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Introduction to Higher Algebra (Dover Books on Mathematics), by Maxime Bocher, Mathematics
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The author of this text ranks among America's most influential teachers, and his stimulating lectures helped train many leaders in mathematical research. Maxime Bocher’s Introduction to Higher Algebra remains a favorite with students and teachers for a number of important reasons: comparatively, brief, it covers a vast amount of material; its elegant presentation of concepts and theorems is unsurpassed in the literature; its specific and concrete approach makes the content easier to learn and understand; and it offers a rich repository of often-neglected theorems.
This text presents the fundamentals of higher algebra — including polynomials, determinants, matrices, and elimination theory — and a thorough foundation in algebraic principles. Beginning with an account of polynomials and their basic properties, it examines the properties of determinants and Laplace's development, multiplication theorem, bordered and adjoint determinants, the theory of linear dependence, linear equations, and related topics. A treatment of theorems concerning the rank of a matrix is followed by chapters on linear transformations and the combination of matrices, invariant, and bilinear forms.
Additional topics include quadratic forms, factors of polynomials, general theorems on integral rational invariants, symmetric polynomials, polynomials symmetric in pairs of variables, and elementary divisors.
- Sales Rank: #4349640 in Books
- Published on: 2004-06-10
- Released on: 2004-06-10
- Original language: English
- Number of items: 1
- Dimensions: .85" h x 6.48" w x 8.64" l, 1.26 pounds
- Binding: Hardcover
- 336 pages
Most helpful customer reviews
3 of 3 people found the following review helpful.
If you're curious as to how Algebra works read this.
By Joe B.
I really am enjoying this book. I have to admit that as a Mathematician I have been greatly biased towards Geometry. Having been so fond of the classics of Geometry I have never given much thought to Algebra at the higher levels. What got me so interested in this book is that Bocher does not write in the dry banal style typical of most mathematics books. He has a great ability to present mathematical topics in a way that I personally believe clever high school students could learn from this.
In short I would recommend this book for people who are:
1. Thinking of becoming a Math Major/Minor.
2. Students curious as to how "Math works/Algebra works"
3. Preparing to take a course in Analysis or Linear Algebra
4. Want a fun and interesting challenge.
5. Wants to grapple with higher algebra without being overwhelmed with it.
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