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| discrete math study guide: 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. |
| discrete math study guide: A Student's Guide to the Study, Practice, and Tools of Modern Mathematics Donald Bindner, Martin Erickson, 2010-11-29 A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R. Along with a color insert, the text include |
| discrete math study guide: The Discrete Math Workbook Sergei Kurgalin, Sergei Borzunov, 2020-08-12 This practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity. This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions. Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, 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 Turing machines, 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 workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language. |
| discrete math study guide: Discrete Mathematics and Graph Theory K. Erciyes, 2021-01-28 This textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer Science or Mathematics curricula. The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications. |
| discrete math study guide: 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. |
| discrete math study guide: Discrete Mathematics with Applications, Metric Edition Susanna Epp, 2019 DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology. |
| discrete math study guide: A Beginner's Guide to Discrete Mathematics W.D. Wallis, 2011-10-07 Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a 'beginner's guide', this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. —Zentralblatt Math (Review of the First Edition) This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter * Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and computer science, however, featured special topics and applications may also interest graduate students. |
| discrete math study guide: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
| discrete math study guide: Discrete Mathematics and Its Applications Kenneth H. Rosen, 2018-05 A precise, relevant, comprehensive approach to mathematical concepts... |
| discrete math study guide: 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. |
| discrete math study guide: 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. |
| discrete math study guide: 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. |
| discrete math study guide: Discrete Mathematics Using a Computer John O'Donnell, Cordelia Hall, Rex Page, 2007-01-04 Computer science abounds with applications of discrete mathematics, yet s- dents of computer science often study discrete mathematics in the context of purely mathematical applications. They have to ?gure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad success in this enterprise, which is not surprising, since many of the most important advances in science and engineeringhavebeen, precisely, applicationsofmathematicstospeci?cscience and engineering problems. Tobesure,mostdiscretemathtextbooksincorporatesomeaspectsapplying discrete math to computing, but it usually takes the form of asking students to write programs to compute the number of three-ball combinations there are in a set of ten balls or, at best, to implement a graph algorithm. Few texts ask students to use mathematical logic to analyze properties of digital circuits or computer programs or to apply the set theoretic model of functions to understand higher-order operations. A major aim of this text is to integrate, tightly, the study of discrete mathematics with the study of central problems of computer science. |
| discrete math study guide: Introductory Discrete Mathematics V. K . Balakrishnan, 2012-04-30 This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition. |
| discrete math study guide: Pre-Calculus Demystified Rhonda Huettenmueller, 2005-02-04 Pre-Calculus Demystified leads the reader through all the intricacies and requirements of this essential course Whether you need to pass a class, a college requirement, or get a leg up on more advanced topics, this book provides clear explanation with a wealth of questions, answers and practical examples. Packed with practical examples, graphs, and Q&As, this complete self-teaching guide from the best-selling author of Algebra Demystified covers all the essential topics, including: absolute value, nonlinear inequalities, functions and their graphs, inverses, proportion and ratio, and much more. |
| discrete math study guide: Discrete Mathematics with Ducks Sarah-marie Belcastro, 2018-11-15 Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study |
| discrete math study guide: Loose Leaf for Discrete Mathematics and Its Applications Kenneth H. Rosen, 2011-06-14 Discrete Mathematics and its Applications, Seventh Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. |
| discrete math study guide: A Short Course in Discrete Mathematics Edward A. Bender, S. Gill Williamson, 2005-01-01 What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index. |
| discrete math study guide: 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! |
| discrete math study guide: 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. |
