| computer science degree math: 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 degree math: 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 degree math: 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 degree math: 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 degree math: 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 degree math: 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 degree math: 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 degree math: Geometric Algebra for Computer Science Leo Dorst, Daniel Fontijne, Stephen Mann, 2010-07-26 Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA |
| computer science degree math: 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 degree math: Connecting Discrete Mathematics and Computer Science David Liben-Nowell, 2022-08-04 Computer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures – like logic, proofs, number theory, counting, probability, graphs – are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures. |
| computer science degree math: 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 degree math: 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 degree math: Sets, Logic and Maths for Computing David Makinson, 2012-02-27 This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions. |
| computer science degree math: Mathematical Foundation of Computer Science Y. N. Singh, 2005 The Interesting Feature Of This Book Is Its Organization And Structure. That Consists Of Systematizing Of The Definitions, Methods, And Results That Something Resembling A Theory. Simplicity, Clarity, And Precision Of Mathematical Language Makes Theoretical Topics More Appealing To The Readers Who Are Of Mathematical Or Non-Mathematical Background. For Quick References And Immediate Attentions3⁄4Concepts And Definitions, Methods And Theorems, And Key Notes Are Presented Through Highlighted Points From Beginning To End. Whenever, Necessary And Probable A Visual Approach Of Presentation Is Used. The Amalgamation Of Text And Figures Make Mathematical Rigors Easier To Understand. Each Chapter Begins With The Detailed Contents, Which Are Discussed Inside The Chapter And Conclude With A Summary Of The Material Covered In The Chapter. Summary Provides A Brief Overview Of All The Topics Covered In The Chapter. To Demonstrate The Principles Better, The Applicability Of The Concepts Discussed In Each Topic Are Illustrated By Several Examples Followed By The Practice Sets Or Exercises. |
| computer science degree math: 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 degree math: 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 degree math: Mathematics for Computer Graphics John Vince, 2005-11-09 This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses. |
| computer science degree math: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
| computer science degree math: 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 degree math: 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 degree math: Infinite Words Dominique Perrin, Jean-Éric Pin, 2004-02-18 Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures. |
| computer science degree math: Practical Discrete Mathematics Ryan T. White, Archana Tikayat Ray, 2021-02-22 A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book. |
| computer science degree math: BIO2010 National Research Council, Division on Earth and Life Studies, Board on Life Sciences, Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st Century, 2003-02-13 Biological sciences have been revolutionized, not only in the way research is conductedâ€with the introduction of techniques such as recombinant DNA and digital technologyâ€but also in how research findings are communicated among professionals and to the public. Yet, the undergraduate programs that train biology researchers remain much the same as they were before these fundamental changes came on the scene. This new volume provides a blueprint for bringing undergraduate biology education up to the speed of today's research fast track. It includes recommendations for teaching the next generation of life science investigators, through: Building a strong interdisciplinary curriculum that includes physical science, information technology, and mathematics. Eliminating the administrative and financial barriers to cross-departmental collaboration. Evaluating the impact of medical college admissions testing on undergraduate biology education. Creating early opportunities for independent research. Designing meaningful laboratory experiences into the curriculum. The committee presents a dozen brief case studies of exemplary programs at leading institutions and lists many resources for biology educators. This volume will be important to biology faculty, administrators, practitioners, professional societies, research and education funders, and the biotechnology industry. |
| computer science degree math: Lessons in Enumerative Combinatorics Ömer Eğecioğlu, Adriano M. Garsia, 2021-05-13 This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters. |
| computer science degree math: 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 degree math: 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 degree math: 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 degree math: What Can Be Computed? John MacCormick, 2018-05-01 An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com |
| computer science degree math: 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 degree math: Discrete Mathematics and Computing Malik Magdon-Ismail, 2019-12-14 This text is a semester course in the basic mathematical and theoretical foundations of computer science. Students who make heavy use of computing should learn these foundations well, setting a base for a follow-on course in algorithms. A solid theoretical and algorithmic foundation in computer science sets the stage for developing good programs, programs that work, always and efficiently.Each chapter is a lecture that has been taught as such. Part I starts with basic logic, proofs and discrete mathematics, including: induction, recursion, summation, asymptotics and number theory. We then continue with graphs, counting and combinatorics, and wrap up the coverage of discrete mathematics with discrete probability. Part II presents the blockbuster application of discrete mathematics: the digital computer and a theory of computing. The goal is to understand what a computer can and cannot do. We start small, with automata, and end big with Turing Machines.Our approach is Socratic. The reader is encouraged to participate actively in the learning process by doing the quizzes and exercises that are liberally sprinkled through the text. The pace and level is appropriate for readers with one year of training in programming and calculus (college sophomores). |
