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    Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

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    PEDERSONThe Unforgettable Psychological ThrillerWinner of the Nobel PrizeEXCERPTS"I opened the window and looked out. From where I was standing I had a view of a clothes, line and an open field. Farther away lay the ruins of a burnt-out smithy, which some labourers were busy clearing away. I leant with my elbows resting on the window-frame and gazed into open space. It promised to be a clear day--autumn, that tender, cool time of the year, when all things change their colour, and die, had come to us. The ever- increasing noise in the streets lured me out. The bare room, the floor of which rocked up and down with every step I took across it, seemed like a gasping, sinister coffin. There was no proper fastening to the door, either, and no stove. I used to lie on my socks at night to dry them a little by the morning. The only thing I had to divert myself with was a little red rocking-chair, in which I used to sit in the evenings and doze and muse on all manner of things." "Yes, it was clear that it was the same man he had driven. He recognized him--and he drove so that the horse's shoes struck sparks as they touched the stones.All through this phase of excitement I had not for one second lost my presence of mind. We pass a policeman, and I notice his number is 69. This number struck me with such vivid clearness that it penetrated like a splint into my brain--69--accurately 69. I wouldn't forget it.I leant back in the vehicle, a prey to the wildest fancies; crouched under the hood so that no one could see me. I moved my lips and commenced to I talk idiotically to myself. Madness rages through my brain, and I let it rage. I am fully conscious that I am succumbing to influences over which I have no control. I begin to laugh, silently, passionately, without a trace of cause, still merry and intoxicated from the couple of glasses of ale I have drunk. Little by little my excitement abates, my calm returns more and more to me. I feel the cold in my sore finger, and I stick it down inside my collar to warm it a little. At length we reach Tomtegaden. The driver pulls up.I alight, without any haste, absently, listlessly, with my head heavy. I go through a gateway and come into a yard across which I pass. I come to a door which I open and pass through; I find myself in a lobby, a sort of anteroom, with two windows. There are two boxes in it, one on top of the other, in one corner, and against the wall an old, painted sofa-bed over which a rug is spread. To the right, in the next room, I hear voices and the cry of a child, and above me, on the second floor, the sound of an iron plate being hammered. All this I notice the moment as I enter.I step quietly across the room to the opposite door without any haste, without any thought of flight; open it, too, and come out in Vognmansgaden. I look up at the house through which I have passed. "Refreshment and lodgings for travellers."It is not my intention to escape, to steal away from the driver who is waiting for me. I go very coolly down Vognmansgaden, without fear of being conscious of doing any wrong. Kierulf, this dealer in wool, who has spooked in my brain so long--this creature in whose existence I believe, and whom it was of vital importance that I should meet--had vanished from my memory; was wiped out with many other mad whims which came and went in turns. I recalled him no longer, except as a reminiscence--a phantom."