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| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: Generatingfunctionology Herbert S. Wilf, 2014-05-10 Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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 |
| best math courses for computer science: Good Math Mark C. Chu-Carroll, 2013-07-18 Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular Good Math blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you. |
| best math courses for computer science: 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 |
| best math courses for computer science: Computer Science Robert Sedgewick, Kevin Wayne, 2016-06-17 Named a Notable Book in the 21st Annual Best of Computing list by the ACM! Robert Sedgewick and Kevin Wayne’s Computer Science: An Interdisciplinary Approach is the ideal modern introduction to computer science with Java programming for both students and professionals. Taking a broad, applications-based approach, Sedgewick and Wayne teach through important examples from science, mathematics, engineering, finance, and commercial computing. The book demystifies computation, explains its intellectual underpinnings, and covers the essential elements of programming and computational problem solving in today’s environments. The authors begin by introducing basic programming elements such as variables, conditionals, loops, arrays, and I/O. Next, they turn to functions, introducing key modular programming concepts, including components and reuse. They present a modern introduction to object-oriented programming, covering current programming paradigms and approaches to data abstraction. Building on this foundation, Sedgewick and Wayne widen their focus to the broader discipline of computer science. They introduce classical sorting and searching algorithms, fundamental data structures and their application, and scientific techniques for assessing an implementation’s performance. Using abstract models, readers learn to answer basic questions about computation, gaining insight for practical application. Finally, the authors show how machine architecture links the theory of computing to real computers, and to the field’s history and evolution. For each concept, the authors present all the information readers need to build confidence, together with examples that solve intriguing problems. Each chapter contains question-and-answer sections, self-study drills, and challenging problems that demand creative solutions. Companion web site (introcs.cs.princeton.edu/java) contains Extensive supplementary information, including suggested approaches to programming assignments, checklists, and FAQs Graphics and sound libraries Links to program code and test data Solutions to selected exercises Chapter summaries Detailed instructions for installing a Java programming environment Detailed problem sets and projects Companion 20-part series of video lectures is available at informit.com/title/9780134493831 |
| best math courses for computer science: The Discrete Math Workbook Sergei Kurgalin, Sergei Borzunov, 2018-07-31 This practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments. Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language. |
| best math courses for computer science: 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 |
| best math courses for computer science: 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. |
| best math courses for computer science: Methods of Mathematics Applied to Calculus, Probability, and Statistics Richard W. Hamming, 2012-06-28 This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: Probability and Statistics for Computer Science David Forsyth, 2017-12-13 This textbook is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning. With careful treatment of topics that fill the curricular needs for the course, Probability and Statistics for Computer Science features: • A treatment of random variables and expectations dealing primarily with the discrete case. • A practical treatment of simulation, showing how many interesting probabilities and expectations can be extracted, with particular emphasis on Markov chains. • A clear but crisp account of simple point inference strategies (maximum likelihood; Bayesian inference) in simple contexts. This is extended to cover some confidence intervals, samples and populations for random sampling with replacement, and the simplest hypothesis testing. • A chapter dealing with classification, explaining why it’s useful; how to train SVM classifiers with stochastic gradient descent; and how to use implementations of more advanced methods such as random forests and nearest neighbors. • A chapter dealing with regression, explaining how to set up, use and understand linear regression and nearest neighbors regression in practical problems. • A chapter dealing with principal components analysis, developing intuition carefully, and including numerous practical examples. There is a brief description of multivariate scaling via principal coordinate analysis. • A chapter dealing with clustering via agglomerative methods and k-means, showing how to build vector quantized features for complex signals. Illustrated throughout, each main chapter includes many worked examples and other pedagogical elements such as boxed Procedures, Definitions, Useful Facts, and Remember This (short tips). Problems and Programming Exercises are at the end of each chapter, with a summary of what the reader should know. Instructor resources include a full set of model solutions for all problems, and an Instructor's Manual with accompanying presentation slides. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz, 2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutions If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! |
