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Gives an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. In particular, this book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Caratheodory extension theorem.

Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes.

Helps in the understanding of continuous and differentiable functions. This book emphasises on real functions of a single variable. It contains topics that include: continuous functions, the intermediate value property, uniform continuity, mean value theorems, Taylors formula, convex functions, and sequences and series of functions.

Ramanujan is recognized as one of the great number theorists of the twentieth century. This book provides an introduction to his work in number theory. It also examines subjects that have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research.

Offers an introduction to the theory of finite fields and to some of their many practical applications. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications.

Based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute (Utah), this title is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the program. It concludes with a number of problems ranging from routine to very difficult.

It is rarely taught in undergraduate or graduate curricula that the only conformal maps in Euclidean space of dimension greater than 2 are those generated by similarities and inversions in spheres. This is in stark contrast to the conformal maps in the plane. This book gives a treatment of this paucity of conformal maps in higher dimensions.

Introduces $p$-adic numbers from the point of view of number theory, topology, and analysis. Covering several topics from real analysis and elementary topology, this book includes totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, and surjectivity of isometries of compact metric spaces.

Presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples.

Introduces algebraic geometric coding theory. This book covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors.

Suitable for undergraduate students as well as professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma, this text introduces the main subjects of 'naive' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, and operations on ordinals.