Customer Reviews

Schaum's Outline of Theory and Problems of Geometry: Includes Plane, Analytic, Transformational, and Solid Geometries (Schaum's Outlines)

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

 

 

This is not only the best elementary geometry (and related subjects) outline, but also the best text in its field, in my opinion. The student will find as many theorems and definitions as in very long and detailed texts, presented much more concisely and in a much more organized fashion here in categories that are easily understood. As with my review of Schaum's algebra, I recommend strongly that the student make flash cards from Schaum's theorems and definitions before trying to work out or even read the numerous solved problems by themselves. Close to 95% of students, in my opinion, make the mistake of doing massive amounts of geometry problems and homework before learning what the theorems and definitions say. This is like trying to learn to play the violin by playing symphonies before one knows how to move the bow and fingers, and is probably the main cause of middle school, high school, and college elementary geometry failure.

This book is suitable for high school or first year college students who have to take geometry. It is a no-frills, basics package that all students can master, if they take the time. I agree with the previous reviewer that students should make flash cards of definitions and theorems, but doing problems simultaneously, section-by-section, will not hurt.

For students, this is a good book to practice basic math study skills: (1) predict what you are going to learn by skimming, (2) survey the material, (3) question the material (what do I not know now?) (4) read (no more than 45 minutes at a setting -- or you'll get a brain cramp), (5) recite (from your outline and flash cards, and (6) review and prepare for your test. This book is well written but for new geometry students, it can be pretty dense, so you should practice reading and concentrating every day, up to 45 minutes at a setting.

I found two problems with the book: (1) It says on the cover that it covers "solid" geometry. It does not. All the geometry is in 2 dimensions. (2) It says that it covers analytic geometry. It touches analytic geometry only peripherally.

Good luck!

This is definitely a great review book, but the review problems are very, very easy and not at all like the ones on the actual test. That is definiely my biggest gripe about the book.

However there are many pluses to this book as well. Each theoreom comes with examples, pictures, and definitions so you can easily understand them.

Also, every concept is well defined and in a way that is helpful and concise.

I bought this book to use with my daughter for added drill and review of Geometry and was shocked to find an inaccurate mathematical statement after the Commutative Law of Multiplication (3a X 5 = 5 X 2a = 10a) and three errors in the solutions provided to practice questions in the first eight pages. I haven't ventured further, but based on my experience thus far, I will need to review every example and problem for accuracy, something I hadn't planned to do and shouldn't need to do.

For the most part this book is great as a tutorial with ample exercises that provide critical thinking pertaining to proving triangles congruent and reasoing in general. Thats the way geometry should be taught critical thinking unlike most books that regurgitate and are watered down. Even though this book is modern, its not as great as plane geometry munro 1959, theres not ample exercises on tedious proofs. My favorite sections are proving quadrilaterals are parallelograms and areas of polygons because these problems force the individual (student) to think outside the box. For example, there are problems where circles are inscribed in circles, sectors inscribed in equilateral triangles, right triangles part of circles, etc.

The weakness is the fact that this book does not provide surface area of hexagonal prisms, polygonal pyramids involve apothems, radii, surface area of cones, no composite figures, just surface area of rectangular prisms and cubes, its the same like schaums outline for algebra in regards to this section and the same regarding reflections and translations. I therefore give this 3 stars because of some redundancies.

I found myself needing to review geometry for the SAT and needed a succinct, clear, and accurate guide. This outline has more than exceeded my expectations. By the time I worked through most of the problems in this book, my geometry skills had doubled and the SAT geometry was relatively easy.

I highly reccomend this book as either a refresher guide or as a textbook.

This is a great way to reivew principles and then use the problems for additional practice. Some problems are fully worked, others have only the answer listed. Great addition for someone who learns best by doing problems.

I am using this book as a refresher while studying for an upcoming qualification exam. In just the opening chapters covering Algebra review, I was appalled at the number of errors made. These are not typographical errors as is the case where the book says that something weighs "11 km", but flagrant syntactical errors that produce a muddled understanding of the underlying concepts.

Luckily, I am still fresh enough with Algebra to catch these errors, however, I have to question their ability to clearly convey geometry material without confusion.

This is not to say that the text is a total wash, but I do expect a certain level of accuracy from outline materials such as this.