| best math courses for computer science: 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. |
| best math courses for computer science: Statistical Methods in Bioinformatics Warren J. Ewens, Gregory R. Grant, 2005-09-30 Advances in computers and biotechnology have had a profound impact on biomedical research, and as a result complex data sets can now be generated to address extremely complex biological questions. Correspondingly, advances in the statistical methods necessary to analyze such data are following closely behind the advances in data generation methods. The statistical methods required by bioinformatics present many new and difficult problems for the research community. This book provides an introduction to some of these new methods. The main biological topics treated include sequence analysis, BLAST, microarray analysis, gene finding, and the analysis of evolutionary processes. The main statistical techniques covered include hypothesis testing and estimation, Poisson processes, Markov models and Hidden Markov models, and multiple testing methods. The second edition features new chapters on microarray analysis and on statistical inference, including a discussion of ANOVA, and discussions of the statistical theory of motifs and methods based on the hypergeometric distribution. Much material has been clarified and reorganized. The book is written so as to appeal to biologists and computer scientists who wish to know more about the statistical methods of the field, as well as to trained statisticians who wish to become involved with bioinformatics. The earlier chapters introduce the concepts of probability and statistics at an elementary level, but with an emphasis on material relevant to later chapters and often not covered in standard introductory texts. Later chapters should be immediately accessible to the trained statistician. Sufficient mathematical background consists of introductory courses in calculus and linear algebra. The basic biological concepts that are used are explained, or can be understood from the context, and standard mathematical concepts are summarized in an Appendix. Problems are provided at the end of each chapter allowing the reader to develop aspects of the theory outlined in the main text. Warren J. Ewens holds the Christopher H. Brown Distinguished Professorship at the University of Pennsylvania. He is the author of two books, Population Genetics and Mathematical Population Genetics. He is a senior editor of Annals of Human Genetics and has served on the editorial boards of Theoretical Population Biology, GENETICS, Proceedings of the Royal Society B and SIAM Journal in Mathematical Biology. He is a fellow of the Royal Society and the Australian Academy of Science. Gregory R. Grant is a senior bioinformatics researcher in the University of Pennsylvania Computational Biology and Informatics Laboratory. He obtained his Ph.D. in number theory from the University of Maryland in 1995 and his Masters in Computer Science from the University of Pennsylvania in 1999. Comments on the first edition: This book would be an ideal text for a postgraduate course...[and] is equally well suited to individual study.... I would recommend the book highly. (Biometrics) Ewens and Grant have given us a very welcome introduction to what is behind those pretty [graphical user] interfaces. (Naturwissenschaften) The authors do an excellent job of presenting the essence of the material without getting bogged down in mathematical details. (Journal American Statistical Association) The authors have restructured classical material to a great extent and the new organization of the different topics is one of the outstanding services of the book. (Metrika) |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: Discrete Structures, Logic, and Computability James L. Hein, 2001 Discrete Structure, Logic, and Computability introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic, and computability. The emphasis is on the computational aspects, so that the reader can see how the concepts are actually used. Because of logic's fundamental importance to computer science, the topic is examined extensively in three phases that cover informal logic, the technique of inductive proof; and formal logic and its applications to computer science. |
| best math courses for computer science: Discrete Mathematics for Computer Science Jon Pierre Fortney, 2020-12-23 Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook. |
| best math courses for computer science: 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. |
| best math courses for computer science: 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. |
| best math courses for computer science: Math for Programmers Paul Orland, 2021-01-12 In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks |
| best math courses for computer science: White Awareness Judy H. Katz, 1978 Stage 1. |
| best math courses for computer science: The Science of Reading Margaret J. Snowling, Charles Hulme, 2008-04-15 The Science of Reading: A Handbook brings together state-of-the-art reviews of reading research from leading names in the field, to create a highly authoritative, multidisciplinary overview of contemporary knowledge about reading and related skills. Provides comprehensive coverage of the subject, including theoretical approaches, reading processes, stage models of reading, cross-linguistic studies of reading, reading difficulties, the biology of reading, and reading instruction Divided into seven sections:Word Recognition Processes in Reading; Learning to Read and Spell; Reading Comprehension; Reading in Different Languages; Disorders of Reading and Spelling; Biological Bases of Reading; Teaching Reading Edited by well-respected senior figures in the field |
