Textbook in PDF format

This book presents a compendium style account of a comprehensive mathematical journey from Arithmetic to Algebra. It contains material that is helpful to graduate and advanced undergraduate students in mathematics, university and college professors teaching mathematics, as well as some mathematics teachers teaching in the final year of high school. A successful teacher must know more than what a particular course curriculum asks for. A number of topics that are missing in present-day textbooks, and which may be attractive to students at the graduate or advanced undergraduate level in mathematics, for example, continued fractions, arithmetic progressions of higher order, complex numbers in plane geometry, differential schemes, path semigroups and path algebras, have been carefully presented. This reflects the aim of the book to attract students to mathematics.
The origins of the book lie in a set of lecture notes prepared by the first author for students in an introductory algebra course given at Carleton University in Ottawa in the academic year 2005-2006. These notes were subsequently revised for courses given by the first author at Charles University in Prague during the years 2008 to 2012. More recently they have been revised again in conjunction with the second author taking into account the many valuable suggestions received from colleagues. They have also benefited from notes given in a variety of algebra courses by both authors. Tested in this way our book should provide useful guidance and reference to graduate students and advanced undergraduates in mathematics.
This book emphasizes the relationship between algebra and other parts of mathematics, especially geometry but also combinatorics and number theory, which are either missing from present algebra textbooks or are mentioned only marginally. It contains varied and diverse material that every mathematics graduate student and advanced undergraduate should be acquainted with