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| computer science without math: Computer Mathematics for Programmers Darrell H. Abney, Laurence Rubin, Donald W. Sibrel, 2014-05-09 Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer. The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer programming. Subsequent chapters focuses on specific mathematical topics such as algebra, sets, logic, Boolean algebra, matrices, graphing and linear programming, and statistics. Students of computer programming will find the text very useful. |
| computer science without 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 without 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 without 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 without 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 without 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 without math: 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 without math: 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 without 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 without math: Building Bridges Martin Grötschel, Gyula O.H. Katona, 2010-05-28 Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers. |
| computer science without 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 without 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 without math: Classic Computer Science Problems in Java David Kopec, 2020-12-21 Sharpen your coding skills by exploring established computer science problems! Classic Computer Science Problems in Java challenges you with time-tested scenarios and algorithms. Summary Sharpen your coding skills by exploring established computer science problems! Classic Computer Science Problems in Java challenges you with time-tested scenarios and algorithms. You’ll work through a series of exercises based in computer science fundamentals that are designed to improve your software development abilities, improve your understanding of artificial intelligence, and even prepare you to ace an interview. As you work through examples in search, clustering, graphs, and more, you'll remember important things you've forgotten and discover classic solutions to your new problems! Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Whatever software development problem you’re facing, odds are someone has already uncovered a solution. This book collects the most useful solutions devised, guiding you through a variety of challenges and tried-and-true problem-solving techniques. The principles and algorithms presented here are guaranteed to save you countless hours in project after project. About the book Classic Computer Science Problems in Java is a master class in computer programming designed around 55 exercises that have been used in computer science classrooms for years. You’ll work through hands-on examples as you explore core algorithms, constraint problems, AI applications, and much more. What's inside Recursion, memoization, and bit manipulation Search, graph, and genetic algorithms Constraint-satisfaction problems K-means clustering, neural networks, and adversarial search About the reader For intermediate Java programmers. About the author David Kopec is an assistant professor of Computer Science and Innovation at Champlain College in Burlington, Vermont. Table of Contents 1 Small problems 2 Search problems 3 Constraint-satisfaction problems 4 Graph problems 5 Genetic algorithms 6 K-means clustering 7 Fairly simple neural networks 8 Adversarial search 9 Miscellaneous problems 10 Interview with Brian Goetz |
| computer science without 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 without 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 without math: Introduction to Computational Science Angela B. Shiflet, George W. Shiflet, 2014-03-30 The essential introduction to computational science—now fully updated and expanded Computational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This textbook provides students with a versatile and accessible introduction to the subject. It assumes only a background in high school algebra, enables instructors to follow tailored pathways through the material, and is the only textbook of its kind designed specifically for an introductory course in the computational science and engineering curriculum. While the text itself is generic, an accompanying website offers tutorials and files in a variety of software packages. This fully updated and expanded edition features two new chapters on agent-based simulations and modeling with matrices, ten new project modules, and an additional module on diffusion. Besides increased treatment of high-performance computing and its applications, the book also includes additional quick review questions with answers, exercises, and individual and team projects. The only introductory textbook of its kind—now fully updated and expanded Features two new chapters on agent-based simulations and modeling with matrices Increased coverage of high-performance computing and its applications Includes additional modules, review questions, exercises, and projects An online instructor's manual with exercise answers, selected project solutions, and a test bank and solutions (available only to professors) An online illustration package is available to professors |
| computer science without 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 without 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 without 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 without math: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| computer science without math: A Tour of the Calculus David Berlinski, 2011-04-27 Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others.--New York Times Book Review |
| computer science without math: 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 without math: Supervised Learning with Quantum Computers Maria Schuld, Francesco Petruccione, 2018-08-30 Quantum machine learning investigates how quantum computers can be used for data-driven prediction and decision making. The books summarises and conceptualises ideas of this relatively young discipline for an audience of computer scientists and physicists from a graduate level upwards. It aims at providing a starting point for those new to the field, showcasing a toy example of a quantum machine learning algorithm and providing a detailed introduction of the two parent disciplines. For more advanced readers, the book discusses topics such as data encoding into quantum states, quantum algorithms and routines for inference and optimisation, as well as the construction and analysis of genuine ``quantum learning models''. A special focus lies on supervised learning, and applications for near-term quantum devices. |
| computer science without math: Logic for Mathematics and Computer Science Stanley Burris, 1998 This text is intended for one semester courses in Logic, it can also be applied to a two semester course, in either Computer Science or Mathematics Departments. Unlike other texts on mathematical logic that are either too advanced, too sparse in examples or exercises, too traditional in coverage, or too philosophical in approach, this text provides an elementary hands-on presentation of important mathematical logic topics, new and old, that is readily accessible and relevant to all students of the mathematical sciences -- not just those in traditional pure mathematics. |
| computer science without math: 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 without math: Doing Math with Python Amit Saha, 2015-08-01 Doing Math with Python shows you how to use Python to delve into high school–level math topics like statistics, geometry, probability, and calculus. You’ll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once you’ve gotten the hang of things. Along the way, you’ll discover new ways to explore math and gain valuable programming skills that you’ll use throughout your study of math and computer science. Learn how to: –Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots –Explore set theory and probability with programs for coin flips, dicing, and other games of chance –Solve algebra problems using Python’s symbolic math functions –Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set –Write programs to find derivatives and integrate functions Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. You’ll write an inequality solver, plot gravity’s effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 darts at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more. Whether you’re interested in math but have yet to dip into programming or you’re a teacher looking to bring programming into the classroom, you’ll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math. Uses Python 3 |
| computer science without 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 without 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 without 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 without math: Constructive Analysis E. Bishop, Douglas Bridges, 2012-12-06 This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett. |
| computer science without math: 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 without math: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| computer science without math: 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 without 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 without math: The Multivariate Algorithmic Revolution and Beyond Hans L. Bodlaender, Rodney Downey, Fedor V. Fomin, Dániel Marx, 2012-06-16 Parameterized complexity is currently a thriving field in complexity theory and algorithm design. A significant part of the success of the field can be attributed to Michael R. Fellows. This Festschrift has been published in honor of Mike Fellows on the occasion of his 60th birthday. It contains 20 papers that showcase the important scientific contributions of this remarkable man, describes the history of the field of parameterized complexity, and also reflects on other parts of Mike Fellows’s unique and broad range of interests, including his work on the popularization of discrete mathematics for young children. The volume contains several surveys that introduce the reader to the field of parameterized complexity and discuss important notions, results, and developments in this field. |
| computer science without math: 3D Math Primer for Graphics and Game Development, 2nd Edition Fletcher Dunn, Ian Parberry, 2011-11-02 This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves. |
| computer science without math: Principles of Mathematics Carl Barnett Allendoerfer, Cletus Odia Oakley, 1953 |
| computer science without math: Types and Programming Languages Benjamin C. Pierce, 2002-01-04 A comprehensive introduction to type systems and programming languages. A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems—and of programming languages from a type-theoretic perspective—has important applications in software engineering, language design, high-performance compilers, and security. This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages. |
| computer science without 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 without 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 - Wikipedia
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