View
0
Download
0
Category
Preview:
Citation preview
ST PETER’S COLLEGE KOLENCHERY ERNAKULAM
DEPARTMENT OF MATHEMATICS
PROGRAMME - M.Sc. Mathematics
M.Sc. Mathematics- Mahatma Gandhi University, Kottayam, Kerala
Programme Outcome
PO1 Critical Thinking
PO2 Environment and Sustainability
PO3 Self-directed and Life-long learning
PO4 Computational Thinking
PO5 Problem Solving
PO6 Research Orientation
Programme Specific Outcome (PSO)
PSO 1 Provide high quality education in higher mathematics committed to
excellence in research
PSO 2 Develop the skills in objectivity, creativity, independent thinking and
analyzing
PSO 3 Abstract the core concept of modern mathematics
PSO 4 Think critically the mathematical concepts and clearly communicate
solutions to real-world problems
PROGRAMME - STRUCTURE
SEMESTER I
Course No Name of Course Credit Total
Credits/Semester
MT01C01 Linear Algebra 4
20
MT01C02 Basic Topology 4
MT01C03 Measure Theory and Integration 4
MT01C04 Graph Theory 4
MT01C05 Complex Analysis 4
SEMESTER II
Course No Name of Course Credit Total
Credits/Semester
MT02C06 Abstract Algebra 4
20
MT02C07 Advanced Topology 4
MT02C08 MT02C08 -Advanced Complex Analysis 4
MT02C09 MT02C09 -Partial Differential Equations 4
MT02C10 MT02C10 -Real Analysis 4
SEMESTER III
Course No Name of Course Credit Total
Credits/Semester
MT03C11
Multivariate Calculus and Integral
Transforms
4
20
MT03C12 Functional Analysis 4
MT03C13 Differential Geometry 4
MT03C14 Number Theory and Cryptography 4
MT03C15 Optimization Techniques 4
SEMESTER IV
Course No Name of Course Credit Total
Credits/Semester
MT04C16 Spectral Theory 3
20
MT04E01 Analytic Number Theory 3
MT04E05 Mathematical Economics 3
MT04E06 Mathematics for Computing 3
MT04E07 Operations Research 3
Project (PP) 3
Viva-voce (PV) 2
COURSE OUTCOME (CO)
Name of Course: MT01C01: LINEAR ALGEBRA
Credits given: 4
CO No. CO Statement
CO1 Understand the basic concepts of linear transformation, its algebra, null space
and range. Determinants and its properties, characteristic values,
diagonalization of linear transformations
CO2 Identify a linear transformation by a matrix
CO3 Relate matrices of linear transformations with respect to different bases
CO4 Analyze determinant function and its properties
CO5 Determine characteristic values and characteristic vectors
CO6 Understand the basic theory of simultaneous triangulations and
diagonalizations, direct sum decompositions and invariant direct sums
CO7 Realize how linear algebra uses and unifies ideas for functional analysis, the
spectral theory.
