Lecture Discrete Structures for Computing: Chapter 0 - University of Technology - VNUHCM

Discrete Structures for Computing represent a foundational pillar in the realm of computer science, providing the essential mathematical framework upon which complex algorithms, data structures, and computational models are built. This document serves as an introduction to a comprehensive course designed to equip students with a robust understanding of these fundamental concepts. It underscores the critical role of discrete mathematics in problem-solving and logical reasoning within computational science, laying the groundwork for advanced studies and practical applications. The course aims to develop analytical skills through the exploration of core topics, emphasizing their relevance and applicability in the modern technological landscape.

Undergraduate students in Computer Science and Engineering, or related disciplines, seeking to establish a strong mathematical foundation for computational studies.

This academic manuscript details the structure and objectives of a course on Discrete Structures for Computing, a subject identified as the mathematical base for numerous topics in Computational Science. The curriculum is meticulously organized into 12 principal chapters, covering a broad spectrum of subjects including Logic, Set theory, Number theory, Combinatorics (enumerative combinatorics, graph theory, counting, inclusion-exclusion), Algorithmics, Information theory, Complexity theory, and Probability theory. The course adopts an approach centered on understanding and applying fundamental concepts, including various Proof methods (induction, contradiction), and delving into specific topics like relations, functions, cardinalities, graph structures (directed, undirected, weighted, shortest paths, spanning trees, flows network), and probabilistic modeling with introductory random variables. The learning outcomes emphasize the ability to model and formulate generic problems in real life using discrete mathematical structures and languages, culminating in the application of this knowledge to compute quantities and solve basic problems optimally, such as those involving shortest paths and minimum spanning trees. This comprehensive overview highlights the course's value in developing critical thinking and problem-solving skills essential for computing professionals.