M Sc Mathematics-Course-outcomes-19.09.2024
19/09/2024 2024-09-20 15:39M Sc Mathematics-Course-outcomes-19.09.2024
Course Outcomes - M Sc Mathematics
I year – I Semester
- CLO 1: Recall basic counting principle, define class equations to solve problems, explain Sylow’s theorems and apply the theorem to find number of Sylow subgroups
- CLO 2: Define Solvable groups, define direct products, examine the properties of finite abelian groups, define modules
- CLO 3: Define similar Transformations, define invariant subspace, explore the properties of triangular matrix,to find the index of nilpotence to decompose a space into invariant subspaces, to find invariants of linear transformation, to explore the properties of nilpotent transformation relating nilpotence with invariants.
- CLO 4: Define Jordan,canonical form, Jordan blocks, define rational canonical form, define companion matrix of polynomial, find the elementary devices of transformation, apply the concepts to find characteristic polynomial of linear transformation.
- CLO 5: Define trace, define transpose of a matrix,explain the properties of trace and transpose, to find trace, to find transpose of matrix,to prove Jacobson lemma using the triangular form, define symmetric matrix, skew symmetric matrix, adjoint,to define Hermitian, unitary, normal transformations andto verify whether the transformation in Hermitian, unitary and normal
- CLO1:Analyze and evaluate functions of bounded variation and Rectifiable Curves.
- CLO2:Describe the concept of Riemann-Stieltjes integral and its properties.
- CLO3:Demonstrate the concept of step function, upper function, Lebesgue function and their integrals.
- CLO4:Construct various mathematical proofs using the properties of Lebesgue integrals and establish the Levi monotone convergence theorem.
- CLO5: Formulate the concept and properties of inner products, norms and measurable functions.
- CLO1:Establish the qualitative behavior of solutions of systems of differential equations .
- CLO2:Recognize the physical phenomena modeled by differential equations and dynamical systems.
- CLO3: Analyze solutions using appropriate methods and give examples.
- CLO4:Formulate Green’s function for boundary value problems.
- CLO5:Understand and use various theoretical ideas and results that underlie the mathematics in this course.
I year – II Semester
- CLO1: Prove theorems applying algebraic ways of thinking.
- CLO2: Connect groups with graphs and understanding about Hamiltonian graphs.
- CLO3: Compose clear and accurate proofs using the concepts of Galois Theory.
- CLO4: Bring out insight into Abstract Algebra with focus on axiomatic theories.
- CLO5: Demonstrate knowledge and understanding of fundamental concepts including extension.
- CLO1: Understand and describe the basic concepts of Fourier series and Fourier integrals with respect to orthogonal system.
- CLO2: Analyze the representation and convergence problems of Fourier series.
- CLO3: Analyze and evaluate the difference between transforms of various functions.
- CLO4: Formulate and evaluate complex contour integrals directly and by the fundamental theorem.
- CLO5: Apply the Cauchy integral theorem in its various versions to compute contour integration.
- CLO1: To understand and classify second order equations and find general solutions.
- CLO2: To analyse and solve wave equations in different polar coordinates.
- CLO3: To solve Vibrating string problem, Heat conduction problem, to identify and solve Laplace and beam equations.
- CLO4: To apply maximum and minimum principle’s and solve Dirichlet, Neumann problems for various boundary conditions.
- CLO5: To apply Green’s function and solve Dirichlet, Laplace problems, to apply Helmholtz operation and to solve Higher dimensional problem
II year – III Semester
- CLO1:Analyze and evaluate local properties of analytical functions and definite integrals.
- CLO2:Describe the concept of definite integral and harmonic functions.
- CLO3:Demonstrate the concept of the general form of Cauchy’s theorem.
- CLO4: Prove Riemann Mapping theorem and Harnack Principle.
- CLO5:The Monodromy Theorem – Branch points.
- CLO1: Demonstrate the knowledge of core principles in mechanics.
- CLO2:Interpret and consider complex problems of classical dynamics in a systematic way.
- CLO3:Apply the variation principle for real physical situations.
- CLO4:Explore different applications of these concepts in the mechanical and electromagnetic fields.
- CLO5:Describe and apply the concept of Angular momentum, Kinetic energy and Moment of inertia of a particle.
- CLO1:Define and illustrate the concept of topological spaces and the basic definitions of open sets, neighbourhood, interior, exterior, closure and their axioms for defining topological space.
- CLO2:Understand continuity, compactness, connectedness, homeomorphism and topological properties.
- CLO3:Analyze and apply the topological concepts in Functional Analysis.
- CLO4:Ability to determine that a given point in a topological space is either a limit point or not for a given subset of a topological space.
- CLO5:Develop qualitative tools to characterize connectedness, compactness, second countable, Hausdorff and develop tools to identify when two are equivalent(homeomorphic)
- CLO1: Demonstrate the knowledge of core principles in Statistics.
- CLO2:Interpret and consider complex problems of statistics in a systematic way.
- CLO3:Apply the variation principle for real physical situations.
- CLO4:Explore different applications of these concepts in the Statistical fields.
- CLO5:Describe and apply the concept of estimation, distribution and TPM.
II year – IV Semester
- CLO1: Explain space curves, Curves between surfaces, metrics on a surface, fundamental form of a surface and Geodesics.
- CLO2: Evaluate these concepts with related examples.
- CLO3:Compose problems on geodesics.
- CLO4:Recognize applicability of developable. CLO5:Construct and analyze the problems on curvature and minimal surfaces.
- CLO1:Understand the Banach spaces and Transformations on Banach Spaces.
- CLO2:Prove Hahn Banach theorem and open mapping theorem.
- CLO3:Describe operators and fundamental theorems.
- CLO4:Validate orthogonal and orthonormal sets.
- CLO5:Analyze and establish the regular and singular elements.
- CO1 Construct frequency tables and graphical representation of data
- CO2 Summarize the whole set of data with a single value that represents the center of its distribution.
- CO3 Interpret the relationship between two variables using correlation coefficient.
- CO4 Make use of specified analysis tools for decision making in business
- CO1 Paraphrase the characteristics of Management information system.
- CO2 Describe the elements and characteristics of system
- CO3 Enumerate the application of information system in business
- CO4 Explain the database management system
- CO5 Elaborate the functional management information system in financial, accounting, marketing and production
- CO1. On the successful completion of the course, the students will be able to: Analyse and evaluate the investment purposes, the efficiency of key stages of the investment process.
- CO2. Calculate the risk and expected return of various financial instruments and investment portfolios.
- CO3. Implement in practice the quantitative methods of investment decision making; apply the principles of portfolio theory in the process of investment portfolio management
- CO4. Explain the various mutual fund scheme and systematic investment plans under SEBI guidelines
- CO5. Elaborate the concepts of portfolio management, selection, and construction
