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| computer science math requirements: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-03-08 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. |
| computer science math requirements: Think Stats Allen B. Downey, 2011-07-01 If you know how to program, you have the skills to turn data into knowledge using the tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts. Develop your understanding of probability and statistics by writing and testing code Run experiments to test statistical behavior, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Learn topics not usually covered in an introductory course, such as Bayesian estimation Import data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data |
| computer science math requirements: The Discrete Math Workbook Sergei Kurgalin, Sergei Borzunov, 2018-07-31 This practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments. Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language. |
| computer science math requirements: Computability and Logic George S. Boolos, John P. Burgess, Richard C. Jeffrey, 2007-09-17 This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem. |
| computer science math requirements: Concrete Mathematics Ronald L. Graham, Donald E. Knuth, Oren Patashnik, 1994-02-28 This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. |
| computer science math requirements: Statistics in Plain English Timothy C. Urdan, 2005 This book is meant to be a supplement to a more detailed statistics textbook, such as that recommended for a statistics course in the social sciences. Also, as a reference book to refresh your memory about statistical concepts. |
| computer science math requirements: 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz, 2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutions If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! |
| computer science math requirements: Java Programming Ralph Bravaco, Shai Simonson, 2009-02-01 Java Programming, From The Ground Up, with its flexible organization, teaches Java in a way that is refreshing, fun, interesting and still has all the appropriate programming pieces for students to learn. The motivation behind this writing is to bring a logical, readable, entertaining approach to keep your students involved. Each chapter has a Bigger Picture section at the end of the chapter to provide a variety of interesting related topics in computer science. The writing style is conversational and not overly technical so it addresses programming concepts appropriately. Because of the flexibile organization of the text, it can be used for a one or two semester introductory Java programming class, as well as using Java as a second language. The text contains a large variety of carefully designed exercises that are more effective than the competition. |
| computer science math requirements: Combinatorics and Graph Theory John Harris, Jeffry L. Hirst, Michael Mossinghoff, 2009-04-03 These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline. |
| computer science math requirements: Fundamentals of Discrete Math for Computer Science Tom Jenkyns, Ben Stephenson, 2012-10-16 This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Features: no university-level background in mathematics required; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question. |
| computer science math requirements: Mathematics of Discrete Structures for Computer Science Gordon J. Pace, 2012-07-09 Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering. |
| computer science math requirements: Essential Logic for Computer Science Rex Page, Ruben Gamboa, 2019-01-08 An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism. For readers who want to see formalization in action, the text presents examples using Proof Pad, a lightweight ACL2 environment. Readers will not become ALC2 experts, but will learn how mechanized logic can benefit software and hardware engineers. In addition, 180 exercises, some of them extremely challenging, offer opportunities for problem solving. There are no prerequisites beyond high school algebra. Programming experience is not required to understand the book's equation-based approach. The book can be used in undergraduate courses in logic for computer science and introduction to computer science and in math courses for computer science students. |
| computer science math requirements: How to Prove It Daniel J. Velleman, 2006-01-16 Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians. |
| computer science math requirements: Discrete Mathematics for Computer Scientists Clifford Stein, Robert L. Drysdale, Kenneth P. Bogart, 2011 Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises. |
| computer science math requirements: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| computer science math requirements: Principles of Digital Logic Naval Education and Training Program Development Center, United States. Naval Education and Training Command, 1979 |
