The following are recommendations for textbooks at various levels of mathematics and statistics:
High School Textbooks
Note that the Prentice Hall Mathematics sequence (Algebra, Geometry, and Algebra II) is also available in a CA edition, and the CA edition conforms to CA learning standards.
Stanley A. Smith, Algebra 1 (California Edition)
Smith & Kennedy, Algebra 1: Student Edition
This Algebra 1 book is one of the classics in the field. It is not terribly colorful, and some even call it "boring", but the mathematics is sound, much better than in many of the newer texts on the market. Instead of simply showing students how to do the various problems, the authors spend some time on the axioms behind the concepts, and on where the formulas come from. This is very important for students who will eventually take Algebra 2 and go on in math. There are several examples in each section, and they are clear and well written. The California edition of this text covers all of the content standards currently required for California's annual standardized testing.
This book has a wide variety of both basic exercises and word problems. The exercises at the end of each section are broken up into three parts. The first problems, "A problems," help students exercise the basics of the concept being studied. The "B problems" help students delve deeper into the concept, and are more challenging, but still manageable. The "challenge" problems at the end of each section are truly meaningful as well as challenging, though the difficulty of the challenge problems varies from one section to the next. If you need to learn or review Algebra 1 on your own, or if you just need a great reference book for Algebra 1, this is your text. You may also want to consider the DVD as an accompaniment to this text. With the combination of the DVD and the text, it should be possible for most students to learn Algebra 1 independently.
Prentice Hall Mathematics: Geometry
I recommend the Practice book along with the text.
Prentice Hall Mathematics: Algebra 2 with Trigonometry
Sullivan, Precalculus: Enhanced with Graphing Utilities (5th Edition)
This book may be used as a substitute for Algebra 2 with Trigonometry, and includes several other advanced topics in addition to the Algebra 2 book, but is only appropriate for more advanced students.
Advanced Placement High School Texts
Note that there are many good calculus textbooks on the market, and so the selection of a particular book should be made based on your level, the level of difficulty of the course or learning goals, the particular material you need to learn, etc. Almost all calculus textbooks contain certain basic material on differential and integral calculus. However, the books vary widely in level of difficulty, and the advanced calculus topics covered/not covered. The books I am recommending are based on quality of the presentation of the material, value for your money, and a thorough coverage of the material.
Demana, Waits, Kennedy, Finney: Calculus: Graphical, Numerical, and Algebraic
I have to admit that I am partial to this book since my company worked extensively on the student edition, and wrote the entire teacher's edition and all the supplementary materials. It is a great book, and is used by many high schools throughout the country. The explanations are clear, and the book covers Advanced Placement calculus very well. It is particularly well suited for the high school Advanced Placement exams in mathematics.
Stewart, Essential Calculus: Early TranscendentalsCalculus Books)
This text covers the first two semesters/three quarters of calculus thoroughly, as well as some additional multivariable calculus that may not be taught during the first year of college calculus. It is not a tome, and yet it presents the material clearly, and makes an excellent reference.
5 Steps to a 5 AP Calculus BC 2018
High School AP Calculus students: This book will help you to review for the exam. My students have had better success with this one than with other similar review workbooks.
Calculus (Also see Calculus books in the High School section)
Thomas & Finney, Calculus and Analytic Geometry (9th Edition)
Thomas and Finney is a classic calculus book that is used by many universities. It is generally considered mainstream and first rate. It is clearly written, and has many excellent modern applications. This text covers the full three semester course in calculus.
Stewart, Multivariable Calculus
Edwards and Penney: Multivariable Calculus (6th Edition)
This is a more advanced approach, but it is excellent! The problems in this text are more difficult than most competing books, but they are well thought out. I worked with these authors on a previous edition.
Ross, Introduction to Ordinary Differential Equations, 4th Edition
This text provides a good introduction to the subject at a level appropriate for good university math departments (e.g., University of California).
