The ideas of probability are all around us. Lotteries, casino gambling, the al- most non-stop polling which seems to mold public policy more and more- these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re- moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac- ing quantum mechanics, has a world view that is at its core...
The ideas of probability are all around us. Lotteries, casino gambling, the al- most non-stop polling which seems to mold public policy more and more-...
This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland’s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on...
This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate m...
This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.
Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions....
This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emph...
