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by Frank Markham Brown
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Mathematics
  • Author:
    Frank Markham Brown
  • ISBN:
    0486427854
  • ISBN13:
    978-0486427850
  • Genre:
  • Publisher:
    Dover Publications; 2nd ed. edition (March 16, 2012)
  • Pages:
    304 pages
  • Subcategory:
    Mathematics
  • Language:
  • FB2 format
    1609 kb
  • ePUB format
    1191 kb
  • DJVU format
    1987 kb
  • Rating:
    4.1
  • Votes:
    911
  • Formats:
    doc lrf mbr lit


CRITICISMS My major criticism of 'Boolean Reasoning' is the large range of detail between some chapter sections. That is also the terminology in the 2011 'Boolean Functions' book I bought in Jan 2014 and have been reading

CRITICISMS My major criticism of 'Boolean Reasoning' is the large range of detail between some chapter sections. Brown often wrote short sections with little detail while other sections were fully detailed and satisfying. That is also the terminology in the 2011 'Boolean Functions' book I bought in Jan 2014 and have been reading. That book rather arbitrarily standardized on DNF, as equivalent SOP was standardized in 'Boolean Reasoning'. The CNF and DNF gy are also found in mathematical logic and especially in computational logic books.

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A systematic treatment of Boolean reasoning, this concise, newly revised .

Brown begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras. Two concluding chapters deal with applications. Beautifully illustrated, low-priced Dover coloring on an amazing variety of subjects. Visit Dover Coloring. Show me . Teacher's Resources.

This book is about the logic of Boolean equations. Such equations were central in the "algebra of logic" created in 1847 by Boole and devel­ oped by others, notably Schroder, in the remainder of the nineteenth century. Digitally watermarked, DRM-free. Included format: PDF. ebooks can be used on all reading devices. Immediate eBook download after purchase.

For the benefit of readers without formal training in mathematics, the text starts with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras, based on Huntington's postulate.

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Brown begins wi. Boolean Reasoning: The Logic of Boolean Equations by Brown. Lehman College - Stacks - QA10.

Boolean reasoning, by Frank Markham Brown. This book is about the logic of Boolean equations. Such equations were central in the "algebra of logic" created in 1847 by Boole and devel-oped by others, notably Schroder, in the remainder of the nineteenth century. p. cm. Includes bibliographical references (p. 247-264).

Boolean Reasoning - Frank Markham Brown. Chapter 1. Introduction. Boolean reasoning differs from the theorem-proving methodology of predicate logic in a number of important ways. Such equations were central in the algebra of logic created in 1847 by Boole and developed by others, notably Schroder, in the remainder of the nineteenth century. Contemporary logicians have abandoned Boole’s equation-based logic in favor of predicate logic, which encompasses a wider range of discourse. Predicates (propositional functions) and propositions are two-valued.

A systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished re.For the benefit of readers without formal training in mathematics, the text starts with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras, based on Huntington's postulate. It defines operators for elimination, division, and expansion, providing a coherent and systematic basis for subsequent discussions of syllogistic reasoning, the solution of Boolean equations, and functional deduction.Examples and end-of-chapter problems appear throughout the book, many taken from the design for switching systems. Two concluding chapters deal with applications; one applies Boolean reasoning to diagnostic problems, and the other discusses the design of multiple-output logic-circuits.


Ximinon
This is a really good book with rich in bibliographies.
I would recommend people to buy this book.
I'm a Computer Programmer Analyst and a Computer Science Graduate
Nelson Hem
Lli
2014
On Tue 14Jan2014, this review was inverted with the most current 2014 book reading at top and with the original Jan 2011 book reading at bottom. The 2011-2012-2013 section stays in the middle. Jan 2014 reading closed to further writing at 19:53 CST of Fri 17Jan14. Just eight days, 10-17Jan14 to do all of the Jan 2014 reading including finishing chapter 2, rereading chapter 1, reading all of chapters 3-5 and half of chapter 6 of 'Boolean Reasoning'.

Resumed further reading of 'BR' on Wed 10Dec14, near end of 2014. In this reading session, I read all of chapter 6, by far most of chapter 7, all of chapters 8, 9, 10 and the Appendix from Wed 10Dec to Mon 22Dec14 at 16:18 CST. Finally done with reading 'Boolean Reasoning' after years of examining it and 3 episodes of reading the book.