I got this book as review of basic geometry. Mostly because they never made a Forgotten Geometry text. It's really not bad. It covers quite a bit of ground, from simple geometry to a taste of analytical and transformational geometry.

Conversely, this book didn't wow me either. It covers some basic algebra in the beginning, which is fine for the easier formulas like area and perimeter, but not nearly enough for a comprehensive study of geometry. One should study Schaum's outline of Intermediate Algebra or College Algebra, or a text of their choosing, before tackling any geometry. Especially if your preparing for a Calculus/Analytical Geometry Course.

I haven't found a good intro geometry book yet(I haven't even looked!), but when I do, I'll be sure to update this review. As always, good luck!

We know from the book's success and from other reviewers that it is good for preparing students who need many easy exercises to drill for a rudimentary exam in geometry. I want to discuss it from the point of view of teaching a student who is interested or could become interested in learning geometry.

In a rigorous presentation of geometry one starts by treating "point", "straight line" (and "plane" in solid geometry) as undefined terms. One states their assumed properties as postulates. One defines all other objects in geometry in terms of these and one derives all other assertions about about geometric objects by logical reasoning alone; one may not use without proof even what is obvious from looking at a figure, e.g., that if two points A, B are inside a triangle then the entire line segment AB is inside.

The teaching of geometry in high school has long been intended as an example of rigorous reasoning but to fully adhere to the above standard would make a course too subtle, long and boring. The challenge for the writer of a school textbook or a curriculum is to present a reasonable amount of geometry, especially geometry needed in applications, and to loosen the standards of rigor by not dwelling much on rigorously proving what is obvious.

How does this book handle the problem? A thin veneer of rigor appears in some places, to be abandoned after a few paragraphs. On pp. 64-65 the book stresses that "point", "line" and "plane" are undefined terms. But it immediately goes on to tell us that if a line segment is divided into parts the length of a line segment is the sum of the lengths of its parts. So, "line" is an undefined term but the book feels free to talk about its segments and their lengths without further explanation.

On pp. 85-86 the book lists 10 postulates of algebra. They are all instances of the fact that in an algebraic expression we may replace any quantity by one that is equal to it. The distributive, associative and commutative laws are not among the postulates but of course the book does not hesitate to use those. After the 10 postulates of algebra come the geometry postulates 11-19. Postulate 14 says that one and only one circle can be drawn with a given point as center and a given radius. Since a circle has been defined on p. 67 as the set of all points at a given distance from the center, it should have been obvious to the authors that there is no need to state this as a postulate. Postulate 15 says that any geometric figure can be moved without changing its size or shape. Needless to say, nowhere was "moving" defined in terms of the undefined concepts point and line.

In sum, there are a few pages in the book where the student is told that geometry is built up by deductive reasoning but they seem to have been inserted as an afterthought and bear no relation to the bulk of the book. With the logic of the book muddled, how are students to know what they can use in a proof? Here "principle"-s come to the rescue. The book contains about 200 "principles". Examples: principle 6 on p. 146: The diagonals of a parallelogram bisect each other. Principle 4 on p. 153: the median of a trapezoid is parallel to its bases and its length is equal to one half the sum of its bases. A few pages later the student is asked to prove some trivialities and if he guesses that of the countless "principles" he has read, the ones he needs to use are among the ones immediately preceding the problem, he will be right.

How far does the book get into geometry? Let A,B,C,D be points on a circle and E be the intersection of AC and BD. Facts about the angles and lengths of this configuration are given much space and, together with Pythagoras' Theorem, represent the limits of the book's scope. As another reviewer noted already, the cover promises solid geometry but the book has none.

Redeeming features of the book are chapter 15, pp. 291-305, which gives the basic ruler and compass constructions and chapter 16, pp. 306-317, which lists and properly proves the theorems of substance in the book. The way I see it, these 27 pages contain the mathematics of the book; the rest is drill.

If your student has or could develop an interest in math, science or technology, the geometry book for him/her is Harold R. Jacobs: Geometry (W.H. Freeman). Math has been my preoccupaton for 60 years but it was still a revelation that geometry could be presented in such a stimulating and attractive manner. There is no straying from or diluting the subject as in other big colorful textbooks. The price is high but worth it. [...]