| discrete math study guide: The Tools of Mathematical Reasoning Tamara J. Lakins, 2016-09-08 This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book. |
| discrete math study guide: Discrete Mathematics with Proof Eric Gossett, 2009-06-22 A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics. |
| discrete math study guide: Essentials of Discrete Mathematics David J. Hunter, 2015-08-21 Written for the one-term course, the Third Edition of Essentials of Discrete Mathematics is designed to serve computer science majors as well as students from a wide range of disciplines. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. tudents will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music. |
| discrete math study guide: Practical Discrete Mathematics Ryan T. White, Archana Tikayat Ray, 2021-02-22 A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book. |
| discrete math study guide: Mtle Minnesota Middle Level Mathematics (5-8) Teacher Certification Test Prep Study Guide Sharon A. Wynne, 2011-05-10 For those who want to earn their Minnesota certification in middle-level mathematics, this guide covers 14 competencies and 57 skills and, includes a 100-question sample test. |
| discrete math study guide: Street-Fighting Mathematics Sanjoy Mahajan, 2010-03-05 An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license. |
| discrete math study guide: Discrete Mathematical Structures for Computer Science Bernard Kolman, Robert C. Busby, 1987 This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow. |
| discrete math study guide: Schaum's Easy Outline of Discrete Mathematics Seymour Lipschutz, Marc Lipson, 2002-08-12 Boiled-down essentials of the top-selling Schaum's Outline series for the student with limited time What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials. Designed to appeal to underprepared students and readers turned off by dense text Cartoons, sidebars, icons, and other graphic pointers get the material across fast Concise text focuses on the essence of the subject Delivers expert help from teachers who are authorities in their fields Perfect for last-minute test preparation So small and light that they fit in a backpack! |
| discrete math study guide: Mathematics Higher Level for the IB Diploma Option Topic 10 Discrete Mathematics Paul Fannon, Vesna Kadelburg, Ben Woolley, Stephen Ward, 2013-04-25 This title forms part of the completely new Mathematics for the IB Diploma series. This highly illustrated book covers topic 10 of the IB Diploma Higher Level Mathematics syllabus, the optional topic Discrete Mathematics. It is also for use with the further mathematics course. Based on the new group 5 aims, the progressive approach encourages cumulative learning. Features include: a dedicated chapter exclusively for mixed examination practice; plenty of worked examples; questions colour-coded according to grade; exam-style questions; feature boxes throughout of exam hints and tips. |
| discrete math study guide: Mathematical Proofs Gary Chartrand, Albert D. Polimeni, Ping Zhang, 2013 This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. |
| discrete math study guide: How to Become a Straight-A Student Cal Newport, 2006-12-26 Looking to jumpstart your GPA? Most college students believe that straight A’s can be achieved only through cramming and painful all-nighters at the library. But Cal Newport knows that real straight-A students don’t study harder—they study smarter. A breakthrough approach to acing academic assignments, from quizzes and exams to essays and papers, How to Become a Straight-A Student reveals for the first time the proven study secrets of real straight-A students across the country and weaves them into a simple, practical system that anyone can master. You will learn how to: • Streamline and maximize your study time • Conquer procrastination • Absorb the material quickly and effectively • Know which reading assignments are critical—and which are not • Target the paper topics that wow professors • Provide A+ answers on exams • Write stellar prose without the agony A strategic blueprint for success that promises more free time, more fun, and top-tier results, How to Become a Straight-A Student is the only study guide written by students for students—with the insider knowledge and real-world methods to help you master the college system and rise to the top of the class. |
| discrete math study guide: 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. |
| discrete math study guide: Book of Proof Richard H. Hammack, 2016-01-01 This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. |
| discrete math study guide: Discrete Mathematics and Its Applications with MathZone Kenneth H. Rosen, 2006-07 Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 600 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide variety of real-world applications ... from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. |
| discrete math study guide: 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. |
| discrete math study guide: Selected Papers on Discrete Mathematics Donald Ervin Knuth, 2003 This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics. |
