Steven Roman Book order

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.

Focusing on elementary category theory, this textbook aims to simplify a complex subject, making it more accessible to readers. The author's extensive experience, gained from writing over 30 university-level mathematics books, is utilized to clarify concepts and enhance understanding. This resource is designed for those looking to grasp the fundamentals of category theory without feeling overwhelmed.

Focusing on the Catalan numbers, this textbook introduces their unique properties and applications in combinatorics. It is designed for students with varying levels of experience, starting with elementary concepts and advancing to more complex topics. Each chapter highlights a specific combinatorial object associated with Catalan numbers, such as paths, trees, staircase tilings, and null sums in Z, making it a comprehensive resource for understanding this important mathematical concept.

The Mathematics of Finance is tailored for advanced undergraduates or beginning graduates in mathematics, finance, or economics. It focuses on discrete derivative pricing models, including a thorough derivation of the Black-Scholes formulas. This second edition features improved organization and expanded discussions on options, while maintaining rigorous mathematics suitable for the target audience.

Exploring the essential concepts of group theory, this book delves into the mathematical structures that define symmetry and transformations. It covers key topics such as group operations, subgroups, and homomorphisms, providing a solid foundation for both beginners and advanced learners. With clear explanations and numerous examples, readers will gain a deeper understanding of the theoretical aspects and applications of group theory in various fields, including physics and chemistry. Ideal for students and enthusiasts alike, it serves as a comprehensive guide to this fundamental area of mathematics.

Focusing on ordered sets and lattices, this comprehensive introduction offers clear explanations and a wealth of exercises, examples, and illustrations to enhance understanding. Its user-friendly approach makes complex concepts accessible, making it an ideal resource for learners seeking to grasp the fundamentals of this mathematical area.

The third edition enhances the text with a new chapter on associative algebras, refined arguments, upgraded proofs, and new theorems, including the spectral mapping theorem. It corrects errors and expands the reference section significantly. Reviewers praise its thoroughness and elegance, making it ideal for graduate study and reference.

Focusing on advanced mathematical concepts, this book covers the fundamental theory of fields, starting with polynomials over a ring and progressing through the division algorithm, irreducibility, field extensions, and embeddings. It then delves into Galois theory, followed by a dedicated section on the theory of binomials. The final chapter explores families of binomials, culminating in the Kummer theory, making it suitable for graduate courses or independent study in mathematics.

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