MATHEMATICS

1.

Robert W. Vallin

The Elements of Cantor Sets: With Applications

This book is a thorough introduction to the Cantor (Ternary) Set and its applications and brings together many of the topics (advanced calculus, probability, topology, and algebra) that mathematics students are required to study, but unfortunately are treated as separate ideas. This book successfully bridges the gap between how several mathematical fields interact using Cantor Sets as the common theme. While the book is mathematically self-contained, readers should be comfortable with mathematical formalism and have some experience in reading and writing mathematical proofs. Chapter coverage includes: a biography of Cantor; an introduction to the Cantor (Ternary) Set; Self-Similar Sets and Fractal Dimensions; sums of Cantor Sets; the role of Cantor Sets to create pathological functions; and additional topics such as continued fractions, Ana Sets, and p-adic numbers.

2.

D. G. Northcott

Ideal Theory (Cambridge Tracts in Mathematics)

Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra.

3.

Howard Anton, Stephen Davis, Irl Bivens

Calculus (10th edition)

The new edition of Calculus continues to bring together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team′s extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful for those going into mathematics and those going into the sciences and engineering. This new text exhibits the same strengths from earlier editions including an emphasis on modeling and a flexible approach to technology.

4.

ASA Samuel A. Broverman PhD

Mathematics of Investment and Credit, 5th Edition

This text is a thorough treatment of the theory of interest, and its application to a wide variety of financial instruments. It emphasizes a direct-calculation approach to reaching numerical results, and uses a gentle, thorough pedagogic style. This edition expands on the treatments of forward contracts of various types, swaps and financial options and option strategies. The text contains a large number of worked examples and end-of-chapter exercises. The fifth edition includes expanded coverage of forwards, futures, swaps and options. This book has been named as an alternatively acceptable reference for the Society of Actuaries Exam FM and the Casualty Actuarial Society Exam 2. It is also listed in the Course of Reading for the EA-1 examination of the Joint Board for the Enrollment of Actuaries.

5.

Roberto Torretti

Relativity and Geometry

This high-level study discusses Newtonian principles and 19th-century views on electrodynamics and the aether. Additional topics include Einstein’s electrodynamics of moving bodies, Minkowski spacetime, gravitational geometry, time and causality, and other subjects. Highlights include a rich exposition of the elements of the special and general theories of relativity. 1983 edition.