| computer science degree math: Number Theory and Cryptography Marc Fischlin, Stefan Katzenbeisser, 2013-11-21 Johannes Buchmann is internationally recognized as one of the leading figures in areas of computational number theory, cryptography and information security. He has published numerous scientific papers and books spanning a very wide spectrum of interests; besides R&D he also fulfilled lots of administrative tasks for instance building up and directing his research group CDC at Darmstadt, but he also served as the Dean of the Department of Computer Science at TU Darmstadt and then went on to become Vice President of the university for six years (2001-2007). This festschrift, published in honor of Johannes Buchmann on the occasion of his 60th birthday, contains contributions by some of his colleagues, former students and friends. The papers give an overview of Johannes Buchmann's research interests, ranging from computational number theory and the hardness of cryptographic assumptions to more application-oriented topics such as privacy and hardware security. With this book we celebrate Johannes Buchmann's vision and achievements. |
| computer science degree math: Introduction to Linear Algebra Gilbert Strang, 2009-02-10 This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book's tried and tested approach is direct, offering practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang's 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned. |
| computer science degree math: Four Colours Suffice Robin J. Wilson, 2003 The four-colour problem was one of the most famous and controversial conundrums ever known, and stumped thousands of puzzlers for over a century. It sounded simple- what is the least number of colours needed to fill in any map, so that neighbouring countries are always coloured differently? However, it would take over a hundred years for amateur problem-solvers and mathematicians alike to answer the question first posed by Francis Guthrie in 1852. And, even when a solution was finally found using computers, debate raged over whether this technology could ever provide the proof that traditional pen-and-paper calculations could. This is the gripping story of the race to solve the riddle - a tale of dedicated puzzlers, mind-boggling maps, human ingenuity and the great rhombicuboctahedron |
| computer science degree math: Ultralearning Scott H. Young, 2019-08-06 Now a Wall Street Journal bestseller. Learn a new talent, stay relevant, reinvent yourself, and adapt to whatever the workplace throws your way. Ultralearning offers nine principles to master hard skills quickly. This is the essential guide to future-proof your career and maximize your competitive advantage through self-education. In these tumultuous times of economic and technological change, staying ahead depends on continual self-education—a lifelong mastery of fresh ideas, subjects, and skills. If you want to accomplish more and stand apart from everyone else, you need to become an ultralearner. The challenge of learning new skills is that you think you already know how best to learn, as you did as a student, so you rerun old routines and old ways of solving problems. To counter that, Ultralearning offers powerful strategies to break you out of those mental ruts and introduces new training methods to help you push through to higher levels of retention. Scott H. Young incorporates the latest research about the most effective learning methods and the stories of other ultralearners like himself—among them Benjamin Franklin, chess grandmaster Judit Polgár, and Nobel laureate physicist Richard Feynman, as well as a host of others, such as little-known modern polymath Nigel Richards, who won the French World Scrabble Championship—without knowing French. Young documents the methods he and others have used to acquire knowledge and shows that, far from being an obscure skill limited to aggressive autodidacts, ultralearning is a powerful tool anyone can use to improve their career, studies, and life. Ultralearning explores this fascinating subculture, shares a proven framework for a successful ultralearning project, and offers insights into how you can organize and exe - cute a plan to learn anything deeply and quickly, without teachers or budget-busting tuition costs. Whether the goal is to be fluent in a language (or ten languages), earn the equivalent of a college degree in a fraction of the time, or master multiple tools to build a product or business from the ground up, the principles in Ultralearning will guide you to success. |
| computer science degree math: Algorithms and Data Structures Niklaus Wirth, 1986 |
| computer science degree math: Mathematics, Statistics & Computer Science Careers Research and Advisory Centre (Cambridge, England), 2007-04-15 Popular among university applicants and their advisers alike, these guides presents a wide range of information on a specific degree discipline, laid out in tabular format enabling at-a-glance course comparison. |
| computer science degree math: Algorithms in Modern Mathematics and Computer Science Ŭzbekiston SSR fanlar akademii︠a︡si, 1981 |
| computer science degree math: Stewart's Single Variable Calculus James Stewart, Richard St. Andre, 2007-04 This helpful guide contains a short list of key concepts; a short list of skills to master; a brief introduction to the ideas of the section; an elaboration of the concepts and skills, including extra worked-out examples; and links in the margin to earlier and later material in the text and Study Guide. |
| computer science degree math: A Quick Steep Climb Up Linear Algebra Stephen Davies, 2021-01-13 A Quick Steep Climb Up Lienar Algebra - and its companion site allthemath - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia! |
| computer science degree math: Learning from Data Yaser S. Abu-Mostafa, Malik Magdon-Ismail, Hsuan-Tien Lin, 2012-01-01 |
Mathematics for Computer Science - Computer Science and …
1 Mathematics for Computer Science revised May 9, 2010, 770 minutes Prof. Albert R Meyer Massachusets Institute of Technology Creative Commons 2010, Prof. Albert R. Meyer.
