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College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
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.
This easy-to-use packet is full of stimulating activities that will give your students a solid introduction to relations and functions! A variety of lessons, puzzles, mazes, and practice problems will challenge students to think creatively as they work to build their precalculus skills. Each lesson begins with a clear explanation and provides extra review and reinforcement.
Currently there is a movement in linguistics towards careful use of corpora in linguistic and text analysis, which has involved both written and spoken corpora and those which combine spoken and written text. Most text analyses address written texts - often literary works - but detailed discussion of the language of a single oral text from multiple perspectives has rarely been published. This book is among the first to integrate the analysis of the language of spoken and written texts. It describes language as a network of functional relations involving a context which is also a network of functional relations. The essays in Part One present several perspectives on the theory of language as functional relations; those in Part Two discuss a single oral text using a variety of functional perspectives. All of the essays are by linguists interested in oral and written texts, who have achieved international recognition in their fields. Illustrated in this book are cognitive, social construction, social praxis and anthropological approaches to the description of text.
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.
When first published in 1959, this book was the basis of a two-semester course in complex analysis for upper undergraduate and graduate students. J. S. Mac Nerney was a proponent of the Socratic, or “do-it-yourself” method of learning mathematics, in which students are encouraged to engage in mathematical problem solving, including theorems at every level which are often regarded as “too difficult” for students to prove for themselves. Accordingly, Mac Nerney provides no proofs. What he does instead is to compose and arrange the investigation in his own unique style, so that a contextual proof is always available to the persistent student who enjoys a challenge. The central idea is to empower students by allowing them to discover and rely on their own mathematical abilities. This text may be used in a variety of settings, including: the usual classroom or seminar, but with the teacher acting mainly as a moderator while the students present their discoveries, a small-group setting in which the students present their discoveries to each other, and independent study. The Editors, William E. Kaufman (who was Mac Nerney’s last PhD student) and Ryan C. Schwiebert, have composed the original typed Work into LaTeX ; they have updated the notation, terminology, and some of the prose for modern usage, but the organization of content has been strictly preserved. About this Book, some new exercises, and an index have also been added.