Let's talk about textbooks. The following is a list of textbooks I used as a math major in my university, and now use for reference, study, and for this blog outside of school. This is not a large collection, but unlike many required textbooks for university, I have enjoyed all of these books and feel they are great textbooks. If you don't have a textbook for your study, I would consider this list as a recommendation list. Below the information for each book, I'll give a short review of it. The textbooks are in order of difficulty, but that, of course, is subjective.
College Algebra: Graphs and Models, Second Edition
Barnett, Ziegler, and Byleen
I didn't actually use this textbook in school because I didn't take College Algebra, but my husband used this text, and I've used it for personal study and reference for this blog. The discussions are thorough, yet clear for a person who may not be strong in math. The examples are helpful for doing the exercises in each section, and the exercises cover a wide range of question types.
College Trigonometry, Fifth Edition
Aufmann, Barker, and Nation
I used the sixth edition of this book for my Trigonometry class, but sold it back to the bookstore and kept my husband's prior edition (I got more money back for the newer edition). I haven't found many differences in the editions. This text is actually enjoyable to me, as someone who likes math. The discussions are concise, the examples are clear, and the exercises are helpful. There are many exercises at the end of each section, probably a few too many, but Trigonometry is a subject that gets easier with practice.
Calculus: Concepts and Contexts, 3E
Ah, Calculus. This is a great Calculus text. I used it for all three of my Calculus courses. After my class got through this subject, the text for the next class was changed. I tutored students using the new book many times and always ended up bringing my old one back to school for tutoring! I love everything about this book--the discussions, the examples, the exercises, the "Focus on Problem-Solving" sections, and the computer discs included with the book. I just love it and highly recommend this text!
Probability and Statistical Inference, Eighth Edition
Hogg and Tanis
This may not be the best book on probability for a non-math person. The discussions are sometimes quite lengthy and detailed, and the examples are not always clear. Also, many exercises in the book do not have a corresponding example, which means they require more thought and background knowledge. I like this book for the integration with the computer that is incorporated. It includes a disc that contains data for exercise problems and some mathematical models, which I found quite helpful while taking the course. If I ever come across a better probability text, I'd probably (ha! pun intended) consider selling this one and keeping another.
Discrete Mathematics and Its Applications, Seventh Edition
Kenneth H. Rosen
I love this textbook. Granted, I've never used any other discrete text, but I very much enjoyed this one! The discussions are lengthy (makes for a big book), but clear. I never grew bored of the long discussion. The examples are clear and helpful, and while there are not a lot of exercises in each section, the included ones are great. I also really like that math history is incorporated throughout the text. Whenever a person is relevant to the discussion (such as George Boole in the section on propositional logic), a short biography is included at the bottom of the page, including the mathematician's contribution to the study! I love this! Sometimes in class, I'd find myself many sections ahead in the text, just reading all of the little biographies. This book also incorporates a fair amount of programming information for the budding computer programmers out there.
Introduction to Linear Algebra With Applications
DeFranza and Gagliardi
This book is decent, I think. The discussions are a little sparse, with many examples crammed in. The examples, though, don't always clarify the topic as I think the authors hoped. The short discussions do make for a light, short book, but don't necessarily help the student get through the class. I struggled a lot with Linear Algebra, and I think it was partly due to this text--when I checked out books from the library to study with, my grade began to improve. The exercises, though, are good and there is a healthy number of them.
Elementary Differential Equations and Boundary Value Problems, Ninth Edition
Boyce and DiPrima
To be honest, I don't have much to say about this book. My professor didn't use this book for his lectures in university, and I failed to study it well as a student. I hope to get back to it sometime and learn all the things I missed in college. It seems to contain a good balance of discussion, examples, and exercises, but that is only my opinion from glancing through the book.
Abstract Algebra: An Introduction, Second Edition
Thomas W. Hungerford
This book is very well-loved, probably because I enjoyed the class so much. My text was bought used and in poor condition, and I've only added wear to it over the years. I like this book. The discussion is sometimes a little wordy and the examples sometimes skip a few too many steps, but studying with this book definitely helped me be a more active student. It may not be ideal for a self-study without a professor, though.
Elementary Number Theory, Seventh Edition
David M. Burton
This is a pretty good introduction to Number Theory. There is a good balance of discussion, example, and exercise, and there is some math history incorporated as well, which by now you know that I like. It would suffice for a self-study, but is better with a professor's guidance or as an accompaniment to a professor's lectures.
David A. Thomas
This book is decent, and it did help me through Geometry even though I had a pretty lousy professor. The accompanying CD is a great tool and resource. The exercises are a little lengthy and require a lot of discussion, but that can be helpful I suppose. I easily made it through the first part of my semester relying solely on this book, but eventually had to seek outside help, as my professor seemed to be deficient in this subject and the book is difficult to chew through in a self-study. I would like to get back to it eventually and get to the second half of the book, which we never even touched. Someday.