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Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics), by Joseph J. Rotman, Mathematics
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Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics.
Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.
- Sales Rank: #401725 in Books
- Published on: 2006-12-27
- Released on: 2006-12-27
- Original language: English
- Number of items: 1
- Dimensions: 8.44" h x .49" w x 5.22" l, .58 pounds
- Binding: Paperback
- 256 pages
From the Back Cover
Rotman, Joseph, Journey into Mathematics: The World of Proof Prompting readers to do mathematics, not merely read about it, this proactive book has users reading and writing proofs at the outset. Complete proofs are given from the start, and coverage begins with elementary mathematics to allow focus on the writing and reading of proofs without the distraction of absorbing new ideas simultaneously.Contains material that is familiar to calculus readers (i.e., induction, binomial theorem, polygonal, using the Diophantine parametrization of the circle by rational functions to solve trigonometric identities, etc.), and engages readers throughout with interesting expositions using history, etymology, and humorous asides. Material is presented as a 'single story' to aid in the subjects progressive growth and development.For mathematicians.
Most helpful customer reviews
46 of 47 people found the following review helpful.
Analysis Without Tears
By Steven Marks
Until I came across this book, I did not believe there existed a decent book to teach proofs that one can use for SELF-STUDY.
The stated aim of this book is to introduce the idea of proofs and analysis on subject matter that is not too difficult. In the ~230 pages one gets introduced to proofs in a total variety of contexts - algebra and geometry and number theory and complex numbers. About 20% of the proofs require calculus -but not at an advanced level.
A number of proofs are demonstrated in these different contexts in a way that one can follow and understand.
It would be great to take a class based upon this book where the instructor follows the author's suggestion of assigning problems to teams and they present to the class.
The author also makes the statement that at the high school level, instead of one year geometry and one year algebra it should be 2 years of a combined class. I think this is a real good idea; the two subjects are articifically separated. This is also the idea of "Numbers and Geometry" by John Stillwell - which I am currently reading and will review in a couple months.
I think this is an excellent book for a good solid introduction to real non-trivial mathematical proofs, but where one is at the same time not really struggling with advanced concepts like one would in a standard analysis class. There are some good digressions with some mathematical history as well; such as the Chinese really had Pascal's triangle centuries before Blasie Pascal. I really recommend it for someone who is looking for a self-study guide AND with Dover you know the price is right!
9 of 18 people found the following review helpful.
A very entertaining read
By Cohan Sujay Carlos
The book has a very interesting approach to a wide range of topics in maths. Uses lots of anecdotes and historical facts to motivate the reader. I haven't really sat down to the exercises, but I love the stories and pointers.. sure shall get at the sources mentioned, sometime.
0 of 0 people found the following review helpful.
It has many good ideas on developing the skills of understanding and using ...
By augustusmax
It has many good ideas on developing the skills of understanding and using proofs (something that always needs to be worked on) and seems to be one of the unique approaches to this subject. I find no fault in the method and I am working through the book to see if I can glean some of the wisdom from it.
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