Name of Course: MT01C02: BASIC TOPOLOGY
Credits given: 4
CO No. CO Statement
CO1 Understand the transition from metric spaces to topological spaces
CO2 Examine whether a given family of subsets is a topology or not
CO3 Develop basic concepts in metric spaces to topological spaces
CO4 Explain smallness conditions defined in topological spaces
CO5 Distinguish between connected and disconnected spaces
CO6 Discuss the concepts of local connectedness and path connectedness
CO7 Analyze hierarchy of separation axioms
Name of Course: MT01C03: MEASURE THEORY AND INTEGRATION
Credits given: 4
CO No. CO Statement
CO1 Recall algebra of sets, open and closed sets of real numbers
CO2 Analyze Lebesgue measure, measure space and measurable functions
CO3 Define Riemann integral and Lebesgue integral
CO4 Explain differentiation of monotone functions and its applications
CO5 Apply signed measure to related theorems
CO6 Understand convergence in measure
CO7 Analyze the theorems related to measurability in product spaces
Name of Course: MT01C04 : GRAPH THEORY
Credits given: 4
CO No. CO Statement
CO1 Explain the basic concepts of graph theory
CO2 Identify induced subgraphs, cliques, vertex cuts, edge cuts, connectivity,
spanning trees, independent sets and covers in graphs
CO3 Model real world problems using graph theory
CO4 Determine whether graphs are Hamiltonian and/or Eulerian
CO5 Discuss problems involving vertex and edge colouring
CO6 Solve problems involving vertex and edge connectivity and Planarity
Name of Course: MT01C05 : COMPLEX ANALYSIS
Credits given: 4
CO No. CO Statement
CO1 Explain the fundamental concepts of complex analysis and their role in
modern mathematics
CO2 Find parametrizations of curves and compute line integrals
CO3 Utilze the residue theorem to compute several kinds of real integrals
CO4 Explain Cauchy’s theorem for a rectangle and a disk
CO5 Discuss local properties of analytic functions
CO6 Construct conformal mappings between many kinds of domain
Name of Course: MT01C06: ABSTRACT ALGEBRA
Credits given: 4
CO No. CO Statement
CO1 Apply the fundamental theorem of finitely generated abelian groups
CO2 Determine zeros of polynomials
CO3 Analyze extensions of fields
CO4 Make use of Sylow’s theorem to find the properties of subgroups of a finite
group
CO5 Understand the concepts of isomorphisms and automorphisms of fields
CO6 Understand the basics of Galois theory
C07 Develop rigorous proofs for theorems arising in the context of abstract
Algebra
Name of Course: MT02C07: ADVANCED TOPOLOGY
Credits given: 4
CO No. CO Statement
CO1 Understand the significance of the classic theorems characterising normality
CO2 Define topology on the product of an arbitrary collection of topological
spaces
CO3 Identify whether a given topological property is productive
CO4 Explain the concept of evaluation functions and embedding lemma
CO5 Apply the concept of nets to study various notions in topology
CO6 Discuss variations of compactness
C07 Construct one-point compactification of given space.
Name of Course: MT02C08: ADVANCED COMPLEX ANALYSIS
Credits given: 4
CO No. CO Statement
CO1 Illustrate the concept of power series
CO2 Explain infinite products and canonical products
CO3 Distinguish between harmonic and subharmonic functions
CO4 Analyze elliptic functions
CO5 Decide when and where a given function is analytic and be able to find it
series development
CO6 Discuss the main ideas in the proof of the Riemann mapping theorem
Name of Course: MT02C09: PARTIAL DIFFERENTIAL EQUATIONS
Credits given: 4
CO No. CO Statement
CO1 Recall basic properties of the partial differential equations
CO2 Apply the techniques to find solutions of the partial differential equations
CO3 Solve linear and nonlinear partial differential equations of both first and
second order
CO4 Classify partial differential equations and apply analytical methods to solve
the equations
CO5 Analyze the existence and uniqueness of solutions of partial differential
equations
CO6 Create an ability to model physical phenomena using partial differential
equations
Name of Course: MT02C10: REAL ANALYSIS
Credits given: 4
CO No. CO Statement
CO1 Remember monotone functions and explore the properties
CO2 Understand bounded variation and total variation
CO3 Explain curves, paths and arc length
CO4 Develop the idea of Riemann Integral to Riemann Stieltjes Integral
