2 edition of Structure of algebra. found in the catalog.
Structure of algebra.
Vincent H. Haag
|Series||Addison-Wesley series in science and mathematics education|
|LC Classifications||QA155 .H2|
|The Physical Object|
|Pagination||vi, 154 p.|
|Number of Pages||154|
|LC Control Number||63012472|
This can be shown to be equivalent with the ring-like structure of the same name above. All groups are monoids, and all monoids are semi-groups. The binary operation can be called either meet or join. The book would be good for a differentiated course, because the problems in each section are grouped into three levels of difficulty, labeled A, B and C. Quadratic space : a vector space V over a field F with a function from V into F satisfying certain properties.
Algebra -like structures: composite system defined over two sets, a ring R and an R-module M equipped with an operation called multiplication. I am very impressed with the way the topics are explained. It combines an abstract set-based approach hence the word "structure" in the title and computational methods hence the word "methods" in the title. They don' t use it at the school I teach, although I have used it in the past.
For example, the set of integers under the operation of addition is a group. The binary operation can be indicated by any symbol, or with no symbol juxtaposition as is done for ordinary multiplication of real numbers. With teacher guidance, one or two more study guides, and most importantly, a dedicated self-motivated mind, you are bound to be a success in algebra. It combines an abstract set-based approach hence the word "structure" in the title and computational methods hence the word "methods" in the title. Have questions about particular items?
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Ring-like structures or Ringoids: two binary operations, often called addition and multiplicationwith multiplication distributing over addition. Vector space : a module where the ring R is a division ring or field. It is straight forward. The idea is that if the grades of two elements a and b are known, then the grade of ab is known, and so the location of the product ab is determined in the decomposition.
Similar Books. Sets : Rather than just considering the different types of numbersabstract algebra deals with the more general concept of sets: a collection of all objects called elements selected by property specific for the set.
A monoid is a semi-group which does have an identity but might not have an inverse for every element. I am especially pleased the more I compare this to other books.
Peano arithmetic. This can be viewed as a system with five binary operations: two operations on R, two on M and one involving both R and M.
I will admit, being a 6th grader, that this had it's downpoints, mainly not giving many clues on how to do the problem, which in it's self is a good thing and bad.
Another thing with algebra, your problems can get quite long and convoluted.
This includes distributivity over addition and linearity with respect to multiplication by elements of R. The only thing I can see being a negative now is the lack of graphing calculator exercises or projects.
Two sets with operations[ edit ] Module -like structures: composite systems involving two sets and employing at least two binary operations.
Sure, there will be students who find this book hard to understand -- they are the ones who are not really ready for algebra and should be either taking pre-algebra or one of the many "algebra lite" books that are available.
Petti on Jan 24, This is the best Algebra I book ever published. One thing about this book is that the explanations in this book at the top of every section summarizes important concepts and gives some examples and definitions; however, the examples often only cover the "A" and half of the "B" problem sets, and the "C" problems are often unexplained.
Exterior algebras and geometric algebras are special cases of this construction. Identity elements : The numbers zero and one are abstracted to give the notion of an identity element for an operation.Pre-Algebra - Fractions Objective: Reduce, add, subtract, multiply, and divide with fractions.
Working with fractions is a very important foundation to algebra.
Here we will brieﬂy review reducing, multiplying, dividing, adding, and subtracting fractions. As this is a review, concepts will not be explained in detail as other lessons are.
Well, I cannot solve your homework for you as that would mean cheating. However, I can give you an idea. Try using Algebrator. You can find detailed and well explained answers to all your queries in algebra structure and method book teachers answers for free.
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Basic Algebra The Laws of Algebra Terminology and Notation. In this section we review the notations used in algebra. Some are peculiar to this book. For example the notation A:= B indicates that the equality holds by de nition of the notations involved.
Two other notations which will become important when we solve equations are =) and ().