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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Description:

This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.


Editorial Reviews

Review

"The instructional material is to the point, with well-considered examples and asides on common mistakes. Good examples of the author's thoughtfulness appear in the discourses on pp. 5-6 of identifying the hypothesis and conclusion when they are not obvious, on pp. 28-29 regarding overlapping notation, and on pp. 190-191 of the advantages and disadvantages of generalization." (Zentralblatt MATH 2016)

About the Author

Daniel Solow is a professor of management for the Weatherhead School of Management at Case Western Reserve University. His research interests include developing and analyzing optimization models for studying complex adaptive systems, and basic research in deterministic optimization, including combinatorial optimization, linear and nonlinear programming. He has published over 20 papers on both topics.

Reviews:

5.0 out of 5 stars Best book eva!

J. · October 7, 2024

Can’t say enough, concise and true for all time! Daniel Solow has done a tremendous favor for all humanity in my opinion!

5.0 out of 5 stars Definitely worth the price

D.D.B.M. · February 20, 2022

Well written, (relatively) easy to understand, and provided background that I wish I had back in elementary school when I was first introduced to proofs. Books like this would help (literally) thousands of students that are frustrated by math textbooks that don't "connect the dots" in a logical and step-wise manner. Kudos for explaining the process behind proofs. Mathematics should not be an "exclusive club" and this text goes a long way to democratizing a topic that can sometimes confound even the most intelligent student!

5.0 out of 5 stars This book is the key to unleashing your full mathematical potential.

J.B.R. · March 6, 2017

Prior to discovering this book, I have read tons of guides and books on how to do proofs. I am an undergrad just entering my final year. I have YET to fully comprehend how to do proos properly. Every book, auther, or professor speaks about proofs without understanding where the bottle neck in a student's knowledge lies.Daniel Solow is the messiah or me. I was lost but now I am found. He sheds away the fluff and gives you a true distilled approach to the matter. By the first two chapthers alone is worth the "price of admission". He gives you a strong foundation in order to build upon. I went back to old proofs that were assigned for homework and I see them with much greater clarity.All I can say is thank you Daniel for showing me the way to become a better mathematician. You don't even need calculus! I wish I read this a lot sooner...

4.0 out of 5 stars A practical book to proofs

L. · November 5, 2018

I tried the book of proofs and how to prove it. I liked both but find that I was struggling with proofs still and didn't feel I was well equipped enough to tackle proofs that required any ingenuity... How to read and do proofs actually gives you many different methods (Forward backwards method should be introduced in all proof books) in your tool box to prepare you for tackling any proof. The author does an excellent job explaining things and even does proof analysis that breaks down the methods that are used. If you want more thorough coverage on how to actually tackle proof problems then I would get this books. Only reason I gave it 4 starts is because you have to go online to see the solutions and I find that their could be more actual proof problems in the back.

5.0 out of 5 stars Best book for math proofs

N. · May 29, 2021

I bought five books from Bolo on how to do math proofs. This is the only one that makes sense to me. The videos and solution manual are the best part. You can check to see if your proof is correct. Solow is not a mathematician, so some of his terminology may not match what you learned in your bridge/transition class. I don’t care as long as I can write a better proof.

1.0 out of 5 stars No margins.

A.C. · April 2, 2025

I've ordered and returned this book three times. As you can see in the photo, the outside margins of pages are tiny. Coming in at about 0.5 cm wide, they are almost non-existent. By looking at pictures of pages of this book in other reviews you can verify that this is not normal and indeed a printing error. Given that I've received copies of this book with the tiny margins more than once, it seems as if there are many copies of this book with this defect and they are selling them to customers at full price.

5.0 out of 5 stars Came Recommended

J.B. · December 15, 2015

This book is among a handful that are recommended for new college math majors, minors, and probably a larger group, computer science students who have to take discrete math. I came across it on a discrete math syllabus. It seems very well put together, some seem to prefer the Velleman, others prefer this. The 2 negative reviews are not actually reviews, just people who could not figure out their kindle, and they should probably be deleted.A benefit of this book is that there are 15 lectures as well as other supplemental material at the wiley website. Personally I bought this as well as the Velleman, and a few others, to try to prep as much as I can, and to have on hand for reference. There is a ton of material out there on college-level math, but not all of it is well organized, clear, and systematic like this.

4.0 out of 5 stars A new one

J. · July 28, 2018

Bought a new one, size was smaller than I thought, price is a little expensive but feel worth it!✋

Nice book.

B. · October 26, 2016

Easy to follow.

A perfect introduction to mathematical logic, thinking processes and proof techniques

A.C. · September 21, 2014

Read this along with the lectures at wiley.com and you have a perfect introduction to mathematical logic, thinking processes and proof techniques.This should seriously become a part of secondary education as the tools are invaluable. For those familiar with the concepts it is perhaps a little laboured, but as an introduction to the subject I doubt it can be surpassed (the lectures really help with this).

Great content; terrible printing.

K. · December 28, 2020

The actual content of the book is fantastic, I had an eBook version but got a physical copy because I loved it so much. As a CS student reading this, I must admit the math majors are up to some very interesting things! However, as you can see in my pictures, the physical copy has missing characters under each square root symbol!!

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Product ID: U1118164024
Condition: New

4.2

AED32103

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

Quantity:

|

Order today to get by 7-14 business days

This item qualifies for free delivery

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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.

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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.

