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Presents a wide range of problems connected with rational approximations of numbers and analytic functions; these problems touch on many topics in contemporary analysis, such as analytic functions, orthogonal polynomials, spectral theory of operators, and potential theory.

Describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.

Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This work starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. It focuses on spectral sequences and their use in generalized cohomology theories.

Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. It is suitable as a supplementary text for an undergraduate or graduate algebra course.

Algebraic geometry plays an important role in several branches of science and technology. This book discusses dimension theory, flat and proper morphisms, regular schemes, smooth morphisms, completion, and Zariski's main theorem. It also presents the theory of algebraic curves and their Jacobians.

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. This book covers the theory of sheaves and their cohomology.

Presents a comprehensive introduction to differential forms. This work begins with a presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems.

An introduction to the work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. It emphasizes the geometric aspects of the theory and discusses topics such as braids, homeomorphisms of surfaces and surgery of 3-manifolds.

An English translation of Sakai's textbook on Riemannian geometry. It explains the fundamental notion of Riemannian geometry. It emphasises on understandability and readability, to guide students who are new to this area. It also deals with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.

Covers topics including fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. This work considers objects and examples including the torus, the Mobius strip, the Klein bottle and closed surfaces.

Presents an understanding of scattering theory, starting with basic principles and extending to research. This work presents a comprehensive exposition of the theory, covering different methods (of trace class and smooth perturbations) and approaches (time dependent and stationary) and discussing the relationships among them.