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 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 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
General computer science Lecture notes
These lecture notes provide broad coverage of general issues in computer science, with an emphasis on discrete mathematics and programming. The topics taught in this course range from representational issues and computation of information, Standard ML, recursion, imperative programming, and encoding of programs as strings. These notes uniquely combine Boolean algebra and propositional logic with the description of machine-oriented calculi such as analytical tableaux and resolution for a wholesome understanding of both the theoretical and practical aspects of computer science.
Author(s): Michael Kohlhase
179 Pages
CS Unplugged is an entertaining way to help learn about the basics of computer science, using snacks, sorting games, and puzzles-none of which require a computer. The PDF covers basic material like data representation, algorithms, and procedures through to advanced and specialized topics such as intractability, cryptography, and human-computer interaction. This is ideal for teachers and students alike who seek knowledge about concepts in computer science using interactives with no digital support; therefore, suitable for any environment where the learning process takes place.
Author(s): Tim Bell, Ian H. Witten, Mike Fellows
243 Pages
Computer Science by Dr. Chris Bourke
Dr. Chris Bourke's book provides an extended textbook introduction to many core areas of computer science. It covers the basics of programming: conditionals, loops, functions, and error handling. More advanced topics concern dynamic memory, collections, and file I/ using both procedural and object-oriented approaches. There are chapters on searching and sorting algorithms, graphical user interface design, and database connectivity. This resource serves well as a starting point, either for beginners or intermediate learners, in terms of providing overall depth regarding key concepts and best practices in the subject of programming.
Author(s): Dr. Chris Bourke, Department of Computer Science and Engineering, University of Nebraska
647 Pages
