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Classical Galois Theory with Examples
Galois theory is one of the most beautiful subjects in mathematics, but it is heard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout the text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is intended for beginning graduate students who already have some background in algebra, including some elementary theoryof groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity. The book is for students and intends to make them take an active part in mathematics rather than merely read, nod their heads atappropriate places, skip the exercises, and continue on to the next section.
Julia: A Life in Mathematics
In high school, Julia Bowman stood alone as the only girl - and the best student - in the junior and senior math classes. She had only one close friend and no boyfriends. Although she was to learn that there are such people as mathematicians, her ambition was merely to get a job teaching mathematics in high school. At great sacrifice, her widowed stepmother sent her to the University of California at Berkeley. But at Berkeley, in a society of mathematicians, she discovered herself. There was also a prince at Berkeley, a brilliant young assistant professor named Raphael Robinson. Theirs was to be a marriage that would endure until her death in 1985. Julia is the story of Julia Bowman Robinson, the gifted and highly original mathematician who during her lifetime was recognized in ways that no other woman mathematician had ever been recognized. This unusual book brings together in one volume the prize winning Autobiography of Julia Robinson by her sister, the popular mathematical biographer Constance Reid, and three very personal articles about her work by outstanding mathematical colleagues.
A Mathematical Gallery
Embark on a playful mathematical tour, aided by Lisl Gaal's illustrations of familiar scenes and whimsical triggers for the imagination. Along the way, find fruit stands arranged using polynomial multiplication, checkerboard tablecloths sewed with patterns of primes in a two-dimensional number system, and deceptive cats revealing that simple counting is not always so simple. Grasping the mathematics in this book requires only a basic background in algebra and geometry, so while the ideas can be understood and enjoyed at a variety of levels, it is recommended for ages 13–99. Touching on topics in current research, this is a book to read and revisit, gaining new insights each time.
Classical Theory of Arithmetic Functions
This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
Abstract Algebra with Applications
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
History of Mathematics
General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify just about everything, the practice of which can scarcely promote a critical approach to the subject. To counter this, History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes the proofs of important results which are typically neglected in the modern history of mathematics curriculum.
Actions of Groups
An undergraduate text with an active learning approach introducing representation theory and Galois theory topics using group actions.
The Collected Works of Julia Robinson
This volume presents all the published works -- spanning more than thirty years -- of Julia Bowman Robinson. These papers constitute important contributions to the theory of effectively calculable functions and to its applications. Outstanding among the latter are Robinson's proof of the effective unsolvability of the decision problem for the rational number field (and, consequently of that for the first-order theory of all fields), and her work that provided the central step toward the negative solution of Hilbert's Tenth Problem. These results provide upper bound for what one can hope to obtain in the way of positive solutions to the decision problem for special classes of fields and for s...
Complexities
Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students. This captivating book gives voice to women mathematicians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring....
Circuits and Systems for Security and Privacy
Circuits and Systems for Security and Privacy begins by introducing the basic theoretical concepts and arithmetic used in algorithms for security and cryptography, and by reviewing the fundamental building blocks of cryptographic systems. It then analyzes the advantages and disadvantages of real-world implementations that not only optimize power, area, and throughput but also resist side-channel attacks. Merging the perspectives of experts from industry and academia, the book provides valuable insight and necessary background for the design of security-aware circuits and systems as well as efficient accelerators used in security applications.
