This text is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus.

Short Description:
This is book one in a six-book series on fundamental mathematics for adult learners. These books include glossaries, self tests, practice requests, grades records, and unit tests. Ancillary Resources include the Instructor's Manual. Topics in this book include: number and number operations, patterns, functions and relations, real life applications, geometry, and time. These books align with the learning outcomes for Adult Fundamental Math as outlined in the BC ABE Articulation Handbook.

Word Count: 22762

ISBN: 978-1-77420-118-3

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

: Fundamental mathematics for adult learners. Book 1 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

: Fundamental mathematics for adult learners. Book 2 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

: Fundamental mathematics for adult learners. Book 3 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

: Fundamental mathematics for adult learners. Book 4 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

: Fundamental mathematics for adult learners. Book 5 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

: Fundamental mathematics for adult learners. Book 6 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

An open-source textbook covering vector calculus, ordinary and partial differential equations, and Fourier series. The textbook is used in a first-year graduate level course in the Department of Mechanical Engineering at the Colorado School of Mines. It undergoes extensive revisions annually, but is relatively complete.

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry 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.

This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove 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.

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.

Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE).

Arithmetic | Algebra Homework book is a static version of the WeBWork online homework assignments that accompany the textbook Arithmetic | Algebra for the developmental math courses MAT 0630 and MAT 0650 at New York City College of Technology, CUNY.

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.
The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.

Christopher Hammond, Professor of Mathematics at Connecticut College, published The Art of Analysis, an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a special case of integrability, with particular properties that are worth noting. This point of view has implications for the treatment of other topics, particularly continuity and differentiability.

Word Count: 10612

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)