Mathematics in Trades and Life

This book is designed to be used for classes supporting trade programs in a variety of fields and also to satisfy baccalaureate general education requirements.

Because of the focus on trade programs, choices of mathematical topics and the extent to which they are covered is more limited than in algebra or precalculus texts. Only those topics that are used in the selected trades and some extensions for quantitative literacy are included. Also examples are designed to look like how a person in a trade would actually perform the calculations. This includes the assumption that all arithmetic will be performed by a device and hence almost all numbers will be in decimal notation. For this reason rounding is covered and consistently required.

The inclusion of general education outcomes motivates the “life” portion of the book. These applications are not restricted to use in one or more trades, rather they enable any person to process simple phenomena they experience. The quantitative literacy sections also contribute to the general education goals. Many topics will conclude with activities designed to help readers see limitations of models and learn to process mathematical information with an appropriately critical eye.

This book is also designed to be used in conjunction with active learning pedagogies rather than as a reference text. That is, it has been designed for students to read the examples, work initial problems (checkpoints) to help them check their ability to mimic or identify questions to ask, and to then seek help while working on exercises. It can be easily incorporated into flipped classrooms and asynchronous learning.

Because of the focus on active learning, MiTaL does not provide an identical example to mimic for each question in the exercises. Rather each section provides an simple example, a more complex example, and some explanation about what is important. There are also examples that present the whole thought process involved in figuring out what to do and executing the method. These are designed to illustrate how a person approaches new problems. There are also a few examples on how to use examples to illustrate how a non-identical example can still be used on a problem. Then exercise sections are provided for them to test their ability to recognize and use the mathematics from that section.

The check points (exercises in the reading) are self-grading (using MyOpenMath) with some feedback so the reader can determine what if any questions they need to ask. Videos, where included, are presentations of the introduction of the concept in that section. Homework by default is live, online problems that provide some feedback. The scores on these cannot be saved in an LMS however. If you wish to use MyOpenMath, the problems, and even a shell, can be provided. Contact the author for information.

Other formats are available. A PDF version, intended for use on devices (as opposed to print), is available from the website. Homework is, naturally, not live. Other formats and even other versions are available, because the text is an open educational resource. Contact the author for access to the PreTeXt source.

The projects are an integral part of the general education goals. These are intended to be assigned after relevant material is covered. They require students to use topics from that chapter to perform calculations and then interpret the results of their work. This is part of achieving general education outcomes. The projects also provide a opportunity for students to express calculations using standard mathematical notation and to communicate mathematical results in clear language.

For context, here is a brief history. The first version of this text was written to transition to an OER for MATH A104 Technical Mathematics at the Univesity of Alaska Anchorage. Commercially available texts emphasized memorizing problem types with limited critical thinking. As such they could not be used to satisfy the general education requirement. There was also a desire to reduce costs including for textbooks and online homework systems. As a result this book was created with matching homework in MyOpenMath.

Served disciplines at UAA included auto/diesel, heavy equipment mechanics, welding and non-destructive testing, aviation mechanics, piloting, air traffic controll, and medical certification programs.