| best math courses for computer science: Handbook of Analysis and Its Foundations Eric Schechter, 1996-10-24 Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/ |
| best math courses for computer science: The Reasoned Schemer, second edition Daniel P. Friedman, William E. Byrd, Oleg Kiselyov, Jason Hemann, 2018-03-09 A new edition of a book, written in a humorous question-and-answer style, that shows how to implement and use an elegant little programming language for logic programming. The goal of this book is to show the beauty and elegance of relational programming, which captures the essence of logic programming. The book shows how to implement a relational programming language in Scheme, or in any other functional language, and demonstrates the remarkable flexibility of the resulting relational programs. As in the first edition, the pedagogical method is a series of questions and answers, which proceed with the characteristic humor that marked The Little Schemer and The Seasoned Schemer. Familiarity with a functional language or with the first five chapters of The Little Schemer is assumed. For this second edition, the authors have greatly simplified the programming language used in the book, as well as the implementation of the language. In addition to revising the text extensively, and simplifying and revising the “Laws” and “Commandments,” they have added explicit “Translation” rules to ease translation of Scheme functions into relations. |
| best math courses for computer science: Discrete Mathematics with Graph Theory (Classic Version) Edgar Goodaire, Michael Parmenter, 2017-03-20 This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. Far more user friendly than the vast majority of similar books, this text is truly written with the beginning reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize Active Reading, a skill vital to success in learning how to think mathematically (and write clean, error-free programs). |
| best math courses for computer science: MODERN ALGEBRA WITH APPLICATIONS William J Gilbert, 2008-09 Market_Desc: Upper undergraduate and graduate level modern algebra courses Special Features: · Includes applications so students can see right away how to use the theory· This classic text has sold almost 12,000 units· Contains numerous examples· Includes chapters on Boolean Algebras, groups, quotient groups, symmetry groups in three dimensions, Polya-Burnside method of enumeration, monoids and machines, rings and fields, polynomial and Euclidean rings, quotient rings, field extensions, Latin squares, geometrical constructions, and error-correcting codes· Andwers to odd-numbered exercises so students can check their work About The Book: The book covers all the group, ring, and field theory that is usually contained in a standard modern algebra course; the exact sections containing this material are indicated in the Table of Contents. It stops short of the Sylow theorems and Galois theory. These topics could only be touched on in a first course, and the author feels that more time should be spent on them if they are to be appreciated. |
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 in Computer Science Curricula
Discrete Math and Logic are essential for CS. Probability & Statistics. Calculus, Discrete Math, Logic, Linear Algebra, Probability, Statistics. Algorithms, Data Structures, Semantics, ... 3.
Quick Guide for Computer Science - Mathematics
The program requires a total of at least 44-47 points: 19-20 points in Computer Science, 19-21 points in Mathematics, and two 3-point electives in either CS or Math. This guide is for your …
CS 311 Discrete Mathematics for Computer Science Fall 2020
Discrete mathematics provides the mathematical foundations for many computer science classes, including data structures, algorithms, database theory, automata theory, formal languages, …
Computer Studies or Cybersecurity MATH PATHS
Picking the math courses that fast-track you towards your goals? It’s as easy as 1-2-3. If your goal is to enter the workforce in Cybersecurity or transfer to a four-year Computer Science or …
Mathematics for Computer Science - Massachusetts Institute …
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. …
CS230 Spring 2024 Discrete Math for Computer Science …
Familiarize yourself with math concepts and tools essential for advanced topics in computer science. Is the writing logically solid? Is the writing clear and easy to understand? Does the …
Mathematics B.S. Degree - Computational Track - College of …
Computational math students can receive an override from the CS undergraduate advisor into the courses that have this prerequisite, as long as they have completed COP 3503C. Note: …
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 …
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 …
Mathematics for Computer Science Eric Lehman and Tom …
CONTENTS 5 6.1.3 Graph Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.1.4 Applications of Graphs ...
Computer Science/Mathematics Curriculum Pepperdine …
The computer science part of the contract major is satisfied by completing a core of seven courses plus one elective. Contract major core Math 220, Formal Methods CoSc 220, …
Mathematics for Computer Science First Edition
Let’s number the students by their order in line, starting the count with 0, as usual in Computer Science. Now we can understand the second rule as a short description of a whole sequence …
MATHEMATICS OF COMPUTATION B.S.
