Customer Reviews

Schaum's Outline of Theory and Problems of Modern Algebra

5 star:		(1)
4 star:		(5)
3 star:		(3)
2 star:		(1)
1 star:		(0)

 

 

I purchased this book as a supplement to my text for my Abstract Algebra course. I highly recommend any of the Schaum's Outlines whenever you want a clear and concise summary of ideas with valuable problems (both solved and unsolved). The solved problems in this book take you step by step through several key ideas without spoon feeding the entire subject.

Here are some caveats though. In case you are trying to purchase this book for a junior high or high school algebra class, let me warn you, This is NOT the same thing! Pick up the Elementary Algebra outline instead. Trust me.

Next, my class concentrated more on groups than this particular outline did. I found the Group Theory outline to be a useful "co-supplement" for my particular class. Since different teachers accentuate different things, I recommend talking to the teacher and asking what they would suggest.

Finally, I think that this book would have been served by including a few geometric arguments for groups including isometry groups in 2D. The lack thereof does not truly detract from the book but I feel the extra clarification would have been helpful.

This book has some good theoretical mathematics content, unfortunately not much of it is about the subject of abstract algebra. The first 80 pages of this book talk about sets, relations, operators, and number systems. The next 50 pages or so consist of elementary material on groups, rings, fields, and polynomials, and act as a very basic introduction to abstract algebra. Then the author again diverges off into mathematics that does not relate to abstract algebra and talks about vector spaces, matrices, matrix polynomials, linear algebra, and boolean algebra. Again, this is all good mathematical material with some good problems, but I don't see what it has to do with learning abstract algebra. A better title for this book would have been "Schaum's Outline on the Foundations of Mathematics" since it is really supplying a good theoretical introduction to mathematics for the mathematics major at about the college sophomore level. If that is what you are looking for, I would give this book about four stars.
If you want a good introductory textbook on abstract algebra might I recommend "A First Course in Abstract Algebra, Seventh Edition" by Fraleigh. The author explains the concepts very clearly, has plenty of examples, and motivates the reader by showing example uses of the theory in applications such as error coding. There are more rigorous books out there, but Fraleigh's book is a great introduction, and used copies can usually be found for roughly $60, or about half of the price of a new book.

I am an undergrad student in Computer Science. The content in this book is terse and very cohesive. And its cohesiveness is what I like most. Each successive chapter is developed rigorously upon previous chapters. A lot of proofs of most important theorems have been supplemented. These proofs I have been reading in awe, are real eye-openers. Mathematics had never been this entertaining.

I strongly recommend this book, especially if you don't know what Abstract Algebra is all about. I had no idea when I ordered...

Gallian's Contemporary Abstract Algebra is my required textbook for this course. I bought Schaum's Outline to supplement it and help me with some of the proofs. Instead, I found exactly the same worked-out examples from Gallian. My homework problems I was having trouble with were also under the "extra" problems section which does not have solutions. Basically this book was useless to me. If you aren't already using Gallian, that's the book you should get; this one would be okay if you want to save a few bucks.

Shortly after graduating from college with a math major, I realized that I needed some experience in modern or abstract algebra. For reasons that I no longer recall, I was able to obtain the major without taking a course in algebra. My undergraduate college offered two courses in abstract algebra, but rather than pay the full tuition, I asked the chair of the department if I could take some form of challenge exam for the credit.
She agreed and gave me the complete set of take-home graded questions that she had given out the previous year. I then worked through the exercises and submitted them to her for feedback. I passed both courses.
One of the primary reasons for my achievement was this book. From my perspective, the strongest point of the book is the extensive lead-in before group theory is introduced. The background review in the area of sets, relations, integers, rational, real and complex numbers was something I really needed. These chapters forced me to look at these things in ways that I had not done so in the past and prepared me to better think abstractly.
After this solid introduction, I was able to proceed into the study of groups, rings, integral domains, ideals and fields on my own. By design, the books in the Schaum's series are better used as supplemental rather than core texts. I found this one to be the exception; it is stronger in the preliminaries than it is in presenting the core material of the title.

I think this book would be good by itself in picking up algebraic theories and methods. Each section is well explained and the sample problems take you through the process step-by-step.

The only problem I have with the book is that not all the supplementary exercises (to test your understanding) have the answers. Some have an answer, some have a partial answer, some have a hint, and some have nothing. This is a little aggravating, but it does not take away from the book.

Excellent for a quick and rigorous grasping of basic concepts. A huge number of problems helps fix the theory and gain problem solving capability.

I really liked this book. It broke down abstract/modern algebra basics very well; however, i thought it would be more detailed about groups (the subject my professor spent much of his time on). It helped with the rules of integers and real numbers and, etc. But I was disappointed with how little of number theory it really covered. I needed to know more about rings and groups and subgroups. If you just need a little help this would be a great book for you. HOWEVER I would suggest looking for a more advanced book if you need information on groups and rings. Good supplementary text, but was not exactly what I thought it was.

This was an average resource for me in my advanced algebra course. I suggest if you are to use this book, to also get Joseph Gallian's Contemporary Algebra book as well.

This installment in the Schaum's outline series doesn't do it for me. I had reason to pick this one up simply out of curiousity (and out of habit, by using other titles in this series for other lower-level undergraduate courses). It hardly stimulates any interest on the part of the reader; and the presentation is dry; not to mention that the selection of solved problems wasn't carefully thought out (most, I found, were proofs of some pretty standard results, which I would have rather not seen all over again). And the bare-hands computations weren't all that exciting, either.

Ploughing through a course text proper would better serve the serious student of mathematics. There are other well-written books devoted to solved problems in algebra (group/ring theory, for instance). It's just a matter of scoping them out carefully, and dishing out the money (for photocopies, even).