Precalculus 30 Textbook Pdf

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Enrique Fats

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Aug 3, 2024, 11:50:06 AM8/3/24

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I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor exposition (in my opinion). I feel that reading a mathematics text is a skill in itself, a skill that becomes lost if one subsists on these "modern" books and the bite-sized morsels of knowledge they impart.

I'm in need of a thorough and dry pre-calculus text that will prove worthwhile to work through. I'm not looking for a laundry of list of definitions and theorems. I want as much rigour as a textbook at this level can allow, however not at the expense of clarity.

But the book I still treasure and hold close is one named "Elements of Pure Mathematics by S Nadarasar". Written in the 50's. It's a Sri Lankan book and very rare even here. They don't print the original English version anymore - only the translation. So this is of no use to you since you can't get a hold of it but I owe a lot to this text and not mentioning it on this thread would be a crime.

As dry, old and rigorous as it gets "Advanced Mathematics Precalculus with discrete mathematics and data analysis." It's what I had in High School, although I had a modern textbook as a suppliment. There might be newer versions out, but I assume you want the older ones.

I think you will probably like any of the introductory books by Rey Pastor. The issue there is that he was Spanish, so you won't probably be able to find a book by him in English. I have the three volumes of his Calculus course, and it's the most comprehensive book I've ever seen on the subject.

A book I like that has a small introduction including some pre-calculus concepts is Calculus by Tom Apostol. I'm not sure if that's what you're looking for, I suppose you're looking for a complete book on the subject.

It includes nearly 1000 problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the American Invitational Mathematics Exam and the USA Mathematical Olympiad. Almost half of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual.

As with all of the books in Art of Problem Solving's Introduction and Intermediate series, Precalculus is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which new techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text.

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarterpre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of,and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, aswell as the important characteristics needed in calculus.

The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisted more extensively in the third chapter. As with thefirst part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.

In addition to the paper homework sets, algorithmically generated online homework is available as part of a complete course shell package, whichalso includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere,you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.

The whole book or individual chapters are available for download below, or you can order a bound printed copy from Lulu.com or Amazon. If you are providing a link to students or a bookstore to purchase printed copies of the book, please direct them to this page. If you are an instructorand are using this book with your class, please drop us an email so we can track use and keep youupdated with changes.

Accessibility Note: The Word files contain equations in Equation Editor format, and graphs and images have alt-text in the primary text, but not the exercises. A screen reader friendly HTML version of the book can be read on LibreTexts

Note on versions: The links above will redirect you to the latest edition of the chapters. Older versions remain on the website, and can be accessed using direct links to the specific edition's file name, like 1.pdf

Note: On June 5, 2017, Edition 2.0 was released. The links below point to this, the most current version. This revision is not page number or section equivalent to the previous 1.x editions. If you are looking for the originalfirst edition (black cover), please go here

The book is very clear, almost to a fault. It seems to gloss over some things that are harder to understand and focus on the typical student's experience. An advanced student or a teacher might occasionally find the rigor lacking, but most users will find it very readable.

There are certainly no interface issues. I feel that the online view could take advantage of more features (hyperlinks, for example) but I understand the desire for consistency between the pdf version and the online version.

I think it's a very good, student-centric book. I imagine some professors will lament the lack of rigor, but I think that was an intentional choice made for ease of reading for the target audience. The instructor can add rigor as desired.

The topics covered are standard in state articulation guides, for example, the 2019 Illinois Mathematics & Computer Science Articulation Guide. See the topics covered under "Elementary Functions (Precalculus)" which refers back to the tables of contents for College Algebra and Trigonometry. Therefore this text is very suitable for helping two-year community college students articulate with the third year at a four-year public university's Calculus I course. It is also compatible with a private university's precalculus and later calculus sequence.

The actual mathematical content as such should not change much. However, mathematical modeling problems ("story problems," "applications") are in a variety that represent daily adult life, post-college careers, various majors other than mathematics such as science, health, ecology, and medicine for example. These examples are fairly applicable in a non-dated, but modern vein.

It can be organized in modules as long as necessary topic sequencing is maintained. For example, jumping into the topic in vectors concerning the angle between two vectors should honor the necessary trigonometry needed to built that topic upon. There are appropriate subheadings to signal the student as to the organization and connections being made under a new subheading with previous subheaded topics.

This is topic sequencing, and I have mentioned that this text maintains a logical, developmental topic sequencing structure. I've mentioned its simple and clear explanations while maintaining mathematical accuracy and completeness.

I did not detect any distracting or blatant biases in any examples or discussions of any "culturally insensitive" or "offensive" nature at all, or in the nature of any social or ethnic exclusiveness of any kind.

Whenever I have reviewed either new textbooks or revisions of current textbooks for remuneration by a publisher, I have followed my practice of looking for the following for strengths or weaknesses. I ask if the text:
1. is mathematically complete and accurate,
2. teaches clearly, simply, and logically so that a student can learn from studying it,
3. has good problems in the exercises and discussion examples, and
4. has good end materials for review and test practice,
5. has computational skills balanced with applications (i.e. both procedural skills with applications which are connected to discussion topics and require practicing the skills and knowledges learned for the procedural skills).

This text is designed to be modularized. Most Precalculus courses will not cover all of the topics from this text but will cover a subset of these and the text is written with the goal to accommodate that. Rearranging the order of topics could be an issue because of the hierarchical structure of mathematics in general.

Very good overall. As I mentioned above, this book probably has more than most of us can fit into our typical Precalculus course but it is certainly not missing anything and could be easily customized.

I used Sullivan's Calculus (9e) as a standard for comparisons. The book is very similar in scope and sequencing to Sullivan, but does group some topics differently. For example, Sullivan combines linear and quadratic functions into one short chapter while this text dedicates a long chapter solely to linear functions and uses that space to develop them more coherently. Sullivan pulls together some topics into an appendix as a review while this text does not. However, this text develops much of that material in context, which I prefer. Both give a brief, but useful few pages of formulas, identities, and standard functions. Each chapter reviews key-concepts and has a glossary of terms. There is an index which seems adequate though it is considerably smaller than Sullivan's.