For more information and help with enrollment in CS courses, contact Engineering. THE MAJOR: 14 COURSES Students must declare the major before reaching 160 units (not including AP …
Mathematics for Computer Science - MIT OpenCourseWare
lems that arise in computer science. The notion of a proof plays a central role in this work. Simply put, a proof is a method of establishing truth. Like beauty, “truth” some-times depends on the …
Course Information Sheet [Mathematics and Computer Science]
Mathematics is a fundamental intellectual tool in computing, but computing is increasingly used as a key component in mathematical problem-solving. The course concentrates on areas where …
Mathematics for Computer Science - IIT Guwahati
Mathematics for Computer Science revised Monday 9th May, 2011, 20:49 Eric Lehman Google Inc. F Thomson Leighton Department of Mathematics and CSAIL, MIT Akamai Technologies ...
Mathematics for Computer Science - Massachusetts Institute …
Jun 17, 2010 · 4 CONTENTS Potential Pitfall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 2.3 Good Proofs in Practice ...
Mathematics for Computer Science - MIT OpenCourseWare
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. …
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 in Computer Science Curricula
Discrete Math and Logic are essential for CS. Probability & Statistics. Calculus, Discrete Math, Logic, Linear Algebra, Probability, Statistics. Algorithms, Data Structures, Semantics, ... 3.
Quick Guide for Computer Science - Mathematics
The program requires a total of at least 44-47 points: 19-20 points in Computer Science, 19-21 points in Mathematics, and two 3-point electives in either CS or Math. This guide is for your …
Department of Mathematics - MIT Course Catalog
Course 18 includes two undergraduate degrees: a Bachelor of Science in Mathematics and a Bachelor of Science in Mathematics with Computer Science. Undergraduate students may …
CS 311 Discrete Mathematics for Computer Science Fall 2020
Discrete mathematics provides the mathematical foundations for many computer science classes, including data structures, algorithms, database theory, automata theory, formal languages, …
Computer Studies or Cybersecurity MATH PATHS
Picking the math courses that fast-track you towards your goals? It’s as easy as 1-2-3. If your goal is to enter the workforce in Cybersecurity or transfer to a four-year Computer Science or …
Mathematics for Computer Science - Massachusetts Institute …
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. …
CS230 Spring 2024 Discrete Math for Computer Science …
Familiarize yourself with math concepts and tools essential for advanced topics in computer science. Is the writing logically solid? Is the writing clear and easy to understand? Does the …
Mathematics B.S. Degree - Computational Track - College of …
Computational math students can receive an override from the CS undergraduate advisor into the courses that have this prerequisite, as long as they have completed COP 3503C. Note: …
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 …
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 …
Mathematics for Computer Science Eric Lehman and Tom …
CONTENTS 5 6.1.3 Graph Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.1.4 Applications of Graphs ...
Computer Science/Mathematics Curriculum Pepperdine …
The computer science part of the contract major is satisfied by completing a core of seven courses plus one elective. Contract major core Math 220, Formal Methods CoSc 220, …
Mathematics for Computer Science First Edition
Let’s number the students by their order in line, starting the count with 0, as usual in Computer Science. Now we can understand the second rule as a short description of a whole sequence …
MATHEMATICS OF COMPUTATION B.S.
For more information and help with enrollment in CS courses, contact Engineering. THE MAJOR: 14 COURSES Students must declare the major before reaching 160 units (not including AP …
Mathematics for Computer Science - MIT OpenCourseWare
lems that arise in computer science. The notion of a proof plays a central role in this work. Simply put, a proof is a method of establishing truth. Like beauty, “truth” some-times depends on the …
Course Information Sheet [Mathematics and Computer Science]
Mathematics is a fundamental intellectual tool in computing, but computing is increasingly used as a key component in mathematical problem-solving. The course concentrates on areas where …
Mathematics for Computer Science - IIT Guwahati
Mathematics for Computer Science revised Monday 9th May, 2011, 20:49 Eric Lehman Google Inc. F Thomson Leighton Department of Mathematics and CSAIL, MIT Akamai Technologies …
Mathematics for Computer Science - Massachusetts Institute …
Jun 17, 2010 · 4 CONTENTS Potential Pitfall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 2.3 Good Proofs in Practice ...