TAKING ANOTHER SHOT AT READING THIS BOOK IN EARLY 2014
In mid 2013, while fully finishing chapter 8 of 'Ones and Zeros' and RE-writing its review, I revisited chapter 4 of Boolean Reasoning. Now in Jan 2014, I finished rereading chapter 2, reread chapter 1 again, and strongly tackled long chapter 3 on 'Boolean Algebras' again. Some of the motivation for this January rereading is my immediate plan to buy Boolean Functions: Theory, Algorithms, and Applications (Encyclopedia of Mathematics and its Applications) as a 710 page and 2011 published expansion of subjects similar to those in 1990 Boolean Reasoning. Ordered that book on Sat 11Jan14 afternoon and received it on Thu 16Jan14 afternoon. An excellent and thorough Boolean book also much more modern than 'Boolean Reasoning'.

FURTHER ABOUT THE 2014 READING
This second reading sequentially thru BR is going much more smoothly than exactly 3 years ago's read #1, primarily because of my reading of the very clear 'Ones and Zeros' book last year. That was the intervening clearer Boolean read wished for during the Jan 2011 reading of chapter 3 in the second paragraph from bottom of this inverted review. Other factors in last 3 years making this book easier are much more reading of mathematical logic, computability theory, computational logic, ZFC set theory, and in 2013 other alternative logics such as several types of modal logic, quite a bit on higher-order logics, and just a touch of mathematical fuzzy logic. So by now, Boolean algebra and Boolean functions are simply a welcome other type of alternative logic to read about.

BASIC BOOK CONTENTS
For use in this review, here is a basic list of contents of 'Boolean Reasoning': Dedication-iii / Preface for the Dover Edition-v / 1 Introduction-1 / 2 Fundamental Concepts-9 / 3 Boolean Algebras-29 / 4 The Blake Canonical Form-77 / 5 Boolean Analysis-93 / 6 Syllogistic Reasoning-131 / 7 Solution of Boolean Equations-163 / 8 Functional Deduction-205 / 9 Boolean Identification-217 / 10 Combinational Circuits-233 / Appendix A Syllogistic Formulas-259 / Bibliography-267 / Index-283

(AMAZON HAS STARTED A MOSTLY OPEN FOR PAGE VIEWING 'LOOK INSIDE' VIA THE TABLE OF CONTENTS, SO CHECK THAT OUT!)

CRITICISMS
My major criticism of 'Boolean Reasoning' is the large range of detail between some chapter sections. F.M Brown often wrote short sections with little detail while other sections were fully detailed and satisfying. This was frustrating in the sense that often those short sections were fascinating, so more detail was desirable. Of the chapters read or partially read in Jan 2014, chapters 3, 4 and 6 had this frequent lack of detailed coverage of subjects. Chapter 5 was the one exception and was quite thorough. Another more minor criticism is that the Boolean algebraic notation used by the author is of the old style used when the subject was rediscovered in the late 1950s / early 1960s. That should have been modernized by 1990.

ALTERNATE TERMINOLOGY
In this book, the acronyms 'SOP' for 'Sum of Products' and 'POS' for 'Product of Sums' can now be re-identified respectively as 'DNF' for 'Disjunctive Normal Form' and 'CNF' for 'Conjunctive Normal Form'. That is also the terminology in the 2011 'Boolean Functions' book I bought in Jan 2014 and have been reading. That book rather arbitrarily standardized on DNF, as equivalent SOP was standardized in 'Boolean Reasoning'. The CNF and DNF structures/terminology are also found in mathematical logic and especially in computational logic books. A DNF is a disjunction of conjuncts while a CNF is a conjunction of disjuncts. The famous Boolean satisfiability problem (SAT) generally deals with a very large CNF expression.
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2014
READING THE MAIN TECHNICAL CHAPTERS

CHAPTER 3
The supposedly missing 'absorption rule' is actually 'Useful Property 4' in section 3.5 on page 37, so that was great to find and may clarify some of the mysteries found in chapter 4 last time. Looking forward to that test! Finished reading mostly great Chapter 3 on Mon 13Jan14 at 16:40 CST. In the difficult back half of chapter 3, sections 3.10 thru 3.13 and 3.16 thru 3.17 were sketchy and non-thorough enough to not be worth much. Then final section 3.18 seemed like a longer axe-grinding sermon by the author, seemingly directed at his adversaries rather than at his general readers, but examples in 3.18 do tend to bear out his point. Sections 3.8 on Boole's Expansion Theorem, 3.9 on Minterm Canonical Form, and 3.14 on Orthonormal Expansions were more thorough and were quite interesting. Section 3.15 on the Boolean Quotient was also a fully described subject and was well worth reading.

