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Florentina Holcombe

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Aug 2, 2024, 8:12:52 PM8/2/24

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The main difference between these two textbooks is the level of difficulty. "Sheldon Axler's Algebra & Trigonometry" is designed for a college-level course, while "Precalculus: A Prelude" is typically used in high school courses.

Both textbooks cover a wide range of topics in algebra and trigonometry, but "Sheldon Axler's Algebra & Trigonometry" may be considered more comprehensive as it goes into more depth and includes more advanced topics.

Both textbooks can be used for self-study, but "Precalculus: A Prelude" may be more user-friendly for students who are learning independently. It includes more examples and practice problems, as well as step-by-step explanations.

Both textbooks cover topics that are important for calculus, but "Sheldon Axler's Algebra & Trigonometry" may be more beneficial for preparing for calculus as it includes more advanced concepts and a greater emphasis on problem-solving skills.

Yes, these textbooks can be used together. "Precalculus: A Prelude" can serve as a foundation for "Sheldon Axler's Algebra & Trigonometry," providing a review of basic concepts before delving into more advanced material.

There are classic textbooks for Calculus like Spivak, Courant, Apostol, etc that do a fantastic job at explaining the fundamental concepts and theory along with great problem sets. My question is the following:

When I say "Algebra" I mean elementary algebra not abstract algebra. I would like a book that explains concepts like polynomials, factoring, sequence and series, inequalities, absolute value, and other interesting algebraic structures with non trivial problem sets. Something like the algebra in the math olympiad.

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks on some elementary undergraduate courses such as College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE as I would love my students to read textbooks written by the best mathematicians.

Books about middle school algebra and trigonometry written by someone like Gelfand are rare (I don't know other examples; for example V.I. Arnold's books nomially for children are aimed at very special children, their author's claims to the contrary), but there are many undergraduate textbooks written by superb mathematicians. I list below some that occur to me now. However, most of those I list are aimed at a level probably a bit above that which interests the OP.

While not exactly a textbook, the book of Persi Diaconis and Brian Skyrmes called "Ten great ideas about chance" is an excellent introduction to probabilistic thinking directed at a general undergraduate audience.

Marcel Berger wrote some textbooks directed at future math teachers that treat classical affine and projective geometry (they have been translated into English). They would be hard for a US educated audience.

Elias Stein has coauthored with Rami Shakarchi a series of books on real, complex, fourier, and functional analysis. The only one I've read is the book on Fourier analysis, and it is excellent and pedagogical, the book I always wished I had encountered as a student.

I found the examples relevant and the topics organized in a good way. For instance, when teaching the Law of Sines, I was so happy to see Abramson included area. Also, I liked the organization of the section on Vectors. We are lucky in algebra and trigonometry where the topics are not changing.

I am unsure if my confusion with the Identities chapter was just me or if others will feel the same. I try to keep identities as simple as possible, but that is hard to do. Many problems were set as true or false, so would have liked to have more true examples. Well, I would have preferred to not have them set as true or false. Again, this may be just me.

I enjoyed experimenting with the html version and pdf version. Both have navigation panels for good movement through the text by section. In the HTML version of the book, the solutions of the examples in the section are hidden. This feature will be helpful for anyone using a touchscreen device, and OpenStax has an App for this.

I found Algebra and Trigonometry on OpenStax a while ago. When I had to find a book quickly for a dual enrollment (DE) class this semester, I began using the book. The class went well. Students did not have any complaints with not having a book in hand. Now that I have approval from my department chair to run a pilot in Fall 2021, I will have the book in our bookstore for purchase and copies in our library on reserve. The pilot classes will use this text for MAT 110- College Algebra and MAT 111-Trigonometry, but could have used Precalculus as it has the same layout and text.

There are several support documents in Instructor Resources on OpenStax. One is the Solutions Manual. I used this regularly, which had good explanations. I did not like the formatting being in Word but it was easy to find what I needed. Also, the site has recorded lectures and notes for you to use. There are two support documents I will definitely use for the pilot, the PowerPoint slides and the Corequisite Skillsheets. One caution, the PowerPoint slides are not whole presentations but instead are the slides of graphs to embed in your presentations. Since I change all presentations from books to my own style, this is perfect for me. Finally, I cannot wait to utilize the Corequisite Skillsheets that provide a little more background for students who may need that.

Many examples from different fields of study are presented. They are classic problems arranged by level of difficulty. In addition, the use of a graphing calculator to model real life data makes the problems interesting and real.

The structure of his textbook makes it easy for students to follow the presentations of the topics. Important concepts and formulas are highlighted to promote easy access to information, understanding, and retention of the subject.

Topics are clearly explained and organized in subsections. Consistently, introductions and explanations of new concepts are backed up with examples explained in details and extra practice exercises. PowerPoint slides are also corresponding in pattern with the textbook

The textbook is comprehensive. I've used the Algebra and Trigonometry textbook in a face-to-face co-requisite College Algebra class for 2 years without problems. Most students utilize the textbook digitally. The textbook is set up as a...read more

The book does a wonderful job of presenting the material in a logical manner. Diagrams and illustrations are clear and understandable. The book is written in an appropriate manner for learners of varying levels of readiness.

The textbook can be subdivided into smaller sections. I have changed the order of topics covered to match my individual style of teaching. The subheadings break the material down into logical units so that the instructor can pick and choose topics.

The organization of topics are logically ordered. Topics are revisited, much like a spiral curriculum, where students see concepts in several places. Students are able to see the relevancy of the topics and deepen understanding as the course progresses.

The online version is easy to navigate. Images and charts are clear and do not distract. I like that students who use the online version can click on the Show Solution option to display the answer. This allows the learner to try the problem on their own without seeing the solution. Many of my students routinely use this interactive feature.

An index or glossary would be a helpful addition to the textbook. I would also like the selection of practice problems to be expanded in varying degree of difficulty so that learners, who are at different levels of readiness, can practice.

I like the book the way it is organized. First, the author explained the theoretical concept, then example and finally the exercise. I think most of our students need this pattern to succeed the course.

I use this book in foundational math class. There are three things in particular that make this book appeal to me. I like the modularity of this book as it allows me jump around to shape each class based on the students' needs. I also utilized the accompanying PowerPoints as a foundation for my presentations. Lastly and most importantly is the connection to WebAssign for online homework. The ability of WebAssign to deliver additional content to supplement this text in the modality that each student desires based on their learning style makes a huge impact in outcomes. I highly recommend this text.

I did not see a glossary, but there was an effective index. From what I see, you cannot get to the index unless you download the book from the website. Once I downloaded it, I could see the index.read more

There were some formatting things I noticed in the online version. Specifically, on page 605, any time there is a formula, after it, there is a space that is missing between it and the next word. However, when I downloaded the PDF version, that formatting error is gone.

All areas of the subject are covered. The index is easy to use. Each section contains a glossary which can be helpful and convenient, but for instructors who limit their teaching to specific sections, a comprehensive glossary that is easily...read more