The new edition of "Denumerrible Markov Chains" features updated bibliographic material, including an "Additional Notes" section on recent developments in Markov chain theory. It corrects an error from the first edition and adds a twelfth chapter on Markov random fields by David Griffeath, while maintaining the original text of the first eleven chapters.
Designed for beginners, this book offers a clear and accessible introduction to fundamental algebraic concepts. It covers essential topics such as equations, inequalities, functions, and graphing, with step-by-step explanations and numerous examples. The engaging exercises reinforce learning and help build problem-solving skills. Ideal for students or anyone looking to strengthen their math foundation, it emphasizes practical applications and real-world scenarios to make algebra relatable and understandable.
Focusing on essential algebraic concepts, the two volumes cater to both aspiring and established mathematicians. Advanced Algebra delves into modern topics such as commutative and noncommutative algebra, associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Together, these books provide a comprehensive overview of algebra's significance in mathematics, making them ideal for a two-semester advanced undergraduate or first-year graduate course sequence.
This book serves as a comprehensive guide to fundamental algebra concepts, making it suitable for beginners and those looking to refresh their skills. It covers essential topics such as equations, inequalities, functions, and graphing techniques, presented in an accessible manner. The inclusion of numerous examples and practice problems aids in reinforcing understanding, while clear explanations help demystify complex ideas. Ideal for students and self-learners, it provides a solid foundation for further mathematical studies.
Basic Real Analysis and Advanced Real Analysis systematically develop essential concepts and tools in real analysis crucial for all mathematicians, whether aspiring or established. These works offer a comprehensive treatment with a global perspective, highlighting the connections between real analysis and various mathematical branches. The development progresses from specific examples to general theories, often introducing practical applications before formal theory. The texts integrate real analysis with topics in algebra, topology, complex analysis, probability, differential geometry, and various applied mathematics fields. They feature numerous examples and hundreds of problems, with extensive sections providing hints or complete solutions for most. Aimed at young mathematicians, these books serve as excellent course texts and self-study resources, particularly for graduate students preparing for qualifying exams. Their scope and approach are appealing to instructors and professors across pure mathematics and to applied mathematicians in analytic fields such as statistics, mathematical physics, and differential equations. The clarity and breadth of these works make them a valuable addition to any mathematician's personal library.
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
An Overview Based on Examples (PMS-36)
Focusing on the representation theory of semisimple Lie groups, Anthony W. Knapp presents a comprehensive survey that aligns with the natural learning process of the subject. The book is praised for its clear exposition, making it an essential resource for graduate students and researchers alike. It features precise theorem statements complemented by numerous illustrative examples. Additionally, a 300-item bibliography and an extensive notes section enhance the reader's understanding and exploration of the material.