| computer science math requirements: Discrete Mathematics with Graph Theory (Classic Version) Edgar Goodaire, Michael Parmenter, 2017-03-20 This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. Far more user friendly than the vast majority of similar books, this text is truly written with the beginning reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize Active Reading, a skill vital to success in learning how to think mathematically (and write clean, error-free programs). |
| computer science math requirements: Discrete Mathematics for Computer Science Gary Haggard, John Schlipf, Sue Whitesides, 2006 Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career. |
| computer science math requirements: Mathematical Structures for Computer Science Judith L. Gersting, 2007 This edition offers a pedagogically rich and intuitive introduction to discrete mathematics structures. It meets the needs of computer science majors by being both comprehensive and accessible. |
| computer science math requirements: Functional Differential Geometry Gerald Jay Sussman, Jack Wisdom, 2013-07-05 An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding. |
| computer science math requirements: Elementary Math for Computer Science with Python Eric Bennett, 2020-04-26 Learning to code is an attractive option for many parents and elementary-aged students. Most simple computer programs, however, rely on math concepts that are not yet part of a typical, elementary school curriculum. This text solves that problem by presenting math concepts selected for their importance to computer science in a way that is accessible to a younger audience through: visual models and worked examples; thoughtfully sequenced, scaffolded practice problems; written introductions, illustrations and word problems that provide real-world context; coding examples and projects written in Python; coding challenges and extensions; solutions to all practice problems, comprehension questions and selected challenges. While many math and computer science courses equip students to complete problems by rote and copy an instructor's code, this curriculum is aimed toward facilitating the meaningful learning necessary for students to solve problems and produce original work. Note: it is recommended that students are reading at a third grade level and familiar with whole-number addition, subtraction, multiplication and division. |
| computer science math requirements: Essential Discrete Mathematics for Computer Science Harry Lewis, Rachel Zax, 2019-03-19 Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. |
| computer science math requirements: Essential Discrete Mathematics for Computer Science Todd Feil, Joan Krone, 2003 This book introduces readers to the mathematics of computer science and prepares them for the math they will encounter in other college courses. It includes applications that are specific to computer science, helps learners to develop reasoning skills, and provides the fundamental mathematics necessary for computer scientists. Chapter topics include sets, functions and relations, Boolean algebra, natural numbers and induction, number theory, recursion, solving recurrences, counting, matrices, and graphs. For computer scientists and the enhancement of programming skills. |
| computer science math requirements: Mathematical Logic for Computer Science Mordechai Ben-Ari, 2012-12-06 This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science. |
| computer science math requirements: Computer Science Handbook Allen B. Tucker, 2004-06-28 When you think about how far and fast computer science has progressed in recent years, it's not hard to conclude that a seven-year old handbook may fall a little short of the kind of reference today's computer scientists, software engineers, and IT professionals need. With a broadened scope, more emphasis on applied computing, and more than 70 chap |
| computer science math requirements: How to Design Programs, second edition Matthias Felleisen, Robert Bruce Findler, Matthew Flatt, Shriram Krishnamurthi, 2018-05-25 A completely revised edition, offering new design recipes for interactive programs and support for images as plain values, testing, event-driven programming, and even distributed programming. This introduction to programming places computer science at the core of a liberal arts education. Unlike other introductory books, it focuses on the program design process, presenting program design guidelines that show the reader how to analyze a problem statement, how to formulate concise goals, how to make up examples, how to develop an outline of the solution, how to finish the program, and how to test it. Because learning to design programs is about the study of principles and the acquisition of transferable skills, the text does not use an off-the-shelf industrial language but presents a tailor-made teaching language. For the same reason, it offers DrRacket, a programming environment for novices that supports playful, feedback-oriented learning. The environment grows with readers as they master the material in the book until it supports a full-fledged language for the whole spectrum of programming tasks. This second edition has been completely revised. While the book continues to teach a systematic approach to program design, the second edition introduces different design recipes for interactive programs with graphical interfaces and batch programs. It also enriches its design recipes for functions with numerous new hints. Finally, the teaching languages and their IDE now come with support for images as plain values, testing, event-driven programming, and even distributed programming. |