CO5 Analyze the relation between uniform convergence and continuity
CO6 Construct power series of logarithmic and exponential functions
C07 Discuss Fourier series expansions of functions
Name of Course: MT02C11: MULTIVARIATE CALCULUS AND INTEGRAL
TRANSFORMS
Credits given: 4
CO No. CO Statement
CO1 Understand Weirstrass approximation theorem
CO2 Explain other forms of Fourier series
CO3 Make use of Fourier integral Theorem to find definite integrals
CO4 Develop the relation between beta and gamma functions using convolution
theorem
CO5 Evaluate extremum problems
CO6 Discuss multivariable differential calculus
Name of Course: MT03C12: FUNCTIONAL ANALYSIS
Credits given: 4
CO No. CO Statement
CO1 Make use of basic concepts of normed and inner product spaces
CO2 Understand the basic theory of bounded linear operators
CO3 Identify the role of Zorn's lemma
CO4 Apply the theory of Hilbert spaces to other areas including Fourier series
CO5 Analyze uniform boundedness principle
CO6 Discuss Hahn-Banach theorem
Name of Course: MT03C13: DIFFERENTIAL GEOMETRY
Credits given: 4
CO No. CO Statement
CO1 Define graphs, level sets, vector fields, surfaces and orientation
CO2 Explain Gauss Map
CO3 Understand geodesics and parallel transport
CO4 Determine Weingarten Map
CO5 Evaluate curvature of plane curves and higher surfaces
CO6 Utilize line integrals to find length of connected plain curves
Name of Course: MT03C14: NUMBER THEORY AND CRYPTOGRAPHY
Credits given: 4
CO No. CO Statement
CO1 Understand the basic concepts of number theory and cryptography
CO2 Explain the significance of time estimate
CO3 Make use of properties of congruence to compute solutions of problems
CO4 Solve the problems related to factoring
CO5 Evaluate discrete log using Silver Pohlig Hellman algorithm
CO6 Determine whether a given number is prime or not
Name of Course: MT03C15: OPTIMIZATION TECHNIQUES
Credits given: 4
CO No. CO Statement
CO1 Recall basic concepts of general programming and Integer programming
problem
CO2 Classify the programming problems and its importance
CO3 Discuss the importance of sensitivity analysis in programming problems
CO4 Understand the use of minimum path, maximum flow and maximum potential
difference in a network
CO5 Make use of game theory in competitive games
CO6 Understand methods in non linear programming problem and its applications
Name of Course: MT04C16: SPECTRAL THEORY
Credits given: 3
CO No. CO Statement
CO1 Extend basic concepts of convergence of elements to operators and
functionals
CO2 Understand open mapping theorem and closed graph theorem
CO3 Explain fundamentals of spectral theory of operators
CO4 Identify self adjoint operators
CO5 Analyze the theory of compact linear operators and their spectrum
CO6 Discuss basic theory of Banach algebras and unbounded operator theory
Name of Course: MT04E01: ANALYTIC NUMBER THEORY
Credits given: 3
CO No. CO Statement
CO1 Analyze arithmetical functions
CO2 Understand formal power series
CO3 Apply Euler’s summation formula
CO4 Discuss elementary theorems on the distribution of prime numbers
CO5 Apply congruences to prove Lagrange’s theorem and Euler-Fermat theorem
CO6 Understand primitive roots and partitions of a positive integer
Name of Course: MT04E05: MATHEMATICAL ECONOMICS
Credits given: 3
CO No. CO Statement
CO1 Understand the theory of consumer behavior
CO2 Analyze production function
CO3 Determine economic region of production
CO4 Apply input output analysis
CO5 Classify difference equations
CO6 Apply difference equations in economic models
Name of Course: MT04E06: COMPUTING FOR MATHEMATICS
Credits given: 3
CO No. CO Statement
CO1 Understand the basic concepts of object oriented programming
CO2 Make use of tokens to write programs in C++
CO3 Apply constructors, destructors and operator overloading in C++
programming
CO4 Analyze inheritance in C++ programming
CO5 Build formatted I/O operations
CO6 Develop a document using Latex
Name of Course: MT04E07: OPERATIONS RESEARCH
Credits given: 3
CO No. CO Statement
CO1 Understand the concepts of inventory modelling
CO2 Measure total expected cost in inventory models
CO3 Identify queuing models and their uses
CO4 Estimate measures of performance in queuing models
CO5 Discover the technique of dynamic programming to solve practical problems
CO6 Evaluate optimal sequences in sequencing problems
CO7 Develop simulation methods to solve real life situations
Recommended