Mathematics for Computing

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People today say that subjects like mathematics are of no use in real life. Friend request suggestions on facebook, the google maps that you rely on, the suggested products for you on all the online shopping sites; are all the result of data and analytics.

Course content

Now, thinking about the innumerable uses of the subject, it would be easier for you to estimate the growing demand in the coming future. Covering the major areas in demand today, this course is of utmost value to the aspiring engineers.

The course provides students with comprehensive theoretical knowledge and also practical training in computer science, numerical computing and mathematical finance. This programme has been introduced due to the need for sophisticated mathematics for modern scientific investigations and technological developments.

Bibliographic Information

The curriculum is designed to provide students with in depth theoretical background and practical training in computer science, numerical computing and mathematical finance. Indian Institute of Technology defines the course as a unique programme and the first of its kind in the country. The curriculum for this program is designed to meet the need of sophisticated mathematics in modern scientific investigations and technological innovations.

The programme has three components: mathematics, computing and financial engineering which are perfectly blended so that the strong mathematical and analytical components that are in-built in the curriculum form the basis on which the technological aspects of computing and finance are developed. Consequently, the programme, which is run by a team of committed faculty as instructors, produces a group of students with multiple skills in mathematics, computer science and financial engineering.

Introductory Discrete Mathematics for Computer Science

The course is 4-year programme, referred to as B. Tech in Mathematics and Computing. Prerequisites VCE Specialist Mathematics or Mathematical Methods units 3 and 4 with a study score of at least 25 or Further maths with a study score of at least At the completion of this unit, students should be able to: identify basic methods of proof, particularly induction, and apply them to solve problems in mathematics and computer science; manipulate sets, relations, functions and their associated concepts, and apply these to solve problems in mathematics and computer science; use and analyse simple first and second order recurrence relations; use trees and graphs to solve problems in computer science; apply counting principles in combinatorics; describe the principles of elementary probability theory, evaluate conditional probabilities and use Bayes' Theorem.

Minimum total expected workload equals 12 hours per week comprising: Contact hours for on-campus students: Three hours of lectures One 90 minute tutorial Additional requirements all students : A minimum of 7. See also Unit timetable information.

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One may wonder whether physical quantities are discrete or continuous. Calculus has certainly helped to model all kinds of physical phenomena, but when digging deep enough, we are confronted with quantum physical aspects that show a more discrete character of nature.

When looking at a large scale, then it is generally assumed that our universe is immense but finite. So we might consider the physical world to be a finite and discrete system.

Mathematics for Computing - Department of Computer Science and Information Systems

Digital computers are also by definition finite and discrete, but at a much smaller scale than the cosmological universe and coarser than the subatomic level, although modern basic hardware components using nanotechnology are scraping against an atomic scale. The software that runs on this hardware is essentially a sequence of bits describing how bits are transformed into bits, and hence also this is finite and discrete.

So one may say that calculus formulates continuous models as approximation of a discrete reality and numerical analysis simulates these models on computers by producing a discrete approximation at a much coarser level of the continuous models. To describe the behaviour of a computer, it is clear that it can be in many, but eventually, only a finite number of different states.

No wonder that students in computer science will have to learn about discrete mathematics.

Mathematics for Computer Science

This involves traditionally graphs, Boolean calculus, complexity, and sometimes also algebraic relations and structures like finite groups, rings, etc. In the early days of computer science, it was the playground of engineers and mathematicians who simulated their numerical models.

Therefore many of the "discrete mathematics courses for computer science" were given to mathematics or engineering students who wanted to specialize in computers. However computer science is now a mature topic in its own right, and students of computer science may not have the traditional mathematical background of previous generations. This book is taking this observation into account, and starts at a very elementary mathematical level, even explaining proof techniques, while introducing the first concepts of induction, sets, formal logic, The text is largely self-contained.