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How to Read and Do Proofs
This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.
Discrete Mathematics with Proof
A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the c...
Intermediate Statistical Investigations
Intermediate Statistical Investigations provides a unified framework for explaining variation across study designs and variable types, helping students increase their statistical literacy and appreciate the indispensable role of statistics in scientific research. Requiring only a single introductory statistics course as a prerequisite, the program uses the immersive, simulation-based inference approach for which the author team is known.Students engage with various aspects of data collection and analysis using real examples and clear explanations designed to strengthen multivariable understanding and reinforce first-course concepts. Each chapter contains in-depth exercises which follow a con...
Explicit Cost Dynamics
GETTING TO THE BOTTOM OF THE BOTTOM LINE Traditional cost management systems typically defeat their own purpose by leading corporations to make decisions that ultimately do not optimize performance. These systems are the foundation for decisions that are made throughout the corporation. In order for organizations to increase performance beyond current capabilities, a new approach is needed that addresses issues such as understanding the true impact of various actions on the bottom line-and eliminating methods that distort numbers and narrow options. Explicit Cost Dynamics (ECD) offers such an alternative, and this expertly written, revolutionary book provides an indispensable introduction to...
Debugging by Thinking
Debugging by Thinking: A Multi-Disciplinary Approach is the first book to apply the wisdom of six disciplines-logic, mathematics, psychology, safety analysis, computer science, and engineering-to the problem of debugging. It uses the methods of literary detectives such as Sherlock Holmes, the techniques of mathematical problem solving, the results of research into the cognitive psychology of human error, the root cause analyses of safety experts, the compiler analyses of computer science, and the processes of modern engineering to define a systematic approach to identifying and correcting software errors. * Language Independent Methods: Examples are given in Java and C++ * Complete source code shows actual bugs, rather than contrived examples * Examples are accessible with no more knowledge than a course in Data Structures and Algorithms requires * A "thought process diary" shows how the author actually resolved the problems as they occurred
New Directions for Mathematics Education Research on Proving
This book summarizes new directions in mathematics education research on proving at the university level, thereby providing contemporary extensions of the sub-fields of proof that Annie and John Selden introduced to the field. The chapters each describe an emerging new area of proof research, review the relevant findings in this area, present open research questions and the tools to address them. The book also discusses proof as a literary genre, and how students' feelings during the proof writing process can influence their behavior. The concluding chapter of the book reflects on new directions for research on proving. As such, this book provides mathematics educators, who have extensive experience researching proof, with an up-to-date review of the new methodologies and research questions with regard to proof, and young scholars, interested in proof, can use these chapters as primers on which they can build a research program.
Train Your Brain
This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required. The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It c...
Elementary Linear Algebra
Elementary Linear Algebra: Applications Version, 11th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.
Decomposition in Fixed Point Computation
One result of this paper is the most efficient complementary pivot algorithm to date for handling the optimization problem. The second major contribution is a general structure on fixed point problems which, when present, enables one to work in a lower dimensional space. It is shown that the general constrained optimization problem may sometimes be formulated as a fixed point problem possessing this property. The basic approach adopted in this work for handling the general constrained optimization problem is to use an implicit function (derived from the equality constraints) to solve for some dependent variables in terms of the remaining independent ones. Under certain circumstances, a fixed point algorithm may be used to search for optimal values of the independent variables while Newton's method is used to determine values of the dependent variables. Theoretical conditions on the original functions are developed to guarantee that the fixed point algorithm converges to a solution and various techniques are devised to enhance the overall efficiency.
