"College Algebra" by Larson & Hostetler.This is one of the best books I've read for this subject. It gives very comprehensive examples and details out everything step by grueling step. I think one of the things that makes reading a mathematics text book overly difficult is some assume the readers know something about the topic already. With a myriad topics in the field of mathematics "College Algebra" makes no such assumptions. It even includes a preliminary section of very basic concepts to help those who may need a refresher. It has hundreds of examples to work through to give the student the practice they really need. Another boon is the book has a lot of Applied Mathematics examples as well and even includes projects. I found the book very readable and I recommend it to anyone that wants to delve into the subject of Algebra. it likely wouldn't suffice for an Algebra 1 text as it moves much too fast. The Algebraic sections of this book are designed more as refreshers for those who already have a basic understanding of Algebra. The edition shouldn't make a difference, I happen to have the 7th and an earlier edition. I felt the 7th was much more relevant to what needs to be learned than the much earlier edition I used to have. Don't let the cover price intimidate you, you can probably find a decently priced copy used.
Cover Price: $183.95
Pages: 816
ISBN: 978-0618643103
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This subject is absolutely essentially to harness if you want to move on and study Calculus in any form. As you move deeper in mathematics Trigonometry just seems to get more and more important. So it is extremely necessary to devote a lot of time to working with this subject.
Pages: 627
ISBN: 0-534-38027-1
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When it comes to learning a mechanical approach to Calculus this is my preferred choice. There are multiple versions of the books by Stewart, so beware if you want to get one of these. This particular edition will bring you through all the usual course work covered in Calculus I, II, and III. There is a smaller more abridged version that covers Calculus I and II at a faster pace, but I believe some level of detail and complexity was allowed to suffer for it. It is still a very good book if that is all you need to know mathematically. However, if you want to study Mathematics or something like Physics, you will find that reading a full behemoth of a text book like the full edition will give you the tools you need to meet with mathematical success. As a pre-requisite you should really know your Algebra in and out. One of the main reasons students have a terrible time with Calculus is because they have a lack of Algebraic knowledge. Also you should know a lot about Trigonometry before tackling this kind of a book. Sure it brings you through a bit of a refresher, but it is simply no substitute for studying the real topic in detail. One other thing readers should keep in mind is that I am not convinced there is really any Multivariable Calculus section or book that brings you through all the necessary details of Vector Analysis. It brings you just to the cusp of the topic, but you will need to supplement that knowledge with something else. It certainly does not prepare you to go right into a course like Electromagnetism, this is why if you get a book on Electromagnetism a considerable portion of the first part of the course is spent teaching Vector Analysis.
Cover Price: $224.95
Pages: 1,368
ISBN: 978-0538497817
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This book is widely used in courses like Discrete Structures. Discrete Structures is the type of course that is really the gateway to higher level mathematics. It covers topics like Logic, Mathematical Proof, Set Theory, Combinatorics, Relations, Matrix Algebra, Number Theory, etc. It really starts you thinking about mathematics in a whole different way. Unfortunately the problem with this is that it is usually very hard for people to start doing this. Because of that I think the reviews for this book suffer quite a bit. This particular book has another problem with it, I do not think this is a great text for introductory material. When I read this, I feel like knowing how to do this material makes this book ten times better. I can definitely understand why professors love this book, it has everything and done out in enough rigorous detail that makes it a very careful read. That being said, my recommendation before taking on this text is to maybe look over the material a little bit. Go in knowing some general things about Logic, Mathematical Proof, and Set Theory. I will eventually create Tutorials that will hopefully supplement this text quite well and reading those will prepare you to take on this other behemoth fundamental math text. The one thing I really don't like is the way Rosen handles the truth tables. There is a relation between truth tables and binary. If you change the T to 1 and F to 0 then do Rosen's truth tables backwards, you'll be doing binary! This is one of the many reasons Computer Science majors are also expected to take this type of course. After reading the above three text books, I feel, one has completed the basics of Mathematics and is ready to move on to considerably more challenging material. Some of which is much easier than others.
Cover Price: $146.19
Pages: 1,008
ISBN: 978-0073229720
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Once you've completed the course in Discrete Structures, you are ready to take on Linear Algebra. I do not recommend taking it on without the prior course. There is usually a little bit of a review for Matrix Algebra, but these kinds of texts assume you already know how to do Mathematical Proof. It took me a long time to find a Linear Algebra book that was actually artfully written. I've read through a number of text before finding "Elementary Linear Algebra: Applications Version" by Howard Anton and Chris Rorres. This book will take you through all the nitty gritty details, but it does assume the reader has a certain level of Mathematical sophistication. It brings you through all the usual topics of Determinants, Vector Spaces, Eigenvalues, Eigenvectors, Inner Product Spaces, and Linear Transformations. In addition the Applications version has some wonderful Numerical and applied problems you can work through. Linear Algebra is one of the greatest topics I've had the pleasure of reading through, so you can certainly expect some tutorials coming from me very soon.
Cover Price: $125.13
Pages: 773
ISBN: 978-0470432051
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Pages: 752
ISBN: 978-0-321-50031-1
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