| computer science math requirements: Mathematics for Computer Programmers Christine Benedyk Kay, 1984 Number systems I. Sets. Integer and real number sets. Format arithmetic. Algorithms. Solving problems using input. process, and output. Algorithms. Flowcharts. Algebraic applications for programming. Language of algebra. Algebraic expressions of not equal. Exponents. Equations. Advanced algebra concepts. Quadratic equations. Linear equations. Linear programming. Functions. Sequence and subscripted variables. Matrices. Binary systems. Number base concepts. Binary, octal, and hexadecimal numbers. Computer codes. Boolean algebra concepts. Mathematical logic. Boolean algebra and computer logic. |
| computer science math requirements: The Calculus Lifesaver Adrian Banner, 2007-03-25 For many students, calculus can be the most mystifying and frustrating course they will ever take. Based upon Adrian Banner's popular calculus review course at Princeton University, this book provides students with the essential tools they need not only to learn calculus, but also to excel at it. |
| computer science math requirements: Computer Science J. Glenn Brookshear, 2012 Computer Science: An Overview uses broad coverage and clear exposition to present a complete picture of the dynamic computer science field. Accessible to students from all backgrounds, Glenn Brookshear uses a language-independent context to encourage the development of a practical, realistic understanding of the field. An overview of each of the important areas of Computer Science (e.g. Networking, OS, Computer Architecture, Algorithms) provides students with a general level of proficiency for future courses. The Eleventh Edition features two new contributing authors (David Smith -- Indiana University of PA; Dennis Brylow -- Marquette University), new, modern examples, and updated coverage based on current technology. |
| computer science math requirements: Discrete Mathematics for Computer Science Jon Pierre Fortney, 2020-12-23 Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook. |
| computer science math requirements: Security Informatics Christopher C. Yang, Michael Chau, Jau-Hwang Wang, Hsinchun Chen, 2010-01-08 Intelligence and Security Informatics (ISI) is defined as the study of the development and use of advanced information systems and technologies for national, international, and societal security-related applications. With the rise of global terrorism, the field has been given an increasing amount of attention from academic researchers, law enforcement, intelligent experts, information technology consultants and practitioners. SECURITY INFORMATICS is global in scope and perspective. Leading experts will be invited as contributing authors from the US, UK, Denmark, Israel, Singapore, Hong Kong, Taiwan, Europe, etc. It is the first systematic, archival volume treatment of the field and will cover the very latest advances in ISI research and practice. It is organized in four major subject areas: (1) Information and Systems Security, (2) Information Sharing and Analysis in Security Informatics, (3) Infrastructure Protection and Emergency Responses, and (4) National Security and Terrorism Informatics. |
| computer science math requirements: Mindset Carol S. Dweck, 2007-12-26 From the renowned psychologist who introduced the world to “growth mindset” comes this updated edition of the million-copy bestseller—featuring transformative insights into redefining success, building lifelong resilience, and supercharging self-improvement. “Through clever research studies and engaging writing, Dweck illuminates how our beliefs about our capabilities exert tremendous influence on how we learn and which paths we take in life.”—Bill Gates, GatesNotes “It’s not always the people who start out the smartest who end up the smartest.” After decades of research, world-renowned Stanford University psychologist Carol S. Dweck, Ph.D., discovered a simple but groundbreaking idea: the power of mindset. In this brilliant book, she shows how success in school, work, sports, the arts, and almost every area of human endeavor can be dramatically influenced by how we think about our talents and abilities. People with a fixed mindset—those who believe that abilities are fixed—are less likely to flourish than those with a growth mindset—those who believe that abilities can be developed. Mindset reveals how great parents, teachers, managers, and athletes can put this idea to use to foster outstanding accomplishment. In this edition, Dweck offers new insights into her now famous and broadly embraced concept. She introduces a phenomenon she calls false growth mindset and guides people toward adopting a deeper, truer growth mindset. She also expands the mindset concept beyond the individual, applying it to the cultures of groups and organizations. With the right mindset, you can motivate those you lead, teach, and love—to transform their lives and your own. |
