The K-book: An introduction to algebraic K-theory

Algebraic K-theory is an important part of homological algebra. From the table of contents: Projective Modules and Vector Bundles; The Grothendieck group K_0; K_1 and K_2 of a ring; Definitions of higher K-theory; The Fundamental Theorems of higher K-theory.

Modeling and Analytical Methods in Tribology

Improving our understanding of friction, lubrication, and fatigue, Modeling and Analytical Methods in Tribology presents a fresh approach to tribology that links advances in applied mathematics with fundamental problems in tribology related to contact elasticity, fracture mechanics, and fluid film lubrication. The authors incorporate the classical tenets of tribology while providing new mathematical solutions that address various shortcomings in existing theories.

Algebraic Techniques and Semidefinite Optimization

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements.

First-Grade Math: A Month-To-Month Guide

Planning math instruction is a demanding aspect of teaching. Teachers need to have an overall sense of the curriculum for the whole year, of what's going to be taught each month, and of what specifically to teach each day. This guide makes it easy to plan all three. It offers helpful mathematical strands organized month by month and covering grade-relevant topics. Includes reproducibles.

Discrete Mathematics: An Introduction to Proofs and Combinatorics

Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for students who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs;