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Mathematical Thinking and Problem Solving
In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed ...
Sophie’s Diary
Sophie Germain overcame gender stigmas and a lack of formal education to prove that for all prime exponents less than 100 Case I of Fermat's Last Theorem holds. Hidden behind a man's name, her brilliance as mathematician was first discovered by three of the greatest scholars of the eighteenth century, Lagrange, Gauss, and Legendre. In Sophie's Diary, Germain comes to life through a fictionalized journal that intertwines mathematics with historical descriptions of the brutal events that took place in Paris between 1789 and 1793. This format provides a plausible perspective of how a young Sophie could have learned mathematics on her own—both fascinated by numbers and eager to master tough subjects without a teacher's guidance. Her passion for mathematics is integrated into her personal life as an escape from societal outrage. Sophie's Diary is suitable for a variety of readers—both young and old, mathematicians and novices—who will be inspired and enlightened on a field of study made easy, as told through the intellectual and personal struggles of an exceptional young woman.
Lobachevski Illuminated
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2015! Lobachevski Illuminated provides an historical introduction to non-Euclidean geometry. Within its pages, readers will be guided step-by-step through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels. Extensive commentary situates Lobachevski's work in its mathematical, historical, and philosophical context, thus granting readers a vision of the mysterious and beautiful world of non-Euclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170-year-old text is challenging to read on its own, Seth Braver's carefully arranged “illuminations” render this classic accessible to any modern reader (student, professional, or layman) undaunted by high school mathematics.
Symmetry
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The Random Walks of George Polya
Both a biography of Plya's life, and a review of his many mathematical achievements by today's experts.
Five Hundred Mathematical Challenges
This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied. Teachers at both the college and secondary levels will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. This collection provides a solid base for students who wish to enter competitions at the Olympiad level. They can begin with easy problems and progress to more demanding ones. A special mathematical tool chest summarizes the results and techniques needed by competition-level students.
Beautiful Mathematics
Mathematical ideas with aesthetic appeal for any mathematically minded person.
A Mathematician Comes of Age
This book describes and analyses how a mathematics student can develop into a sophisticated and rigorous thinker.
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.