| discrete math study guide: Student Solutions Manual with Study Guide for Epp's Discrete Mathematics with Applications Susanna S. Epp, 2019-07-10 The Student Solutions Manual contains fully worked-out solutions to all of the exercises not completely answered in Appendix B, and is divisible by 3. The Study Guide also includes alternate explanations for some of the concepts and review questions for each chapter enabling students to gain additional practice and succeed in the course. |
| discrete math study guide: Eureka Math Curriculum Study Guide Common Core, 2015-03-23 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 4 provides an overview of all of the Grade 4 modules, including Place Value, Rounding, and Algorithms for Addition and Subtraction; Unit Conversions and Problem Solving with Metric Measurement; Multi-Digit Multiplication and Division; Angle Measure and Plane Figures; Fraction Equivalence, Ordering, and Operations; Decimal Fractions; and Exploring Measurement with Multiplication. |
| discrete math study guide: Eureka Math Grade 3 Study Guide Great Minds, 2015-11-09 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 3 provides an overview of all of the Grade 3 modules, including Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10; Place Value and Problem Solving with Units of Measure; Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10; Multiplication and Area; Fractions as Numbers on the Number Line; and Collecting and Displaying Data. |
| discrete math study guide: 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. |
Notes on Discrete Mathematics - Yale University
May 9, 2025 · CONTENTS v 5.5 Stronginduction. . . . . . . . . . . . . . . . . . . . . . . . .87 5.5.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . .88
Guide to Studying Discrete Mathematics - Florida State …
Learn definitions, properties, theorems, and formulas. Flash cards can be useful for learning definitions, properties, theorems, and formulas. Complete graded assignments. Work on the …
A Beginner’s Guide to Discrete Mathematics (Second Edition)
This text is a basic introduction to those areas of discrete mathematics of interest to students of mathematics. Introductory courses on this material are now standard at many colleges and …
Discrete Structures Lecture Notes - Stanford University
Discrete Structures Lecture Notes Vladlen Koltun1 Winter 2008 1Computer Science Department, 353 Serra Mall, Gates 374, Stanford University, Stanford, CA 94305, USA; …
Discrete Mathematics - StudyNotesUnisa
This study guide shows you • which parts of the textbook you need to study • which definitions you should learn • which theorems you should be able to prove • which types of problems you …
FRANKLIN UNIVERSITY PROFICIENCY EXAM (FUPE)
STUDY GUIDE Course Title: Discrete Math (MATH 170) Recommended Textbook(s): Discrete Mathematics and its Applications, seventh edition, by Kenneth H. Rosen. The sections noted …
Math 240, Introduction to Discrete Mathematics
This is an introductory course on discrete mathematics. Students will learn: • some fundamental mathematical concepts and terminology; • how to use and analyse recursive definitions; • …
A Beginner’s Guide to Discrete Mathematics - Lakehead …
Text: A Beginner’s Guide to Discrete Mathematics, W.D. Wallis, 2nd edition, Birkh auser, Boston. (Note: This book is available for free download from the Lakehead Library.) Learner …
Final Exam Study Guide Math 181 (Discrete Structures), …
Final Exam Study Guide Math 181 (Discrete Structures), Spring 2024 1. Sets [§1.1] (a) sets of numbers (integers Z and real numbers R), set-builder notation, subsets (A⊆B) (b) operations …
Discrete Math Review - Colorado State University
Discrete Math Review n What you should know about discrete math before the midterm. n Less theory, more problem solving, focuses on exam problems, use as study sheet! CS160 - Fall …
Handout 01: Discrete Math Review Sheet - Department of …
This document is a review of Discrete Math. The following list of definitions, theorems, and examples do not encompass all of Discrete. These are just some aspects we consider to be …
MATH 55 Discrete Mathematics. Course Syllabus
Aug 21, 2016 · Required: \Discrete Mathematics," by Rosen, McGraw-Hill, ISBN 978-0077553487. This is a special version of the textbook, prepared exclusively for the UCB Math Department. …
Discrete Structures Final Exam Study Guide - Kent
Discrete Structures Final Exam Study Guide In what follows, I will give examples for questions similar to the questions in the final exam with a short solution for them. Given a set of possible …
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Math 320 Final Exam Study Guide 1. GENERAL INFORMATION This study guide mostly covers new material since the last midterm, but the final exam will cover all material we have done …
Student's Solutions Guide - Perfect 24 U
This Student's Solutions Guide for Discrete Mathematics and Its Applications, seventh edition, contains several useful and important study aids. • SOLUTIONS TO ODD-NUMBERED …
MATH208: DISCRETE MATHEMATICS - University of North …
11.5 Invertible discrete functions 122 11.6 Characteristic functions 124 11.7 Exercises 125 11.8 Problems 126 12 Special Functions 127 12.1 Floor and ceiling functions 127 12.2 Fractional …