Mathematics & Computer Science, BSLAS - University of …
Mathematics & Computer Science By the time of graduation, students will have the ability to: Computer Science: 1. Analyze a complex computing problem and apply principles of …
Important Information About Your Degree - cos.unt.edu
College of Science Admission Requirement: Students must demonstrate proficiency in College Algebra by placing into Math Level 2 or higher through the UNT Math Placement Exam (Not …
COMPUTER SCIENCE MATH & STAT COMMUNICATION …
The instructions contained in this packet are to be used as a guide in preparing the Department of Computer Science and Engineering (CSCE) Degree Plan Form for the Bachelor's Degree in …
Mathematics with Computer Science (Course 18-C)
Bachelor of Science in Mathematics with Computer Science General Institute Requirement s (GIRs) The General Institute Requirements include a Communication Requirement that is …
Computer and Mathematical Sciences - Iowa State University
The basic math or computer science curriculum provides a foundation for any of the programs listed in this brochure. With a background in math or computer science, you learn the language …
B.S. in Computer Science and Engineering
Below is the advised sequence of courses for this degree program as of 1/15/2025. Official degree requirements and course prerequisites are found in the University General Catalog; …
Bachelor of Science in Mathematics and Computer Science
Bachelor of Science in Mathematics and Computer Science The BS in Mathematics and Computer Science combines related areas of the two disciplines and is an excellent base for …
Applied Math and Computer Science - uwm.edu
The Applied Mathematics and Computer Science (AMCS) program is a special degree program that blends courses from both the College of Letters and Science and the College of …
CURRICULUM EFFECTIVE FALL 2025 Computer Science
To graduate with a B.S. in computer science, students must have at least a 2.3 GPA in all classes at the 400 level or above taken for undergraduate credit from the Carl R. Ice College of …
PROGRAM C, B.A./B.S. MATHEMATICS + COMPUTER SCIENCE …
Mathematics + Computer Science 2023 . page 2 • For a B.S. degree, at least 4 of the 8 electives must be math courses as define here. • Mathematics (MATH) courses: MATH: 3600 or higher, …
University Studies - Mathematics and Natural Science and …
Solve complex problems using mathematics, natural and/or computer science. Utilize high level mathematical skills to analyze data and/or solve problems. Analyze concepts of physical and …
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All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. *Indicates “pre” CS course 2.25 or higher UNLV GPA is …
COMPUTER SCIENCE Calculus I & ENGL-102 ready - University …
Aug 25, 2020 · Computer Science I MATH 143, CS 112 or sufficient test scores 4 *MATH 176 Discrete Mathematics ... COMPUTER SCIENCE YOUR DEGREE IS ACCREDITED Our …
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• Math: courses equivalent to two years up through differential equations • Physics: one year of calculus-based physics, including lab • Chemistry: courses and labs equivalent to one year for …
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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 …
College of Engineering and Computing - George Mason …
The BS in Computer Science program also requires 12 credits of natural science and 20 credits in mathematics and statistics, including calculus, discrete mathematics, linear algebra, and …
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explore and download free Computer Science Degree Math PDF books and manuals is the internets largest free library. Hosted online, this catalog compiles a vast assortment of …
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Degree map is for advising purposes only. Students are responsible for complying with University Catalog requirements. ... To graduate with a B.S. in computer science, students must have at …
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All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. *Indicates “pre” CS course 2.25 or higher UNLV GPA is …
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All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. ... bachelor's degree from UNLV is 120. Computer …
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MATH 2412 with a grade of 'C' or better; or passing the Precalculus Exemption Test administered by the Department of Mathematics. 1 CSCI 1101 Introduction to Computer Science C 4 CSCI …
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All English, math, science, engineering, computer science courses must have a grade of "C" or higher for graduation and to progress. 2.25 or higher UNLV GPA is required for graduation The …
B.S. Computer Science and Engineering
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MATH 106–199, STATS 100A–102C Quarter Grade Quarter Grade MATH 115A+ 1. MATH 131A+ 2. MATH 131B 3. or MATH 132 4. MATH 151A 5. MATH 151B 6. Three upper division computer …
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Sep 23, 2017 · Undergraduate Degree Plan in Computer Science (CPSC), Catalog 139 (2016-2017) Department of Computer Science and Engineering, College of Engineering, Texas A&M …
Bachelor of Science in Mathematics and Computer Science
1 Bachelor of Science in Mathematics and Computer Science The BS in Mathematics and Computer Science combines related areas of the two disciplines and is an excellent base for …
Bachelor of Science in Computer Science - The University of …
