Course outcomes
M.A/M.Sc. (Mathematics)
Teaching Pattern for Semester I, II, III and IV

Four lectures per week per course. Each lecture is of 60 minutes duration.

In addition, there shall be tutorials, seminars as necessary for each of the five courses.
SemesterIV
PSMT401 / PAMT401: ALGEBRA IV
Course Outcomes:

Students will learn about algebraic extensions and their properties.

Splitting fields and their degrees can be computed. The notion of normal extension is
introduced and its equivalent properties are discussed.

Finite fields as splitting fields are visualized and notion of algebraic closure is discussed
in detail.

Galois extensions are studied and the fundamental theorem of Galois theory is established.

Cyclotomic extensions are studied in detail and order of its Galois group is computed.

Examples of fixed fields, field automorphisms and fundamental theorem are studied in
special cases.
PSMT402 / PAMT402: Fourier Analysis
Course Outcomes:

Students will be able to understand the Fourier series expansion of a periodic function
and their convergence.

Students will be able to grasp properties of the Dirichlet kernel, Fejer kernel, Poisson
kernel and the concept of a good kernel.

Students will aware about application of a Fourier series in the solution of the Dirichlet
problem and heat equation.
PSMT 403/PAMT 403: Calculus on Manifolds
Course Outcomes:

Students will be able to grasp the concept of tensor, alternating tensor, wedge product
and differential forms.

Students will be able to understand fields and forms on manifolds.

Students will be able to understand the application of Classical theorems: Stoke’s
theorem, Green’s theorem, Gauss divergence theorem.
Skill Course
Skill Course I: Business Statistics
Course Outcomes: Students should know the following:

Classification of Data: Requisites of Ideal Classification, Basis of Classification.

Organizing Data Using Data Array: Frequency Distribution, Methods of Data Classification, Bivariate Frequency Distribution, Types of Frequency Distributions.

Tabulation of Data: Objectives of Tabulation, Parts of a Table, Types of Tables,
General and Summary Tables, Original and Derived Tables.

Graphical Presentation of Data: Functions of a Graph, Advantages and Limitations
of Diagrams(Graph), General Rules for Drawing Diagrams.

Types of Diagrams: OneDimensional Diagrams, TwoDimensional Diagrams, Three
Dimensional Diagrams, Pictograms or Ideographs, Cartograms or Statistical Maps.

Exploratory Data Analysis: StemandLeaf Displays.

Objectives of Averaging, Requisites of a Measure of Central Tendency, Measures of
Central Tendency.

Mathematical Averages: Arithmetic Mean of Ungrouped Data, Arithmetic Mean of
Grouped (Or Classified) Data, Some Special Types of Problems and Their Solutions,
Advantages and Disadvantages of Arithmetic Mean, Weighted Arithmetic Mean.

Geometric Mean: Combined Geometric Mean, Weighted Geometric Mean, Advan
tages, Disadvantages and Applications of G.m.

Harmonic Mean: Advantages, Disadvantages and Applications of H.M. Relationship
Between A.M., G.M. and H.M.

Averages of Position: Median, Advantages, Disadvantages and Applications of Median.

Partition Values quartiles, Deciles and Percentiles: Graphical Method for Calculating
Partition Values.

Mode: Graphical Method for Calculating Mode Value. Advantages and Disadvantages
of Mode Value.

Relationship Between Mean, Median and Mode, Comparison Between Measures of
Central Tendency.

Significance of Measuring Dispersion (Variation):Essential Requisites for a Measure of
Variation.

Classification of Measures of Dispersion.

Distance Measures: Range, Interquartile Range or Deviation.

Average Deviation Measures: Mean Absolute Deviation, Variance and Standard Deviation.

Mathematical Properties of Standard Deviation, Chebyshev’s Theorem, Coefficient of
Variation.

Measures of Skewness: Relative Measures of Skewness.

Moments: Moments About Mean, Moments About Arbitrary Point, Moments About
Zero or Origin, Relationship Between Central Moments and Moments About Any
Arbitrary Point, Moments in Standard Units, Sheppard’s Corrections for Moments.

Kurtosis: Measures of Kurtosis.
Skill Course II: Statistical Methods
Course Outcomes:Students should know the following:

Measures of central tendencies: Mean, Median, Mode.

Measures of Dispersion: Range, Mean deviation, Standard deviation. Measures of
skewness. Measures of relationship: Covariance, Karl Pearson’s coefficient of Correlation, Rank Correlation. Basics of Probability.

Sampling Distribution, Student’s tDistribution, Chisquare (χ^{2}) Distribution, Snedecor’s
FDistribution. Standard Error. Central Limit theorem. Type I and Type II Errors,
Critical Regions. Ftest, ttest, χ^{2} test, goodness of Fit test.

The Anova Technique. The basic Principle of Anova. One Way ANOVA, Two Way
ANOVA. Latin square design. Analysis of Covariance.

R as Statistical software and language, methods of Data input, Data accessing, usefull
builtin functions, Graphics with R, Saving, storing and retrieving work.
Skill Course III: Computer Science
Course Outcomes:Students should know the following:

Basics of object oriented programming principles, templates, reference operators NEW
and delete in C++, the java innovation which avoids use of delete, classes polymorphism friend functions, inheritance, multiple inheritance operator overloading basics

Basic algorithms, selection sort, quick sort, heap sort, priory queses, radix sort, merge
sort, dynamic programming, app pairs, shortest paths, image compression, topological
sorting, single source shortest paths reference, hashing intuitive evaluation of running
time.

Stacks queues, linked lists implementation and simple applications, trees implementa
tion and tree traversal ( stress on binary trees).

Concept of relational databases , normal forms BCNF and third normal forms. Arm
strongs axioms. Relational algebra and operations in it.
Skill Course IV: Linear and Nonlinear Programming
Course Outcomes:

Understand the concept of an objective function, a feasible region, and a solution
set of an optimization problem.

Understand the broad classification of optimization problems, and where they arise
in simple applications.

Use the simplex method to find an optimal vector for the standard linear program
ming problem and the corresponding dual problem.

Use Lagrange multipliers to solve nonlinear optimization problems.

Write down and apply KuhnTucker conditions for constrained nonlinear optimiza
tion problems.

Apply approximate methods for constraint problems.

Understand the importance of convexity in nonlinear optimization problems.

Apply basic line search methods to onedimensional optimization problems, gradient
methods to optimization problems, ,conjugate gradient methods to optimization
problems.
Skill Course V: Computational Algebra
Course Outcomes:

Students will learn to balance between theory and practicals via the use of computers.

Previously learnt concepts can be strengthened by allowing them to explore topics
using the mathematical softwares.