Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book 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. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.
Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.
by Professor of Mathematics Marywood University Scranton Pennsylvania Craig Johnson
Author: Professor of Mathematics Marywood University Scranton Pennsylvania Craig Johnson
Publisher: Jones & Bartlett Publishers
Includes Access to Student Companion Website! Exploring Mathematics: Investigations with Functions is designed for one- or two- term mathematics courses for humanities and liberal arts majors. This unique ten-chapter text covers modern applications of mathematics in the liberal arts and situates the discipline within its rich and varied history. Exploring Mathematics draws on examples from the humanities, including how math is used in music and astronomy, and features perforated pages for easy study and review. The student-friendly writing style and informal approach demystifies the subject matter and offers an engaging and informative overview that will pique students curiosity and desire to explore mathematics further. Organized around the use of algebraic functions, this text builds conceptual bridges between each chapter so that students develop advanced mathematical skills within a larger context. Unlike other texts that present mathematical topics as a disconnected set of rules and equations, Exploring Mathematics flows seamlessly from one subject to the next, situating each within its historical and cultural context. This text provides a unique opportunity to showcase the richness of mathematics as a foundation upon which to build understanding of many different phenomena. Students will come away with a solid knowledge base of the unifying ideas of mathematics and the ability to explain how mathematics helps us to better our society and understand the world around us. The Text's Objectives: The author chose the topics based on meeting the specific NCTM curriculum standards to: 1. Strengthen estimation and computational skills. 2. Utilize algebraic concepts. 3. Emphasize problem-solving and reasoning. 4. Emphasize pattern and relationship recognition. 5. Highlight importance of units in measurement. 6. Highlight importance of the notion of a mathematical function. 7. Display mathematical connections to other disciplines. Key Features: A full color, interactive design provides students with a safe environment to graph solutions, check off chapter objectives, and answer questions directly in their textbook Piques student interest in math by relating it to areas such as astronomy and music, found in Chapter 4, Astronomy and the Methods of Science and Chapter 9, Mathematics in Music and Cryptology Utilizes the concept of a function as a central theme, providing a common thread through chapters Presents an engaging, student-friendly style with problem sets that incorporate real-world applications and data An abundance of examples illustrating important applications are presented in each section, while four-color pictures and diagrams reinforce key concepts and increase student comprehension Every new, printed copy includes access to a student companion website, featuring a lab manual and student solutions manual"
Modern and comprehensive, the new Fifth Edition of Zill's Advanced Engineering Mathematics, Fifth Edition provides an in depth overview of the many mathematical topics required for students planning a career in engineering or the sciences. A key strength of this best-selling text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fifth Edition is a full compendium of topics that are most often covered in the Engineering Mathematics course or courses, and is extremely flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. The new edition offers a reorganized project section to add clarity to course material and new content has been added throughout, including new discussions on: Autonomous Des and Direction Fields; Translation Property, Bessel Functions, LU-Factorization, Da Vinci's apparatus for determining speed and more. The Essentials of Computer Organization and Architecture, Fourth Edition was recently awarded a "Textbook Excellence Award" (“Texty”) from the Text and Academic Authors Association (TAA) the only association devoted solely to serving textbook and academic authors since 1987 (www.TAAonline.net). The "Textbook Excellence Award" recognizes works for their excellence in the areas of content, presentation, appeal, and teachability. This is the third Texty award for Null and Lobur. They also won for their Second and Third Editions of this text. New and Key Features of the Fifth Edition: - Eight all-new contributed applied project problems spread throughout the text, including an in-depth discussion of the mathematics and history of the Paris Guns of World War I - An all-new section on the LU-factorization of a matrix - Updated examples throughout - Revisions and reorganization throughout the text to improve clarity and flow - An expanded discussion of spherical Bessel functions - All-new boundary-value problems added to the chapters on partial differential equations - Two new chapters, Probability and Statistics, are available online - Projects, formerly found at the beginning of the text, are now included within the appropriate chapters. - The Student Companion Website, included with every new copy, includes a wealth of study aids, learning tools, projects, and essays to enhance student learning - Instructor materials include: complete instructor solutions manual, PowerPoint Image Bank, and Test Bank - Available with WebAssign with full integrated eBook
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in undergraduate Analysis and Transition to Advanced Mathematics. Analysis with an Introduction to Proof, Fifth Edition helps fill in the groundwork students need to succeed in real analysis—often considered the most difficult course in the undergraduate curriculum. By introducing logic and emphasizing the structure and nature of the arguments used, this text helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable, student-oriented, and teacher- friendly.
Designed for economics, business, or social or behavioral science majors in a one- or two-term course, Brief Calculus for the Business, Social, and Life Sciences presents mathematics in a clear and accessible language. Engaging, real-world examples and real data applications make calculus relevant, and the easy-to-read conversational style of the text evokes the one-on-one communication of a personalized tutorial session without sacrificing depth of coverage or intellectual rigor. The revised and updated Third Edition of this popular text includes a new, four-step problem-solving method that allows students to independently find solutions to a broad spectrum of problem sets. Rich in pedagogical features, this text includes comprehensive exercise sets, chapter openers that outline key concepts for each chapter, and Flashback features that revisit and reinforce content from previous chapters. The Third Edition contains all-new exercises, updated real-world data for modeling applications, and Section Objectives that provide students with a clear understanding of learning goals for each section. The text is packaged with a full ancillary suite of instructor resources, including a test bank, lecture outlines in PowerPoint format, WebAssign, and a Complete Solutions Manual; additional student resources include a Student Solutions Manual and access to the student companion website. Brief Calculus for the Business, Social, and Life Sciences is a comprehensive, student-friendly text that will gently push students to new levels of independent problem-solving. Key features of the new Third Edition include: Optional highlighted Technology Option sections that point out how solutions can be found using a graphing calculator From Your Toolbox feature that reinforces previously introduced material Real data applications, fully revised and updated for the Third Edition, that keep problems relevant and interesting Comprehensive exercise sets, including Concept and Writing Exercises, Vocabulary Exercises, and Application Exercises Clearly defined four-step problem-solving method new to the Third Edition User-friendly, conversational approach that mimics the style of an individualized tutorial session Chapter Openers and Section Objectives that clearly outline key concepts for each chapter and section Section Projects that encourage further study, reflection, and independent research A full suite of ancillary student and instructor resources"
This text is designed for the average to strong mathematics major taking a course called Transition to Higher Mathematics, Introduction to Proofs, or Fundamentals of Mathematics. It provides a transition to topics covered in advanced mathematics and covers logic, proofs and sets and emphasizes two important mathematical activities - finding examples of objects with specified properties and writing proofs.
This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content.