Advanced Probability Theory

The main features also include:

• A brief introduction of the material in each chapter, followed by an explanation of the concepts presented.
• Examples and applications in each chapter that will help you cement your knowledge on the topics, encouraging you to participate in the problem-solving process.
• Highlighted key points and important results, helping you remember what you study – especially during the revision process.

In addition to standard introductory material on the subject, such as Lagrange’s and Sylow’s theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet’s theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.