This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Chapter 7, Geometry, has been extensively revised and re-organized to include a new section 7.1 on angles and new section 7.4 devoted to triangles. Increased coverage of estimating with fractions and decimals with new “To Think About” exercises in Sections 2.5, 2.8, and 3.3 and a new lesson in Section 3.7. Coverage of fractions in Chapter 2 has been expanded as follows: Section 2.6 now begins with a discussion of least common multiples so that the subsequent coverage of least common denominators is more complete; a new lesson on order of operations in Section 2.8 offers readers additional review of these rules and practice applying them to fractions; and a new mid-chapter test on fractions appears after Section 2.5. Percent applications are now covered in two sections (Sections 5.4 and 5.5) to allow for a more patient presentation of this important topic.

Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems.