Linear Operator Equations: Approximation and Regularization
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.
The pedagogy used in Saxon Math is unique, effective, and research based. The authors of the Saxon Math series recognized that smaller pieces of information are easier to deliver and easier to learn. Rather than grouping topics into chapters, they separated complex concepts into increments and distributed them throughout each grade level. The result is a distributed approach in which instruction, practice, and assessment of concepts recur continually.
The pedagogy used in Saxon Math is unique, effective, and research based. The authors of the Saxon Math series recognized that smaller pieces of information are easier to deliver and easier to learn. Rather than grouping topics into chapters, they separated complex concepts into increments and distributed them throughout each grade level. The result is a distributed approach in which instruction, practice, and assessment of concepts recur continually.
Algebraic Geometry in Coding Theory and Cryptography
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it.
