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This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ...the other end 6 feet less than of it, and then there remained 25 feet; how long was the line? Ans. 40 ft. 34. In a bag containing eagles and dollars, there are 4 times as many eagles as dollars; but if 6 eagles and as many dollars be taken away, there will be left 6 times as many eagles as dollars; how many were there of each? Ans. Eagles, 60; dollars, 15. 35. A bright young lady being asked her age by a gentleman who was "not very smart at figures," said, "Twice my age 2J years ago will equal 3 times of my age 2i years hence;" what was her age? Ans. 17 yrs. 36. An English lady distributed 20 shillings among 20 persons, giving 6 pence each to some, and 16 pence each to the rest; how many persons received 6 pence each? Ans. 8 persons. 37. A mason receives $450 for building a wall; if he had received $1 more a rod he would have received for the entire w rk 8540; how many rods of wall did he build? Ans. 75 rods. 38. A man loans $8250, part at 5% and part at 6%; how much did he loan at each rate if he receives equal sums of interest for each part? Ans. $4500; $3750. 39. An army lost of its number in killed and wounded and 5000 prisoners; it was then reinforced by 10,000 men, but retreating, it lost- -of its number on the march, when there remained 60,000 men; what was the original force? Ans. 80,000. 40. Find two consecutive numbers, such that the fifth and the seventh of the first taken together shall equal the sum of the fourth and the twelfth of the second taken together. Ans. 35 and 36. 41. A person being asked the time of day, replied," It is between 3 and 4 o'clock, and the hour-and minute-hands of my watch are exactly opposite each other;"what was the time? Arts. 49 min. past 3. 42. A...
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