Discrete Mathematics for Computer Science and Engineering

Birla Institute Of Technology And Science–Pilani (BITS–Pilani) via Coursera

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Provider

Coursera
Pricing

Paid Course
Languages

English
Certificate

Paid Certificate Available
Duration & workload

1 day 19 hours 52 minutes
Sessions

On-Demand
Subtitles

English

Found in

Part of

Mathematics for Engineering

Overview

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Welcome to the Discrete Mathematics course, your gateway to mastering the mathematical foundations essential for modern computing and data science. Designed for aspiring software engineers, computer scientists, data analysts, and cryptographers, this course is ideal for undergraduate students, professionals looking to enhance their analytical skills, and anyone interested in the theoretical underpinnings of computer science. You'll dive into discrete mathematical structures crucial for data structures, algorithms, operating systems, and cryptography. Explore key topics such as sets, relations, functions, graphs, combinatorics, and formal mathematical proofs, equipping you with the logical reasoning and problem-solving skills needed for sophisticated computer science applications. Unlock your potential with structured learning techniques that enhance your analytical thinking. This course is perfect for those aiming to pursue careers in artificial intelligence, cybersecurity, software development, and data science. With engaging lectures and hands-on exercises, you'll master the principles of discrete mathematics and prepare yourself for advanced computing challenges. Gain the confidence to tackle complex mathematical concepts and apply them in practical scenarios, paving the way for a successful and fulfilling career in engineering, computer science, and data analysis.

Syllabus

Proof Methods

In this module, you will first learn the basics of formal logic. With that foundational knowledge, you will learn multiple techniques to write mathematical proof in order to prove a statement. You will gain insights into how to choose proof methods, including direct proofs, indirect proofs, trivial proofs, and vacuous proofs.

More Proof Methods, Sequences, and Summations

In this module, you will learn about more proof techniques, including proof by contradiction, existence proofs, and proof by cases. You will recognise some common fallacies in incorrect proofs. Following this, you will learn about mathematical induction and strong mathematical induction. You will gain insights into writing inductive proof for standard theorems and problems. You will learn about sequences and summations. You will also learn about arithmetic, geometric, and harmonic progressions and their corresponding series.

Sets and Functions

This module introduces you to sets and functions. You will get acquainted with Venn diagrams, the cardinality of a set, power sets, set operations, set identities, and computer representation of sets. You will learn about injective, surjective, and bijective functions.

Relations and Countable Sets

This module introduces you to relations by illustrating n-ary relations, complementary relations, and relations on a set. You will learn about reflexive, symmetric, anti-symmetric, and transitive relations. You will also learn about functionality, composite relations, representing relations, closure of relations, and applications of relations in computer science. You will also learn about the countability and uncountability of sets.

Equivalence and Partial Ordered Relations

In this module, you will learn about equivalence relations, equivalence classes, and partitions. You will gain insights into partial ordering, partial or total ordered sets, and the Hasse diagram. You will also learn about maximal and minimal elements, least upper bound (lub ) and greatest lower bounds (glb ), and lattice.

Counting Techniques

In this module, you will learn about counting techniques, including the pigeonhole principle, permutations and combinations, and the inclusion-exclusion principle. You will gain insights into combinatorics, a subfield of discrete mathematics that deals with arrangements of discrete objects with specific constraints and the number of distinct ways of making such arrangements.

Recursive Functions and Recurrence Relations

In this module, you will learn about definitions of recursive functions. You will learn to use structural induction to prove statements that use recursive definitions. You will also learn about recurrence relations and explore some techniques to solve them.

Introduction to Graphs

This module introduces you to graphs, starting from real-world examples. Following this, you will learn about rigorous definitions of graphs and techniques to represent them. You will also gain insights into bipartite graphs and graph isomorphism.

Advanced Topics on Graphs, Paths, and Connectivity

In this module, you will learn about more advanced topics pertaining to graphs. You will learn about definitions of paths and connectivity. You will also learn about Euler and Hamilton paths, planar graphs, and graph colorings and their applications.

Trees and Basic Algebraic Structures

This module introduces you to the fundamentals of trees and spanning trees of a graph. You will learn about algorithms to identify minimum spanning trees in a graph. Following this, the module introduces you to the notions of basic algebraic structures such as groups, semi-groups, and rings.