MTech Mathematical Foundations Of Computer Science syllabus for 1 Sem 2020 scheme 20SCE11

Module-1 Vector Spaces 0 hours

Vector Spaces:

Vector spaces; subspaces Linearly independent and dependent vectors Basis and dimension; coordinate vectors-Illustrative examples. Linear transformations, Representation of transformations by matrices;

Module-2 Orthogonality and least squares 0 hours

Orthogonality and least squares:

Inner product, orthogonal sets, orthogonal projections, orthogonal bases. Gram-Schmidt orthogonalization process. QR factorizations of a matrices, least square problems, applications to linear models (least square lines and least square fitting of other curves).

A d v e r t i s e m e n t
Module-3 Symmetric and Quadratic Forms 0 hours

Symmetric and Quadratic Forms:

Diagonalization, Quadratic forms, Constrained Optimization, The Singular value decomposition. Applications to image processing and statistics, Principal Component Analysis

Module-4 Statistical Inference 0 hours

Statistical Inference:

Introduction to multivariate statistical models: Correlation and Regression analysis, Curve fitting (Linear and Non-linear)

Module-5 ProbabilityTheory 0 hours

ProbabilityTheory:

Random variable (discrete and continuous), Probability mass function (pmf), Probability density function (pdf), Mathematical expectation, Sampling theory: testing of hypothesis by ttest, 𝜒2  - test.

 

Course Outcomes:

On completion of this course, students are able to:

1. Understand the numerical methods to solve and find the roots of the equations.

2. Apply the technique of singular value decomposition for data compression, least square approximation in solving inconsistent linear systems

3. Understand vector spaces and related topics arising in magnification and rotation of images.

4. Utilize the statistical tools in multi variable distributions.

5. Use probability formulations for new predictions with discrete and continuous RV’s.

 

Question Paper Pattern:

  • The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.
  • The question paper will have ten full questions carrying equal marks.
  • Each full question consisting of 20 marks.
  • There will be two full questions (with a maximum of four sub questions) from each module.
  • Each full question will have sub question covering all the topics under a module.
  • The students will have to answer five full questions, selecting one full question from each module.

 

Textbooks:

1 Linear Algebra and its Applications David C. Lay, Steven R. Lay and J. J. McDonald Pearson Education Ltd 5 th Edition 2015.

2 Numerical methods for Scientific and Engg. Computation M K Jain, S.R.K Iyengar, R K. Jain New Age International 6 th Ed., 2014

3 Probability, Statistics and Random Process T. Veerarajan Tata Mc-Graw Hill Co 3 rd Edition 2016

 

Reference books:

1 Optimization: Theory & Applications Techniques Rao. S.S Wiley Eastern Ltd New Delhi.

2 Signals, Systems, and Inference Alan V. Oppenheim and George C. Verghese Spring 2010.

3 Foundation Mathematics for Computer Science John Vince Springer International

4 Higher Engineering Mathematics B.S. Grewal Khanna Publishers 44th Ed.,2017

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