define continuous linear transformations between linear spaces, bounded linear functionals.
4. apply finite dimensional spectral theorem.
5. identify normal, self adjoint, unitary, Hermit ion operators. |
CC- 202 |
Algebra |
1. study group theory and ring theory in some details.
2. introduce and discuss module structure over a ring.
3. apply Sylow theorems.
4. use homomorphism and isomorphism theorems.
5. check irreducibility of polynomials over Q using Eisenstein criteria. |
CC- 203 |
General Topology |
1. built foundations for future study in analysis, in geometry, and in algebraic topology.
2. introduce the fundamental concepts in topological spaces.
3. acquire demonstrable knowledge of topological spaces, product spaces, and continuous functions on topological spaces.
4. identify compact and connected sets in topological spaces.
5. use Separation and countability axioms, Urysohn lemma, Urysohn metrization theorem and the Tychonoff theorem |
CC- 204 |
Numerical Analysis |
1. apply the methods to solve linear and nonlinear equations.
2. find numerical integration and analyze error in computation.
3. solve differential equations using various numerical methods.
4. determine eigen values and eigen vectors of a square matrix.
5. construct LU decomposition of a square matrix |
CC- 205 |
Partial Differential Equations |
1. classify partial differential equations and transform into canonical form
2. solve linear partial differential equations of both first and second order.
3. solve boundary value problems for Laplace's equation, the heat equation, the wave equation by separation of variables, in Cartesian, polar, spherical and cylindrical coordinates.
4. apply method of characteristics to find the integral surface of a quasi linear partial differential equations.
5. establish uniqueness of solutions of partial differential equations. |
M. Sc. Part-II Semester-III
|
CC- 301 |
Real Analysis |
1. generalise the concept of length of interval.
2. analyse the properties of Lebesgue measurable sets.
3. demonstrate the measurable functions and their properties.
4. understand the concept of Lebesgue integration of measurable functions.
5. characterize Riemann and Lebesgue integrability.
6. prove completeness of 𝐿 Spaces. |
CC- 302 |
Advanced Discrete Mathematics |
1. classify the graphs and apply to real world problems.
2. simplify the graphs using matrix.
3. study Binomial theorem and use to solve various combinatorial problems.
4. simplify the Boolean identities and apply to switching circuits.
5. locate and use information on discrete mathematics and its applications |
CCS-303, CCS-304, CCS-305 |
Number Theory |
1. learn more advanced properties of primes and pseudo primes.
2. apply Mobius Inversion formula to number theoretic functions.
3. explore basic idea of cryptography.
4. understand concept of primitive roots and index of an integer relative to a given primitive root.
5. derive Quadratic reciprocity law and its apply to solve quadratic congruences. |
CCS-303, CCS-304, CCS-305 |
Operations Research – I |
1. identify Convex set and Convex functions.
2. Construct linear integer programming models and discuss the solution techniques,
3. Formulate the nonlinear programming models, 4. Propose the best strategy using decision making methods,
5. solve multi –level decision problems using dynamic programming method. |
CCS-303, CCS-304, CCS-305 |
Fuzzy Mathematics – I |
1. acquire the knowledge of notion of crisp sets and fuzzy sets,
2. understand the basic concepts of crisp set and fuzzy set, 3. develop the skill of operation on fuzzy sets and fuzzy arithmetic,
4. demonstrate the techniques of fuzzy sets and fuzzy numbers.
5. apply the notion of fuzzy set, fuzzy number in various problems. |
CCS-303, CCS-304, CCS-305 |
General Relativity – I |
1. understand Albert Einstein’s special and general theory of relativity.
2. formulate fields of General Relativity.
3. relate the covariant derivative and geodesic curves
4. calculate components of the Riemann curvature tensor form a line element.
5. derive Necessary and Sufficient condition for isometry |
CCS-303, CCS-304, CCS-305 |
Combinatorics |
1. describe Pigeonhole principle and use it to solve problems.
2. use definitions and theorems from memory to construct solutions to problems
3. use Burnside Frobenius Theorem in counting's.
4. use various counting techniques to solve various problems.
5. apply combinatorial ideas to practical problems.
6. improve mathematical verbal communication skills. |
M.Sc. Part-II Semester-IV
|
CC- 401 |
Field Theory |
1) determine the basis and degree of a field over its subfield.
2) construct splitting field for the given polynomial over the given field.
3) find primitive nth roots of unity and nth cyclotomic polynomial.
4) make use of Fundamental Theorem of Galois Theory and Fundamental Theorem of Algebra to solve problems in Algebra.
5) apply Galois Theory to constructions with straight edge and compass. |
CC- 402 |
Integral Equations |
1. classify the linear integral equations and demonstrate the techniques of converting the initial and boundary value problem to integral equations and vice versa.
2. develop the technique to solve the Fredholm integral equations with separable kernel.
3. develop and demonstrate the technique of solving integral equations by successive approximations, using Laplace and Fourier transforms
4. to analyze the properties of symmetric kernel.
5. To prove Hilbert Schmidt Theorem and solve the integral equation by applying it. |
CCS-403, CCS-404, CCS-405 |
Algebraic Number Theory |
1. deal with algebraic numbers , algebraic integers and its applications,
2. concept of lattices and geometric representation of algebraic numbers.
3. Understand the concept of fractional ideals.
4. relate Finitely generated abelian groups and modules
5. derive Minkowski's theorem.
6. compute class groups and class numbers. |
CCS-403, CCS-404, CCS-405 |
Operations Research – II |
1.decide policy for replacement.
2.calculate economic lot size.
3.derivePoission distribution theorem and compute attributes of distribution model.
4.construct Shannon Fano codes.
5.identify optimal path by using CPM and PERT. |
CCS-403, CCS-404, CCS-405 |
Fuzzy Mathematics – II |
1. acquire the concept of fuzzy relations.
2. understand the basic concepts of fuzzy logic and fuzzy algebra.
3. develop the skills of solving fuzzy relation equations.
4. construct approximate solutions of fuzzy relation equations.
5.solve problems in Engineering and medicine. |
CCS-403, CCS-404, CCS-405 |
General Relativity – II |
1. able to solve Einstein field equations under spherical symmetry.
2.understand calculating relativistic frequency shifts for the bending of light passing a spherical mass distribution. 3.understand energy moment tensor, stress energy moment tensor for perfect fluid.
4. understand exterior product, derivative and Pforms.
5. calculate Bianchi identities in tetrad form. |
CCS-403, CCS-404, CCS-405 |
Commutative Algebra |
1. understand Artirian and Noetherion modules.
2. study The Krull-Schmidt theorem.
3. know projective modules for further development in modules.
4. apply integral extensions for going up and going down theorem.
5. derive prime decomposition theorem. |
CCS-403, CCS-404, CCS-405 |
Fractional Differential Equations |
1. analyze existence and uniqueness of solution of fractional differential equations.
2. apply Mittag-Leffler functions to derive the solution of fractional differential equations.
3. analyse data dependency of solution of fractional differential equations.
4. examine the properties of solution of fractional differential equations with initial boundary conditions.
5. derive stability results for fractional differential equations. |