| computer science math requirements: What If? Randall Munroe, 2014 From the creator of the wildly popular webcomic xkcd, hilarious and informative answers to important questions you probably never thought to ask Millions of people visit xkcd.com each week to read Randall Munroe's iconic webcomic. His stick-figure drawings about science, technology, language, and love have an enormous, dedicated following, as do his deeply researched answers to his fans' strangest questions. The queries he receives range from merely odd to downright diabolical: - What if I took a swim in a spent-nuclear-fuel pool? - Could you build a jetpack using downward-firing machine guns? - What if a Richter 15 earthquake hit New York City? - Are fire tornadoes possible? His responses are masterpieces of clarity and wit, gleefully and accurately explaining everything from the relativistic effects of a baseball pitched at near the speed of light to the many horrible ways you could die while building a periodic table out of all the actual elements. The book features new and never-before-answered questions, along with the most popular answers from the xkcd website. What If? is an informative feast for xkcd fans and anyone who loves to ponder the hypothetical. |
| computer science math requirements: Problems with a Point William I. Gasarch, Clyde Kruskal, 2018 Ever notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)? Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques. This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.-- |
| computer science math requirements: Extremal Combinatorics Stasys Jukna, 2013-03-09 This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods. |
| computer science math requirements: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| computer science math requirements: Foundation Mathematics for Computer Science John Vince, 2015-07-27 John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts. |
| computer science math requirements: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| computer science math requirements: Handbook of Analysis and Its Foundations Eric Schechter, 1996-10-24 Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/ |
| computer science math requirements: Formalizing Common Sense John McCarthy, 1998 Extending over a period of 30 years, this is a collection of papers written by John McCarthy on artificial intelligence. They range from informal surveys written for a general audience to technical discussions of challenging research problems that should be of interest to specialists. |
COMPUTER SCIENCE CORE REQUIREMENTS - Utah Valley …
GRADUATION REQUIREMENTS: Completion of a minimum of 120 semester credits, with a minimum of 40 upper-division credits. Overall grade point average of 2.0 or above. Must have …
Computer Science Undergraduate CoreCourses
Students must complete all G.E. courses, all the lower- and upper-division Computer Science core courses, all the required math courses, 12-units of math and science electives, and 15 …
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Mathematics - Students who are strong in math are encouraged to take MATH 330 (Number Systems) instead of MATH 314 (Discrete Mathematics). Students with a strong math …
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Computer Science Departmental Requirements and Prerequisite Structure CSCI-BS Math 122 (4 cr) Pre-Calculus Minimum grade for a required CS course: C Minimum grade for a required …
Computer Science Graduation Requirements
The minimum grade required for math, science, language, reasoning and writing in context, CSE Electives and Computer Science required coursework is a 2.0. A student's cumulative GPA …
Microsoft Word - Requirements for Computer Science
Requirements for the B.S. Degree in Computer Science Department of Computer Science and Engineering, University of Central Arkansas 3/25/22 revised
COMPUTER SCIENCE -MATHEMATICS - Columbia University
Following this, majors begin to learn some aspects of the main branches of modern mathematics: algebra, analysis, and geometry; as well as some of their subdivisions and hybrids (e.g., …
Computer Science Bachelor of Science - UMD
Computer Science Requirements Grade of “C-” or higher is required in all courses
Computer Science-Math major requirement checklist
3 Credits: a score of 4 or 5 on the AP Calculus AB exam, a 4 on the AP Calculus BC exam, or a 6 on the IB Mathematics: analysis and approaches HL exam, upon completion of either Calculus …
COMPUTER SCIENCE UNDERGRADUATE STUDENT HANDBOOK
These six courses along with PHYS 5A or PHYS 11A will satisfy the computer science math and science requirements and earn you a minor at the same time. This path requires 25 units of …
Bachelor of Arts – Computer Science (120 Hours) and …
math sequence below will satisfy the math requirement for this degree. Sequence B. will allow a broader selection of advanced computer science electives. The course work in mathe. atics …
2021-22 Bachelor of Arts - Computer Science Degree …
All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. 4-yr institution. The last 30 credits of your degree need …
COMPUTER SCIENCE - University of New Mexico
Before students are eligible to apply to the CS program, students must complete a minimum of 23 credit hours acceptable towards a degree of a bachelors in Computer Science with a …