A Short Course in Discrete Mathematics - University of …
The University of California, San Diego, has a lower-division two-quarter course sequence in discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, …
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Discrete Math students seem to appreciate seeing what one of my exams looks like before they take the first one. I think that reducing anxiety is a good thing, so here’s a sample first …
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Definition: If a and b are integers with a ≠ 0, we say that a divides b if there is an integer c such that b = ac. When a divides b we say that a is a factor of b and that b is a multiple of a. The …
Notes on Discrete Mathematics - Yale University
May 9, 2025 · CONTENTS v 5.5 Stronginduction. . . . . . . . . . . . . . . . . . . . . . . . .87 5.5.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . .88
Guide to Studying Discrete Mathematics - Florida State …
Learn definitions, properties, theorems, and formulas. Flash cards can be useful for learning definitions, properties, theorems, and formulas. Complete graded assignments. Work on the …
A Beginner’s Guide to Discrete Mathematics (Second Edition)
This text is a basic introduction to those areas of discrete mathematics of interest to students of mathematics. Introductory courses on this material are now standard at many colleges and …
Discrete Structures Lecture Notes - Stanford University
Discrete Structures Lecture Notes Vladlen Koltun1 Winter 2008 1Computer Science Department, 353 Serra Mall, Gates 374, Stanford University, Stanford, CA 94305, USA; …
Discrete Mathematics - StudyNotesUnisa
This study guide shows you • which parts of the textbook you need to study • which definitions you should learn • which theorems you should be able to prove • which types of problems you …
FRANKLIN UNIVERSITY PROFICIENCY EXAM (FUPE)
STUDY GUIDE Course Title: Discrete Math (MATH 170) Recommended Textbook(s): Discrete Mathematics and its Applications, seventh edition, by Kenneth H. Rosen. The sections noted in …
Math 240, Introduction to Discrete Mathematics
This is an introductory course on discrete mathematics. Students will learn: • some fundamental mathematical concepts and terminology; • how to use and analyse recursive definitions; • how …
A Beginner’s Guide to Discrete Mathematics - Lakehead …
Text: A Beginner’s Guide to Discrete Mathematics, W.D. Wallis, 2nd edition, Birkh auser, Boston. (Note: This book is available for free download from the Lakehead Library.) Learner Outcomes: …
Final Exam Study Guide Math 181 (Discrete Structures), …
Final Exam Study Guide Math 181 (Discrete Structures), Spring 2024 1. Sets [§1.1] (a) sets of numbers (integers Z and real numbers R), set-builder notation, subsets (A⊆B) (b) operations of …
Discrete Math Review - Colorado State University
Discrete Math Review n What you should know about discrete math before the midterm. n Less theory, more problem solving, focuses on exam problems, use as study sheet! CS160 - Fall …
Handout 01: Discrete Math Review Sheet - Department of …
This document is a review of Discrete Math. The following list of definitions, theorems, and examples do not encompass all of Discrete. These are just some aspects we consider to be …
MATH 55 Discrete Mathematics. Course Syllabus
Aug 21, 2016 · Required: \Discrete Mathematics," by Rosen, McGraw-Hill, ISBN 978-0077553487. This is a special version of the textbook, prepared exclusively for the UCB Math Department. …
Discrete Structures Final Exam Study Guide - Kent
Discrete Structures Final Exam Study Guide In what follows, I will give examples for questions similar to the questions in the final exam with a short solution for them. Given a set of possible …
Math 320 Final Exam Study Guide
Math 320 Final Exam Study Guide 1. GENERAL INFORMATION This study guide mostly covers new material since the last midterm, but the final exam will cover all material we have done …
Student's Solutions Guide - Perfect 24 U
This Student's Solutions Guide for Discrete Mathematics and Its Applications, seventh edition, contains several useful and important study aids. • SOLUTIONS TO ODD-NUMBERED …
MATH208: DISCRETE MATHEMATICS - University of North …
11.5 Invertible discrete functions 122 11.6 Characteristic functions 124 11.7 Exercises 125 11.8 Problems 126 12 Special Functions 127 12.1 Floor and ceiling functions 127 12.2 Fractional …
A Short Course in Discrete Mathematics - University of …
The University of California, San Diego, has a lower-division two-quarter course sequence in discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, …
Sample First Midterm Exam — The Questions
Discrete Math students seem to appreciate seeing what one of my exams looks like before they take the first one. I think that reducing anxiety is a good thing, so here’s a sample first …
CSE390D—Introduction to Discrete Math Final Cheat Sheet
Definition: If a and b are integers with a ≠ 0, we say that a divides b if there is an integer c such that b = ac. When a divides b we say that a is a factor of b and that b is a multiple of a. The …