Brannan & Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications
This is the textbook currently used at Stanford University in their first course in differential equations. It has wonderful applications problems and projects, and is geared towards engineers and applied mathematicians who will be using differential equations in their careers. To this end, numerical methods are stressed over theoretical ones. The series solutions to differential equations are not covered in this text, but there is a wonderful chapter on nonlinear equations, and numerical methods are stressed throughout the text. Linear algebra is an important tool needed in order to understand the majority of the textbook, but an appendix provides all the linear algebra needed. The link is for the textbook and accompanying student's solutions manual.
McGraw Hill: 3,000 Solved Problems in Linear Algebra
Winston, Operations Research: Applications and Algorithms (with CD-ROM and InfoTrac)
This text gives a good elementary overview to the subject, but does require calculus as a prerequisite. It is not at a super high level. It is appropriate for a high level undergraduate text, or a first year graduate textbook.
Ahuja, Magnanti, & Orlin, Network Flows: Theory, Algorithms, and Applications
This is the classic textbook in this key area of operations research. This book is written at a much higher level than Winston's text, and is most appropriately used as a graduate textbook, though some high level undergraduate students will be able to learn from it as well.
Bazaraa, Jarvis, & Sherali, Linear Programming and Network Flows
This book is another classic in linear programming and network flows, and covers some of the same material as Ahuja, et al. However, the "flavor" of the book is different. Ahuja, et al. very thoroughly covers network flows, but does not cover linear programming as thoroughly. Bazaraa, et al., covers linear programming thoroughly, but doesn't provide as thorough a coverage of networks.
Probability Theory (Note that both of these recommended texts are calculus based.)
Hoel, Introduction to Probability Theory
This text is one of the classics in the field, and I highly recommend it.
Bertsekas & Tsitsiklis, Introduction to Probability, 2nd Edition
This book is a bit "friendlier" than Hoel's, and at a slightly lower level, but the books are still comparable.
Elementary Statistics and Business Statistics (not calculus based)
Triola, Elementary Statistics (11th Edition)
This text is used mostly in undergraduate business/management departments, and in MBA programs.
Aczel & Sounderpandian, Complete Business Statistics with Student CD (The Mcgraw-Hill/Irwin Series)
This text is used in Walden University's required statistics course (AMDS-8437). It provides an excellent and complete overview of business statistics.
Mendenhall, Beaver, A Brief Course in Business Statistics
These two authors also have written several other excellent statistics books at all levels.
Mathematical Statistics (calculus based and rather advanced)
Rice, Mathematical Statistics and Data Analysis (with CD Data Sets)
This book is another classic, and is used at many top universities. I also worked on all three editions of this book. Look for me in the acknowledgements.
Wackerly, Mendenhall, & Scheaffer, Mathematical Statistics with Applications
This is a high level text, generally appropriate for serious graduate students in math or statistics.
Draper & Smith, Applied Regression Analysis (Wiley Series in Probability and Statistics)
This book is the classic in the field, but note that it is a very advanced book that is appropriate for graduate level courses in a math/statistics department at top universities.
Montgomery, Peck, & Vining, Introduction to Linear Regression Analysis (Wiley Series in Probability and Statistics)
This book is calculus based, but is readable, and is at an advanced undergraduate level for math or statistics majors. It is concrete, and far less advanced than Draper & Smith.
Chatterjee & Hadi, Regression Analysis by Example (Wiley Series in Probability and Statistics)
This is a text written by two masters of the subject. It is fairly advanced, but the key parts of it will be accessible to anyone will a good math background.
Anderson, An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics)
Don't let the word introduction in the title fool you. This is a very advanced text, heavily dependent on calculus and linear algebra. However, you will go far if you can get through it!
Gross and Harris, Fundamentals of Queueing Theory, Solutions Manual (Wiley Series in Probability and Statistics)
This text provides an introduction to the topic of queueing theory, and is a calculus based text at a fairly high level. This text is appropriate for high level undergraduates or graduate students. This is the classic in the field.