CHAPTER 4
Chapter 4 on the Blake Canonical Form to 'controversial' p. 79 just after finishing chapter 3. Recognizing the absorption rules in section 3.5, along with two more of those in '1s and Os' chapter 7 makes me understand the 'absorptive' definition this time and that is a relief! Still, the author could just as well have referred us back to equations 3.25 and 3.26 on page 37, which are those absorption rules, to get us more strongly on board with this odd definition of 'absorptive'. That last paragraph of section 4.1 is phrased in a way that seems to indicate more of an automatic absorption by the SOP formula itself, so 'absorptive' is still rather spooky. Also in section 4.1 Sum of Products (SOP) and Product of Sums (POS) were both defined, but only SOPs will be used, and heavily, in future. Read full p. 79-91 to finish difficult but great chapter 4 by 17:19 Tue 14Jan14. Again, sections 4.3-4.4 were tiny general sections, while final 4.6 in particular was fully mathematically developed and worthwhile. In section 4.5 about Iterated Consensus is where some of the ideas around absorption make the most sense in chapter 4.

CHAPTER 5
About several techniques of 'Boolean Analysis'. Gave up on p. 103 at end of section 5.6 in Jan 2011. Will try to push further into the much more difficult sections this time as some of those parameters are used later in the book. A 33 page chapter with 11 sections. By 15:40 on Wed 15Jan14, I read to that same p.103 where I stopped reading in 2011. Will continue for sure this time. In early evening of 15Jan14, sections 5.7 on Elimination and the first piece of long 5.8 on Eliminants were enjoyed. The math about ECON / Conjunctive Eliminant and EDIS / Disjunctive Eliminant were what made me stop reading where I did in 2011, but this time they are fascinating and it looks like useful as well! 5-page section 5.8.1, called 'Calculation of Eliminants' almost has to be the very most difficult hunk of this book, but it was still fairly comprehensible and quite interesting. Several theorems with proofs and some more practical examples. Into section 5.9 after all of 5.8 / 5.81 / 5.82 about 18:00 CST Thu 16Jan14. Finished sections 5.9-5.11 and finally long chapter 5 on Fri 17Jan14 at 12:10 CST. Chapter 5 was the first fully detailed chapter without those short sections noted for chapters 3 and 4.

CHAPTER 6
This chapter should be a quite interesting one on 'Syllogistic Reasoning'. It appears to be quite a bit easier than chapter 5 was. Read thru section 6.3 on Fri 17Jan14 afternoon and that seemed numbingly boring. Section 6.4 on Clausal Form was interesting and practical. However, most of 6.5 (6.51-6.53) on 'Producing and Verifying Consequents' was an extended and strongly hand-waving example, indicating many numerical and Boolean calculations with none of those details shown at all. At end of low detail 6.6, barely about 'Class Logic' and on p.144, I quit reading 'Boolean Reasoning' at 18:50 CST of Fri 17Jan14. We were back into the lack of detail mode of writing noted in my criticism of the 4th paragraph above. /// I restarted reading chapter 6 again from its beginning thru section 6.6 on Wed 10Dec14 and continued thru the rest of chap 6. Section 6.7 on 'Selective Deduction' is entirely long biochemical Example 6.7.1 which produces quite clear clausal forms, after which all is Boolean hand waving including a gigantic 21 term SOP BCF (Blake Canonical Form from chap 4). Hand waving skipping of steps is prominent in chap 6 but most sections are still of decent length. Last sections 6.9-6.11 are the most rigorous in chap 6 and are fascinating. In late chapter 6 and in next chapter 7, the BCF and my friend from chapter 5, ECON both return strongly. Completed reading all of interesting chapter 6 at 8:55 CST on Fri 12Dec14.

