Mathematics for Computer Science

Introduction to Theoretical Computer Science

Introduction to Theoretical Computer Science by Boaz Barak provides an overview of some basic notions. This voluminous note starts with serious foundational mathematics needed to understand the intricacies of computation. Among several models of computation and their representations, he deals with finite and uniform computations. Key topics: It presents efficient algorithms which are essential in solving practical problems and randomized computation, one of whose important features is to bring probabilistic methods into the design of algorithms. Advanced topics broaden the knowledge further towards recent research and trends. This note is intended for students and professionals at large who wish to have a rigorous introduction to theoretical aspects and their practical applications in computer science.

Author(s): Boaz Barak

656 Pages

Overview of Computer Science

Overview of Computer Science by Phillip Barty Crouch Junior is broad but detailed in most key areas of computer science. It deals with algorithms, the prerequisite for problem-solving and data processing. Data representation and logic form the backbone through which computers understand and execute instructions and are thus discussed. It does also touch on the topics of machine organization and Moore's Law, referring to the exponential growth that has occurred in computing power. It also covers topics in computer security and algorithmic complexity, and software development practices. Python references and examples, with practical problems will enable readers to understand and apply the content by matching theory with hands-on programming.

Author(s): Phillip Barty Crouch Junior

238 Pages

Logic for Computer Science Lecture Notes

This lecture note provides a thorough introduction to the principles of propositional logic, an essential component of computer science. It begins with informal propositional logic and then delves into formal syntax, covering functions defined recursively and their semantics. The notes explore logical connectives and their roles in constructing and evaluating logical statements. Key topics include natural deduction, normal forms, and resolution methods, which are crucial for reasoning about logical propositions and solving logical problems. This resource is ideal for students seeking a solid foundation in propositional logic and its applications in computer science.

Author(s): Alexandru Ioan Cuza University

84 Pages

Mathematics for Computer Science

This is a comprehensive textbook, covering some fundamental mathematical concepts underlying computer science. It starts with basic proofs, induction, and recursion; it proceeds to infinite sets, number theory, and graph theory. Further, it outlines the practical usage in the area of communication networks, along with some aspects of probability theory involving random variables and random walks. This merge of mathematical theory with computer science applications provides an excellent framework upon which students can base their study of algorithms, data structures, and other computational concepts.

Author(s): Eric Lehman, F. Thomson Leighton, Alberty R. Meyer

427 Pages

Introduction To Computer System by Tilak Maharashtra Vidyapeeth

Introduction to Computer Systems by Tilak Maharashtra Vidyapeeth presents the fundamental concepts of the computer system. This above PDF describes some important aspects of the computer system: input and output devices, primary and secondary storage devices constituting it. The number system and Boolean algebra have also been explained, which form the basis of logic circuits. It also deals with computer software, programming languages, and program development. It also gives an overview of some popular operating systems, hence enabling the readers to have a broader view on both the hardware and software aspects of computing. This note thus targets serving as an introductory guide for students and individuals that are entering computer systems, hence helping them to develop a solid background in both the theoretical and practical aspects of computing.

Author(s): Tilak Maharashtra Vidyapeeth

109 Pages

Lecture Notes On High Performance Computing

The following Lecture Notes on High Performance Computing from VSS University of Technology deal in-depth with new computing paradigms aimed at the efficient execution of large computations. This PDF covers Cluster Computing, a form of parallel processing wherein a group of computers that are symmetrically linked work symptomatically as one system to enhance computation power. It looks at Scalable Parallel Computer Architectures, which can grow as demand for processing goes up. This discusses key components of clusters and the role of Cluster Middleware in creating a Single System Image. The notes describe the Evolution of Metacomputing, which covers development and integration aspects of distributed computing resources. Other topics that are considered in this regard include resource-sharing concepts like Load Sharing and Balancing. Furthermore, Grid Computing and Cloud Computing, concepts based on distributed resources and remote servers, will also be discussed. It also deals with the provisioning of Virtual Machines and Time and Space-shared provisioning in order to provide insight into some efficient resource management and virtualization issues in high-performance computing environments.

Author(s): VSS University of Technology

69 Pages