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Similar items from “Logic”

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Product ID: U1118164024
Condition: New

4.2

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes-0
Type: Paperback

AED32103

Price includes VAT & Import Duties
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

This item qualifies for free delivery

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:

This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.


Editorial Reviews

Review

"The instructional material is to the point, with well-considered examples and asides on common mistakes. Good examples of the author's thoughtfulness appear in the discourses on pp. 5-6 of identifying the hypothesis and conclusion when they are not obvious, on pp. 28-29 regarding overlapping notation, and on pp. 190-191 of the advantages and disadvantages of generalization." (Zentralblatt MATH 2016)

About the Author

Daniel Solow is a professor of management for the Weatherhead School of Management at Case Western Reserve University. His research interests include developing and analyzing optimization models for studying complex adaptive systems, and basic research in deterministic optimization, including combinatorial optimization, linear and nonlinear programming. He has published over 20 papers on both topics.

Reviews:

5.0 out of 5 stars Best book eva!

J. · October 7, 2024

Can’t say enough, concise and true for all time! Daniel Solow has done a tremendous favor for all humanity in my opinion!

5.0 out of 5 stars Definitely worth the price

D.D.B.M. · February 20, 2022

Well written, (relatively) easy to understand, and provided background that I wish I had back in elementary school when I was first introduced to proofs. Books like this would help (literally) thousands of students that are frustrated by math textbooks that don't "connect the dots" in a logical and step-wise manner. Kudos for explaining the process behind proofs. Mathematics should not be an "exclusive club" and this text goes a long way to democratizing a topic that can sometimes confound even the most intelligent student!

5.0 out of 5 stars This book is the key to unleashing your full mathematical potential.

J.B.R. · March 6, 2017

Prior to discovering this book, I have read tons of guides and books on how to do proofs. I am an undergrad just entering my final year. I have YET to fully comprehend how to do proos properly. Every book, auther, or professor speaks about proofs without understanding where the bottle neck in a student's knowledge lies.Daniel Solow is the messiah or me. I was lost but now I am found. He sheds away the fluff and gives you a true distilled approach to the matter. By the first two chapthers alone is worth the "price of admission". He gives you a strong foundation in order to build upon. I went back to old proofs that were assigned for homework and I see them with much greater clarity.All I can say is thank you Daniel for showing me the way to become a better mathematician. You don't even need calculus! I wish I read this a lot sooner...

4.0 out of 5 stars A practical book to proofs

L. · November 5, 2018

I tried the book of proofs and how to prove it. I liked both but find that I was struggling with proofs still and didn't feel I was well equipped enough to tackle proofs that required any ingenuity... How to read and do proofs actually gives you many different methods (Forward backwards method should be introduced in all proof books) in your tool box to prepare you for tackling any proof. The author does an excellent job explaining things and even does proof analysis that breaks down the methods that are used. If you want more thorough coverage on how to actually tackle proof problems then I would get this books. Only reason I gave it 4 starts is because you have to go online to see the solutions and I find that their could be more actual proof problems in the back.

5.0 out of 5 stars Best book for math proofs

N. · May 29, 2021

I bought five books from Bolo on how to do math proofs. This is the only one that makes sense to me. The videos and solution manual are the best part. You can check to see if your proof is correct. Solow is not a mathematician, so some of his terminology may not match what you learned in your bridge/transition class. I don’t care as long as I can write a better proof.

1.0 out of 5 stars No margins.

A.C. · April 2, 2025

I've ordered and returned this book three times. As you can see in the photo, the outside margins of pages are tiny. Coming in at about 0.5 cm wide, they are almost non-existent. By looking at pictures of pages of this book in other reviews you can verify that this is not normal and indeed a printing error. Given that I've received copies of this book with the tiny margins more than once, it seems as if there are many copies of this book with this defect and they are selling them to customers at full price.

5.0 out of 5 stars Came Recommended

J.B. · December 15, 2015

This book is among a handful that are recommended for new college math majors, minors, and probably a larger group, computer science students who have to take discrete math. I came across it on a discrete math syllabus. It seems very well put together, some seem to prefer the Velleman, others prefer this. The 2 negative reviews are not actually reviews, just people who could not figure out their kindle, and they should probably be deleted.A benefit of this book is that there are 15 lectures as well as other supplemental material at the wiley website. Personally I bought this as well as the Velleman, and a few others, to try to prep as much as I can, and to have on hand for reference. There is a ton of material out there on college-level math, but not all of it is well organized, clear, and systematic like this.

4.0 out of 5 stars A new one

J. · July 28, 2018

Bought a new one, size was smaller than I thought, price is a little expensive but feel worth it!✋

Nice book.

B. · October 26, 2016

Easy to follow.

A perfect introduction to mathematical logic, thinking processes and proof techniques

A.C. · September 21, 2014

Read this along with the lectures at wiley.com and you have a perfect introduction to mathematical logic, thinking processes and proof techniques.This should seriously become a part of secondary education as the tools are invaluable. For those familiar with the concepts it is perhaps a little laboured, but as an introduction to the subject I doubt it can be surpassed (the lectures really help with this).

Great content; terrible printing.

K. · December 28, 2020

The actual content of the book is fantastic, I had an eBook version but got a physical copy because I loved it so much. As a CS student reading this, I must admit the math majors are up to some very interesting things! However, as you can see in my pictures, the physical copy has missing characters under each square root symbol!!

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Similar items from “Logic”