We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space. It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small). These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.We will present some essentials of the theory in this book. Using linear algebra, we have the salient Hamming codes. The next level of coding theory is through the...

From Tzuong-Tsieng Moh, a seasoned expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh covers the many standard aspects comprising linear algebra, such as echelon forms, matrix algebra, linear transformations, and more. Moh further includes several advanced topics and applications, as well as self-correcting codes, Heisenberg's uncertainty principle, Maxwell's equations in relativity form, Google's search engine, and the theory of finitely generated modules over a PID. This book is ideal for both newcomers and...