Graduates who have earned the bachelor’s degree in computer science, within a few years following graduation, will have demonstrated technical proficiency, collaborative activities, and …
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Catalog 2025-2026 Computer Science Computer …
The 3+2 Computer Science-Computer Engineering Dual Degree Program is a collaboration with the University of Notre Dame and with Washington University in St. Louis. Students will spend …
QUEENS COLLEGE Computer Science BS
Our 4-year academic plans are illustrative examples of integrated degree requirements and course sequencing for each of the College’s programs of study ... for MATH 120. Contact the …
Bachelor of Science Degree - Bellevue College
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Mathematics with Computer Science (Course 18-C)
Bachelor of Science in Mathematics with Computer Science General Institute Requirement s (GIRs) The General Institute Requirements include a Communication Requirement that is …
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Computer Science 0701C Bachelor of Science in Computer Science Year FIRST SEMESTER Hours SECOND SEMESTER Hours FRESHMAN ENGL 1113, Prin. of English Composition …
Detailed Syllabus For B.Sc. (Computer Science) (Mathematics) …
Modern College of Arts, Science and Commerce (Autonomous), Shivajinagar, Pune - 5 First Year of B.Sc. (Computer Science) (Mathematics) (2019 Course) Course Code: 19CsMatU103 …
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Computer and Mathematical Sciences - Iowa State University
The basic math or computer science curriculum provides a foundation for any of the programs listed in this brochure. With a background in math or computer science, you learn the language …
Discrete Mathematics for Computer Science - UH
1.12.4 Using Discrete Mathematics in Computer Science 87 CHAPTER 2 Formal Logic 89 2.1 Introduction to Propositional Logic 89 2.1.1 Formulas 92 2.1.2 Expression Trees for Formulas …
B.S. WITH DOUBLE MAJOR IN MATHEMATICS & COMPUTER …
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BA Computer Science
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Computer Science BS 4-Year Plan - Queens College
Fourth Computer Science Elective** 3 credits Fifth Computer Science Elective** 3 credits Computer Science Elective** 3 credits Life & Physical Science (LPS) 4 credits 3 Springtotal …
Bachelor of Science in Computer Science (B235)
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Bachelor of Science in Computer Science (BS) - UTRGV
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A.S. Computer Science / B.S. Computer Science Pathway
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Computer Science Curriculum
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Computer - Northern Illinois University
Department of Computer Science Psychology-Computer Science Building Room 460 Northern Illinois University DeKalb, IL 60115 815-753-0378 Email us: askCSCIundergrad@niu.edu …
Computer Science B235 2024 - The University of Oklahoma
Bachelor of Science in Computer Science (B235) Summer 2024 through Spring 2025 – Total Credit Hours: 120 This flowchart is not an official check sheet of degree requirements. It is …
Applied Math and Computer Science - uwm.edu
Science. The degree is highly technical in nature yet still retains the flavor of a liberal arts degree through humanities and social science course requirements beyond the minimum required by …
Bachelor of Science, Computer Science program guide
Bachelor of Science, Computer Science The Bachelor of Science in Computer Science prepares students for a career in the high demand field of Computer Science. Upon program completion, …
Computer Engineering Graduation Requirements - University …
from the list of approved natural science courses in the CSE Handbook. Five additional credits of natural science (5) from the approved list Computer Science Component Required (29 credits) …
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Bachelor of Science in Computer Science - Florida Atlantic …
Computer. Operating Systems. COP 4610 (3) Introduction to. Microprocessor. Systems. CDA 3331C (3) Data. Structures. COP 3530 (3) Introduction to . Programming. In “C” COP 2220 (3) …
Important Information About Your Degree - cos.unt.edu
With Concentration in Computer Science (BS MATH CSCI) 2024 - 2025 Advising Handout Important Information About Your Degree College of Science Admission Requirement: …
Associate in Science in Computer Science for Transfer …
Computer and Information Sciences San Diego MiraMar College • 2019–2020 Associate in Science in Computer Science for Transfer Degree: The Associate in Science in Computer …
Mathematics for Computer Science - IIT Guwahati
lems that arise in computer science. Proofs play a central role in this work because the authors share a belief with most mathematicians that proofs are essential for genuine understanding. …
B.S. Computer Science (CS 26): Major Checklist, Fall 2021
B.S. Computer Science (CS 26): Major Checklist, Fall 2021 ALL major requirements must be taken for letter grade AND passed with a C- or better with the exceptions ... fulfill other degree …
Transfer Guide: Computer Science - Bachelor of Science
MATH 2305 Linear Algebra MATH 2318: Calculus II MATH 2414 MATH 2414 Computer Science I COSC (Python preferred) 1336 or 1436 CSCI 1470 Computer Science II (Java preferred) …
Degree Pathway for A.S. in Computer Science 2024-25 …
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First Year - Collin College
AS w/Computer Science & Information Technology Field of Study Third Year – University of North Texas Students must fulfill UNT admissions requirements which can be found on the UNT …