Microsoft Word - Requirements for Computer Science
Prerequisites columns: “A,B” means “A and B”; “A/B” means “A or B”. Students who do (not) opt for BIOL sequence must take CHEM 1400/PHYS 1400/PHYS 1401 (BIOL 1400/1440) to fulfill …
Microsoft Word - brochure_BSCS_2021-22.docx
Due to the rigorous nature of our programs, most applicants to Computer Science are required to attain a 550 on the Math section of the SAT, or a 24 on the Math section of the ACT, and have …
CSCheckList2024.xls - Santa Clara University
In order to pursue this emphasis the student must get their courses approved along with their advisor's signature at least three quarters before they graduate. Three of the five upper division …
Computer Science, Bachelor of Science - Johns Hopkins …
Both degree programs require specific courses and/or credits in several key areas: computer science, math, basic science, humanities and social sciences. The Bachelor of Science degree …
COMPUTER SCIENCE CORE REQUIREMENTS - Utah Valley …
GRADUATION REQUIREMENTS: Completion of a minimum of 120 semester credits, with a minimum of 40 upper-division credits. Overall grade point average of 2.0 or above. Must have …
Computer Science Undergraduate CoreCourses
Students must complete all G.E. courses, all the lower- and upper-division Computer Science core courses, all the required math courses, 12-units of math and science electives, and 15 …
Catalog 2025-2026 Computer Science - kings.edu
Computer Science Suggested Sequence gree requirements is listed below. Refer to the college catalog for course title , descriptions, and prerequisites. Always consult your Academic Advisor …
Computer Science, BS - Clemson University - Acalog ACMSTM
A grade of C or better must be earned in all prerequisite courses (including CPSC and MATH courses) before enrolling in the next CPSC course. General Education Cross-Cultural …
2024-25 Computer Science BS Degree Sheet
All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. The last 30 credits of your degree need to be taken …
REQUIREMENTS FOR BACHELOR OF SCIENCE IN …
Mathematics - Students who are strong in math are encouraged to take MATH 330 (Number Systems) instead of MATH 314 (Discrete Mathematics). Students with a strong math …
Computer Science Departmental Requirements BS
Computer Science Departmental Requirements and Prerequisite Structure CSCI-BS Math 122 (4 cr) Pre-Calculus Minimum grade for a required CS course: C Minimum grade for a required …
Computer Science Graduation Requirements
The minimum grade required for math, science, language, reasoning and writing in context, CSE Electives and Computer Science required coursework is a 2.0. A student's cumulative GPA …
Microsoft Word - Requirements for Computer Science
Requirements for the B.S. Degree in Computer Science Department of Computer Science and Engineering, University of Central Arkansas 3/25/22 revised
COMPUTER SCIENCE -MATHEMATICS - Columbia University
Following this, majors begin to learn some aspects of the main branches of modern mathematics: algebra, analysis, and geometry; as well as some of their subdivisions and hybrids (e.g., …
Computer Science Bachelor of Science - UMD
Computer Science Requirements Grade of “C-” or higher is required in all courses
Computer Science-Math major requirement checklist
3 Credits: a score of 4 or 5 on the AP Calculus AB exam, a 4 on the AP Calculus BC exam, or a 6 on the IB Mathematics: analysis and approaches HL exam, upon completion of either Calculus …
COMPUTER SCIENCE UNDERGRADUATE STUDENT …
These six courses along with PHYS 5A or PHYS 11A will satisfy the computer science math and science requirements and earn you a minor at the same time. This path requires 25 units of …
Bachelor of Arts – Computer Science (120 Hours) and …
math sequence below will satisfy the math requirement for this degree. Sequence B. will allow a broader selection of advanced computer science electives. The course work in mathe. atics …
2021-22 Bachelor of Arts - Computer Science Degree …
All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. 4-yr institution. The last 30 credits of your degree need …
COMPUTER SCIENCE - University of New Mexico
Before students are eligible to apply to the CS program, students must complete a minimum of 23 credit hours acceptable towards a degree of a bachelors in Computer Science with a …
Microsoft Word - Requirements for Computer Science
Prerequisites columns: “A,B” means “A and B”; “A/B” means “A or B”. Students who do (not) opt for BIOL sequence must take CHEM 1400/PHYS 1400/PHYS 1401 (BIOL 1400/1440) to fulfill …
Microsoft Word - brochure_BSCS_2021-22.docx
Due to the rigorous nature of our programs, most applicants to Computer Science are required to attain a 550 on the Math section of the SAT, or a 24 on the Math section of the ACT, and have …
CSCheckList2024.xls - Santa Clara University
In order to pursue this emphasis the student must get their courses approved along with their advisor's signature at least three quarters before they graduate. Three of the five upper …
Computer Science, Bachelor of Science - Johns Hopkins …
Both degree programs require specific courses and/or credits in several key areas: computer science, math, basic science, humanities and social sciences. The Bachelor of Science …
