Undergraduate Algebra

Serge Lang (Autor)

Buch | Softcover

389 Seiten

2010 | Softcover reprint of hardcover 3rd ed. 2005
Springer-Verlag New York Inc.
978-1-4419-1959-5 (ISBN)

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This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the hnear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory.

The Integers.- Groups.- Rings.- Polynomials.- Vector Spaces and Modules.- Some Linear Groups.- Field Theory.- Finite Fields.- The Real and Complex Numbers.- Sets.

Erscheint lt. Verlag	29.11.2010
Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	XII, 389 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	1-4419-1959-7 / 1441919597
ISBN-13	978-1-4419-1959-5 / 9781441919595
Zustand	Neuware