--- Programme Specific Outcomes ---

B.Sc Mathematics

  • Be able to explain the core ideas and techniques of Mathematics at the college level
  • Be able to recognize the power of abstraction and generalization
  • Be able for analytical, abstract and structured thinking in the programme with proficiency in problem solving
  • Be able to understand the basic rules of logic, roles of axioms or assumptions
  • Be able for the immediate participation in the workforce

M.Sc Mathematics

  • Be able to develop the mathematical skills and knowledge for their intrinsic beauty, for proficiency in analytical reasoning, utility in modelling and solving the real world problems
  • Be able to carry out investigate mathematical work with independent judgement.
  • Be able to develop analytical and logical thinking and the habit of making conclusions based on quantitative information.
  • Be able to communicate and interact effectively with different audiences, thus developing their ability to collaborate intellectually and creatively in diverse contexts
  • Be able to recognize real world problems that are amenable to mathematical analysis and formulate mathematical models of such problems

Course Outcomes:

B.Sc Mathematics

MAT 1B 01: Foundations of Mathematics

  • Introduce the idea of formalising arguments, both semantically and syntactically and the fundamental connection between these approaches
  • Be able to interpret formulas and sentences of predicate logic in mathematical structures and apply the compactness theorem in simple cases.
  • Promotes the knowledge of expressive power offormal systemsand thedeductivepower of formalproofsystems
  • Describe the role and importance of proof in mathematics, as well as the concept of the assumptions in the proof

MAT 2B 02: Calculus

  • Describe limit, continuity and derivative both algebraically and graphically
  • Describe limits with indeterminate forms using L'hospital's rule
  • Describe the application of differentiation to find linear approximation, extrema, monotonicity, and concavity of functions, to sketch the graph of some functions
  • Describe the applications of integration for finding the area between the curves, length of the curve, area of surface of revolution, volumes of solids of revolution etc

MAT 2B 02: Calculus And Analytic Geometry

  • Describe the study of logarithmic and exponential functions, Hyperbolic and inverse Hyperbolic functions both algebraically and graphically
M.Sc MATHEMATICS
MT 1C 01 – ALGEBRA I
  • Provides a sensitive instrument for investigating symmetry which is very much elemental phenomena of the real world.
  • Present the relationships between abstract algebraic structures with familiar numbers systems such as the integers and real numbers.
  • Present concepts of and the relationships between operations satisfying various properties (e.g. commutative property).
  • Present concepts and properties of various algebraic structures.
  • Discuss the importance of algebraic properties relative to working within various number systems.
  • Develop the ability to form and evaluate conjectures.

MT 1C 02 LINEAR ALGEBRA

  • Develop the ability to manipulate matrices and to do matrix algebra.
  • Develop the ability to solve systems of linear equations.
  • Develop the ability to work within vector spaces and to distil vector space properties and to manipulate linear transformations and to distil mapping properties
  • Develop the notion of eigenvalues and eigenvectors with the applications to the real world.

MT 1C 03 REAL ANALYSIS I

  • Describe fundamental properties of the real numbers that lead to the formal development of real analysis.
  • Comprehend rigorous arguments developing the theory underpinningreal analysis
  • Demonstrate an understanding of limits and how they are used in sequences, series, differentiation and integration
  • Construct rigorous mathematical proofs of basic results in real analysis
  • Describe how abstract ideasand rigorous methods like continuity, uniform continuity and differentiation in mathematical analysis can be applied to important practical problems.

MT 1C 04 NUMBER THEORY

  • Described the concepts and results of Number Theory using axioms, definitions, examples,

theorems and their proofs.

  • Described mathematical proofs of statements and find counterexamples to false statements

in Number Theory.

  • Developed the knowledge of logic and methods behind the major proofs in Number Theory

to solve challenging problems in Number Theory.

  • The course also focuses towards the introduction of network security using various

cryptographic algorithms and understanding network security applications. It also focuses

on the practical applications that have been implemented and are in use to provide email and

web security

MT 1C 05 DISCRETE MATHEMATICS

  • Introduces graph and tree, basic graph algorithms and concepts of treeband the applications of graphs and trees.
  • Described the applications of Boolean algebra and Lattices
  • Explained the different concepts in automata theory and formal languages such as formal proofs, (non-)deterministic automata, regular expressions, regular languages, Explained the power and the limitations of regular languages and context-free languages.
  • Designed automata, regular expressions and context-free grammars accepting or

generating a certain language;

  • Described the language accepted by an automata or generated by a regular expression or

a context-free grammar and to transform between equivalent deterministic and non-

deterministic finite automata, and regular expressions;

MT 2C 07 – ALGEBRA II

  • Described Rings , Fields and Integral Domain in detail and Rings of Polynomials.
  • Described the Galois theory to generalize to polynomials of higher degree the well-known

formula for the roots of a quadratic polynomial and the impossibility of a quantic or higher

polynomials

  • Described the symmetries of a regular n-gon.
  • Explained ruler-and-compass constructions; for instance, we determine all natural numbers n for which the regular n-gon can be constructed

MT 2C 08 - REAL ANALYSIS II

  • Described the limitations of ReimannIntegral , for instance in Fourier Analysis and in the theory of Differential Equations.
  • Described the origin of concept of Measure theory, which has applications in not in analysis alone, but also in the theory of probability.
  • Explained the physical interpretations and applications of Lebesgue outer measure, concept of the almost every where[a.e], measurable functions, integration of measurable functions over measurable sets etc.
  • Described general measure spaces Fubini and Tonelli’s theorems , the Radon- Nikodym theorems and The Riesz Representation theorem

MT 2C 09 – TOPOLOGY

  • Introduced the abstract analytic structures and applications concepts of open and closed sets abstractly, not necessarily only the real line approach.
  • Introduced how to generate new topologies from a given set with bases.
  • Described an understanding of what constitutes a rigorous mathematical argument and how to use reasoning effectively to solve problems.
  • The material lies at the heart of many developments in modern mathematics and provides a perfect example of the breadth and unity of mathematics.

MT 2C -10 ODE AND CALCULUS OF VARIATIONS

  • Explained the power series solutions for second order differential equations with regular singular point and irregular singular point.
  • Explained some special functions of Mathematics Physics
  • Described the method of solving the system of differential equations and also solving special types of non linear equations.
  • Described the Oscillation theory of boundary value problems and the theory of existence and uniqueness of solutions of differential equations.
  • Explained the first and the second variations, conjugate points, generalizations for a vector function, higher order problems, relative maxima and minima and isoperimeterical problems, integrals with variable end points, geodesics, minimal surfaces and their applications in mechanics and optics.

MT 2C 11 OPERATIONS RESEARCH

  • Described the linear optimisation problems involving both continuous and integer variable
  • Explained techniques for optimisation and how to use these techniques on real problems, for example, minimising cost, maximising production capacity, or minimising risk.
  • Described formulation of a linear programming; the Simplex Method; duality and complementary slackness; sensitivity analysis; primal-dual approaches; brand-and-bound
  • Examples will be presented from important application areas, such as the emergency services, telecommunications, transportation, and manufacturing.
  • Described the potential or proven relevance ofgame theoryand its impact in many fields of human endeavour which involve conflict of interest between two or more participants..

MT 3C 12 – COMPLEX ANALYSIS