Mathematical Foundation for Computer Science

omputer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems.[1] See glossary of computer science.

Computer science is the art of solving problems with computers. This is a broad definition that encompasses an equally broad field. Within computer science, we find software engineering, bioinformatics, cryptography, machine learning, human-computer interaction, graphics, and a host of other fields. Mathematics underpins all of these endeavors in computer science. We use graphs to model complex problems, and exploit their mathematical properties to solve them. As We use recursion to break down seemingly insurmountable problems into smaller and more manageable problems. We use topology, linear algebra, and geometry in 3D graphics.

ts fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory (which explores the fundamental properties of computational and intractable problems), are highly abstract, while fields such as computer graphics emphasize real-world visual applications. Other fields still focus on challenges in implementing computation. For example, programming language theory considers various approaches to the description of computation, while the study of computer programming itself investigates various aspects of the use of programming language and complex systems. Humanâ€“computer interaction considers the challenges in making computers and computations useful, usable, and universally accessible to humans.

Course Detail

Course Detail

Syllabus for Internal Examination

**Graph Theory:**Isomorphism, Planar graphs, graph colouring, hamilton circuits and euler cycles. Permutations and Combinations with and without repetition. Specialized techniques to solve combinatorial enumeration problems**Statistics:**Probability mass, density, and cumulative distribution functions, Parametric families of distributions, Expected value, variance, conditional expectation, Applications of the univariate and multivariate Central Limit Theorem, Probabilistic inequalities, Markov chains**Models:**Statistical inference, Introduction to multivariate statistical models: regression and classification problems, principal components analysis, The problem of overfitting model assessment

Video Tutorials

- Video Course by IIT Madras
- Video Lecture Series on Graphy Theory
- Video Lectures on Coursera
- Principal Component Analysis

Web Resources