Textbook recommendations
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.
Algebra 1
Smith & Kennedy, Prentice Hall Mathematics: Algebra 1
Geometry
Prentice Hall Mathematics: Geometry
I recommend the Practice book along with the text.
Algebra 2
Prentice Hall Mathematics: Algebra 2 with Trigonometry
Precalculus
Sullivan, Precalculus
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.
Sullivan's Precalculus text is also available in a hardcover edition: Precalculus (7th Edition)
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.
Calculus
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, Calculus: Early Transcendentals
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.
Kaplan AP Calculus AB & BC, 2008 Edition (Kaplan Ap Calculus Ab and Bc)
Sequoia High School HL students, and others taking the AP exams this spring: This book will help you to review for the exam, and we will use it in class over the next 3 months.
College Textbooks
Calculus (Also see Calculus books in the High School section)
Swokowski, Calculus: The Classic Edition
Larson, Calculus With Analytic Geometry
Stewart, Multivariable Calculus
Edwards and Penney: Multivariable Calculus
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
This text provides a good introduction to the subject at a level appropriate for good university math departments (e.g., University of California).
Linear Algebra
Lay, Linear Algebra and Its Applications, Third Updated Edition
McGraw Hill: 3,000 Solved Problems in Linear Algebra
Operations Research
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 (Norton Critical Edition)
This text is one of the classics in the field, and I highly recommend it.
Bertsekas & Tsitsiklis, Introduction to Probability
This book is a bit "friendlier" than Hoel's, and at a slightly lower level, but the books are still comparable.
Statistics
Elementary Statistics and Business Statistics (not calculus based)
Triola, ELEMENTARY STATISTICS
This text is used mostly in undergraduate business/management departments, and in MBA programs.
Aczel & Sounderpandian, Complete Business Statistics with Student CD
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.
Sampling Theory
Thompson, Sampling (Wiley Series in Probability and Statistics)
Mathematical Statistics (calculus based and rather advanced)
Rice, Mathematical Statistics and Data Analysis
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 (Mathematical Statistics (W/ Applications))
This is a high level text, generally appropriate for serious graduate students in math or statistics.
Regression Analysis
Draper & Smith, Applied Regression Analysis, Includes disk
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
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
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
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!
Queueing Theory
Gross and Harris, Fundamentals of Queueing Theory
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.
