This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses.

Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author's extensive teaching and research experience, the exposition is guided by carefully...

Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.

This textbook presents a collection of interesting and sometimes original exercises for motivated students in mathematics.Written in the same spirit as Volume 1, this second volume of Mathematical Tapas includes carefully selected problems at the intersection between undergraduate and graduate level.

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields.

This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. It includes more than 70 exercises, along with complete solutions, that help illustrate and present all concepts.