Book: All the Mathematics You Missed: But Need to Know for Graduate School

ISBN: 9780521797078

Publisher: Cambridge University Press

Year: 2001

Math is Exciting. We are living in the greatest age of mathematics ever

seen. In the 1930s, there were some people who feared that the rising

abstractions of the early twentieth century would either lead to mathematicians

working on sterile, silly intellectual exercises or to mathematics

splitting into sharply distinct subdisciplines, similar to the way natural

philosophy split into physics, chemistry, biology and geology. But the very

opposite has happened. Since World War II, it has become increasingly

clear that mathematics is one unified discipline. What were separate areas

now feed off of each other. Learning and creating mathematics is indeed a

worthwhile way to spend one's life..

Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

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