Precalculus With Limits by Ron Larson
This book as well as the other two books are for college freshman level or college introductory level mathematics courses. The strengths of the book are mainly focused on its layout. For example, the book has a great way to demonstrate a varied and large amount of information easily and simply. This means that people reading the text just have to look for certain visual cues like colors or pictures that will point the information they seek. For example, the diagrams have a different background color than the text. All of this removes time spent looking for things. The use of bold also further differentiates the text, highlighting key words, phrases and things to memorize.
The weaknesses are in lack of context surrounding the topics and footnotes. Another book reviewed has footnotes and yet another provides adequate background for each topic. This book sacrifices breadth for efficiency. Although that is fine if people do not wish to see the whole picture of mathematics and in particular precalculus, it may not be as helpful for those that do. This is a small weakness as the book also provides many other features available online. However, it would be worth noting in future editions that the author should include footnotes and additional context for students to get a better grasp of the various topics and equations
The first two chapters of the book cover functions and their graphs and polynomial and rational functions. Topics covered are rectangular coordinates, combinations of functions, composite functions, quadratic models and functions, and complex numbers. It is followed by a chapter summary, review exercises, chapter test, and proof in mathematics. This is a very well detailed book offering multiple ways for readers to learn and understand the equations and problems offered in the text. The terms are written clearly with many kinds of visual aids.
For example, in Chapter 1, "Functions and Their Graphs," the problems and exercises are labeled and highlighted through the use of colorful red boxes and bold text. Allowing differentiation between text and spatial area provides those that do the problems and read the chapters with a way to navigate faster. The chapter summary also provides what is learned from the chapter sections as well as offers explanation/examples and where to get review exercises. It is so easy to simply go and review the chapter from the chapter summary by quickly reading what points are covered and then looking for the review exercises.
The third edition of this textbook offers a layout that is even more colorful than the other Larson math textbook. It also includes a summarize feature, located at the end of every section that helps students organize the lesson's key concepts and puts it into a concise summary, offering an excellent and valuable study tool. The other two texts did not have this new feature and the inclusion of colorful graphs also provided enough variety to keep a reader from getting bored with the subject material.
The book also has revised exercise sets as well as data spreadsheets that can be downloaded from the website detailed in the book and various checkpoint problems to allow readers to participate while reading. This book, unlike the others, seems like an interactive book. The features are not completely available in the other Larson book and makes reading and learning more dynamic. It also offers in its beginning pages' instructor resources which are not found in the other Larson book to the extent that was found here. Student resources are made available below that small section and images placed strategically throughout the chapters on each page make for increased variety in layout and visual appeal.
An Introduction to Linear Algebra by L. Mirsk
There are several strengths with this book. It is done in the traditional way with few pictures and visual cues. Therefore, it mainly focuses on equations, theorems, and interpretations. The references used throughout each chapter are neatly organized in the footnotes. Various definitions are used for the topics allowing students to grasp and see completely what they mean and within what context. There is enough material to go and examine for one's self the equations as well as the various meanings behind the terms expressed in these equations.
The weaknesses are lack of exercises, chapter summaries, visual cues, pictures, and differentiation of text. They layout is too simple. It also does not offer any online resources. It is more concerned with demonstrating the mathematics and theorems than providing...
It feels as though the reader has to read everything in order to understand each chapter. That is not helpful when it comes to understanding things because it will take longer. In the end, this kind of textbook is not for independent study as the other two are. Instead it is more for classroom use with an instructor who is able to pinpoint areas of focus for the students.
The teaching approach in this textbook is more simple with footnotes at the bottom and provides much more visualization of equations versus text. For example, when explaining determinants in chapter 1, it uses an explanation with multiple definitions. "Determinants were first written in the form (1.2.3), though without the use of double suffixes, by Cayley in 1841" (Mirsky, 2012, p. 6). By giving examples of how determinants were expressed, they give great breadth of information over the subject. "A determinant is a number associated with a square array. However, it is customary to use the term 'determinant' for the array itself as well as for this number" (Mirsky, 2012, p. 7). Applying theorems following the definitions give a clearer understanding of what entails identifying determinants and how they are used in equations.
Explanations of theorems clarifies any question a student may have concerning the overall outline of the topic as well as provides further transition to other parts of the chapter which are the exercises. Exercises are an important part of learning mathematics. However, the exercises are not as abundant as in the other texts, making practice less frequent.
This book was chosen over the others because of the way it is organized and it covers linear algebra instead of calculus. It begins with determinants, specifically explanation of Jacobi's theorem, and the two special theorems on linear equations. It also covers vector spaces and linear manifolds. The other two textbooks selected cover precalculus and calculus and do so in a manner that is different from this one. This book has simpler pages with only text and formulas, but it is easy to read and absorb in its simplicity.
For example, definitions have equations next to it. There is further explanation and citation as footnotes at the bottom of the page. After the definition follows a brief exercise to explain things. This book lacks color and layout that the other two books have. Although it lacks, it makes up for with the amount of information made available within the text. It is a fairly easy to follow through layout and reminiscent of the old textbook layouts.
Calculus I with Precalculus by Ron Larson
The strengths are that concepts are broken down well and the sections are separate and neatly laid out. They provide adequate visual cues and enough diagrams to give students an idea of what is being explained throughout each chapter. Things are colorful and the left-hand side sometimes provides interesting bits of information that may catch the interest of the reader. Like for example the biography of Rene Descartes. Things like this help keep the student engaged even if it is not something that provides practice for the student. Still, there are several problems with the layout of the textbook and how it approaches learning.
The weaknesses are several. While the text has several visual cues and differentiation in text that makes it easier to read than other math textbooks, it does not have useful summaries for each section. Things are split up and not intermingled enough to provide complete learning. One has to look throughout the chapter for information, especially when it comes to the chapter test. The chapter test seems unnecessary as there are so many exercises already in the exercise sections. Chapter summaries would have been more helpful and less work for the student.
This text opens up with Chapter P for prerequisites. Much like the other Larson text, it uses a lot of colorful text, visual cues, diagrams, and pictures. What is different about this textbook is its lack of organization. There is less text on the left hand side. It is designated more for images, especially diagrams. The "note" parts of each page are useful, but easily dismissed since it does not contain a lot of valuable information. For example, P.3, Graphical Representation of Data. The section begins with explanation of the Cartesian Plane. It has in the left-hand side the portrait of Rene Descartes and a brief bio of him. This is great if one wishes to understand the context surrounding the topic, but takes up more space than necessary, making it less…
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