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Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics)

Description:

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.


Editorial Reviews

About the Author

Joseph Rotman is Professor of Mathematics at the University of Illinois.

Reviews:

5.0 out of 5 stars It has many good ideas on developing the skills of understanding and using ...

a. · May 10, 2016

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.

5.0 out of 5 stars Analysis Without Tears

S.M. · October 15, 2007

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!

5.0 out of 5 stars Five Stars

M.A. · October 24, 2014

a

5.0 out of 5 stars A very entertaining read

C.S.C. · April 21, 2002

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.

Amazing book

I.F.G. · December 27, 2024

This book is very well-written. It is not the classic one that starts with the basics of logic and the usual truth tables. Its style is unique and motivating

Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics)

Product ID: U0486453065
Condition: New

4.8

AED9201

Price includes VAT & Import Duties
Type: Paperback
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

Delivery fee of AED 20. Free for orders above AED 200.

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Imported From: United States

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Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics)

Product ID: U0486453065
Condition: New

4.8

Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics)-0
Type: Paperback

AED9201

Price includes VAT & Import Duties
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

Delivery fee of AED 20. Free for orders above AED 200.

Returns & Warranty policies

Imported From: United States

At BOLO, we work hard to ensure the products you receive are new, genuine, and sourced from reputable suppliers.

BOLO is not an authorized or official retailer for most brands, nor are we affiliated with manufacturers unless specifically stated on a product page. Instead, we source verified sellers, authorized distributors or directly from the manufacturer.

Each product undergoes thorough inspection and verification at our consolidation and fulfilment centers to ensure it meets our strict authenticity and quality standards before being shipped and delivered to you.

If you ever have concerns regarding the authenticity of a product purchased from us, please contact Bolo Support. We will review your inquiry promptly and, if necessary, provide documentation verifying authenticity or offer a suitable resolution.

Your trust is our top priority, and we are committed to maintaining transparency and integrity in every transaction.

All product information, images, descriptions, and reviews originate from the manufacturer or from trusted sellers overseas. BOLO is not affiliated with, endorsed by, or an authorized retailer for most brands listed on our website unless stated otherwise.

While we strive to display accurate information, variations in packaging, labeling, instructions, or formulation may occasionally occur due to regional differences or supplier updates. For detailed or manufacturer-specific information, please contact the brand directly or reach out to BOLO Support for assistance.

Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of United Arab Emirates. Any items found to be restricted or prohibited for sale within the UAE will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in United Arab Emirates are listed on our website.

All items are shipped by air, and any products classified as “Dangerous Goods (DG)” under IATA regulations will be removed from the order and cancelled.

All orders are processed manually, and we make every effort to process them promptly once confirmed. Products cancelled due to the above reasons will be permanently removed from listings across the website.

Description:

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.


Editorial Reviews

About the Author

Joseph Rotman is Professor of Mathematics at the University of Illinois.

Reviews:

5.0 out of 5 stars It has many good ideas on developing the skills of understanding and using ...

a. · May 10, 2016

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.

5.0 out of 5 stars Analysis Without Tears

S.M. · October 15, 2007

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!

5.0 out of 5 stars Five Stars

M.A. · October 24, 2014

a

5.0 out of 5 stars A very entertaining read

C.S.C. · April 21, 2002

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.

Amazing book

I.F.G. · December 27, 2024

This book is very well-written. It is not the classic one that starts with the basics of logic and the usual truth tables. Its style is unique and motivating

Similar suggestions by Bolo

More from this brand

Similar items from “Logic”