APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

This module aims to acquaint you with the mathematical aspects of rings and groups and the underlying algebraic structures and when they are looked at as non-empty sets, how their elements are combined by binary operations as well as how those elements behave under transformations such finding inverses. Some non-empty sets, under the operation of addition or multiplication do not include the inverses of their elements as members of the set and they are called semi-groups. The non-empty sets that include the inverses of their elements are full fledged groups. This module fills the gap arising from basic mathematics.

The Abstract Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in September 2019. Team LeadAnna Davis                                         Ohio Dominican UniversityContent ContributorsMatt Davis                                          Muskingum UniversityRob Kelvey                                        College of WoosterLibrarianDaniel Dotson                                    Ohio State University                     Review TeamJim Cottrill                                          Ohio Dominican UniversityBart Snapp                                          Ohio State University

This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

An interactive applet and associated web page that demonstrate the three types of triangle: acute, obtuse and right. The applet shows a triangle that is initially acute (all angles less then 90 degrees) which the user can reshape by dragging any vertex. There is a message changes in real time while the triangle is being dragged that tells if the triangle is an acute, right or obtuse triangle and gives the reason why. By experimenting with the triangle student can develop an intuitive sense of the difference between these three classes of triangle. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

: 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.

This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss

View our video tutorials here:
openintro.org/casio
openintro.org/TI