CHAPTER 7
Started my first ever read of long chapter 7 on solving Boolean equations on Sun 14Dec14 afternoon and it started off quite well written. Chap 7 looks to be similarly thorough to great chap 5, but a bit less difficult. Fascinating. The numerous examples are again totally hand waving, setting up the problem and then just giving the answer, so those examples are only mildly helpful. Section 7.5 on using Karnaugh maps to solve Boolean equations suffers from no helpful clarification of how strange 'Gray codes' on K-maps actually work. They were barely mentioned in old section 3.9.2, which I reread with Sec 7.5's start on Wed 17Dec14 afternoon. At last on Thu 18Dec afternoon I cut my losses, ending the read of chapter 7 on upper p.189, late in section 7.5 and 11 pages before chapter end.

CHAPTER 8
Started reading this short chapter on Fri 19Dec14 morning, and finished it at 18:13 CST on that Friday evening. A terrific, rather thorough chapter on Functional Deduction, which is a rather new approach to Boolean subjects in this book.

CHAPTER 9
A good reading start on fascinating chap 9 on Boolean identification just after finishing chapter 8 on Fri 19Dec evening. Chap 9 is a spooky Boolean black box oriented chapter. Reminds me of some of the black box, 'government or export only' wide band radios at Universal Radio's online store. Finished this interesting chapter at 14:40 on Sat 20Dec14. The EDIS and ECON from Sections 5.7-5.8 are often used in late chapter 6 thru chapter 10, speaking of which, rather long chapter 10 is my last thing to read to finish all of this book except for late chapter 7.

CHAPTER 10 AND FINAL
First several pages of this moderate length final chapter early evening Sat 20Dec14. Over halfway thru the chapter by mid afternoon of Sun 21Dec. Unfortunately chap 10 is substantially about circuit design but contains no for a long time common logic gate notation, though logic gates are mentioned more than once. Disappointing. A rather tedious final chapter for this reader. At last finished all of chapter 10 and reading of all but 11 pages of 'Boolean Reasoning' at 16:18 CST on Mon 22Dec14!!

APPENDIX A
Also started reading the appendix on Wed 10Dec14 afternoon. It repeats with more formal rigor some of the subjects in closely related great chapter 4 on the Blake Canonical Form. Rather spooky and seemingly automatic 'absorptivity' as 'ABS(F)' reappears in the appendix. A good further detail on Blake's dissertation from 1937, but almost entirely in bare bones definition-theorem-proof format. Completed reading the appendix at 14:14 CST on Fri 12Dec14

BIBLIOGRAPHY
'Boolean Reasoning' has a large 16pg / 194 entry bibliography, and the author frequently references one to several entries at a time within the chapters. I look up nearly all of those references by Mr. Brown. The bibliography covers a large time span as well.
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2014
INVERTED THIS LONG REVIEW
About 01:15 on Tue 14Jan14, I put this 2014 writing at top of review, left the 2011-2012-2013 section in middle of review and put the original 2011-early 2012 section at bottom of the review.

A SHORT SUMMARY OF TECHNICAL BOOLEAN PARTICULARS
In books like this, strings like (ab) mean (a and b), or in terms of sets, (a intersect b), while strings like (a+b) mean (a or b), or in terms of sets (a union b). In addition, logical not or set complement are symbolized as (a'). So these types of symbol strings correspond to basic propositional logic connectives or basic set algebra. The main difference from those two related subjects is that Boolean algebra has expressions such as (a+1=1), (a+a=a) and [a+(ab)=a)] and [a(a+b)=a], the last 2 of which are those absorption rules. There is no such thing in normal propositional logic. '1s and 0s' has two further absorption rules in its chapter 7 than BR has in section 3.5. In BR terms, those other two absorption rules would be: [a+(a'b)]=a+b] and [a(a'+b)=ab]. So there!
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2011-2012-2013
MYSTERIOUS ULTRA HIGH PRICED HARDCOVER
It seems very strange, but since Aug 2011 Amazon has been considering a $152 original 1990 hardcover of this 'BR' book as valid, and they're even keeping it in stock. How can an original hardcover still even be in print after Dover had reprinted this book in 2003 after Kluwer canceled it? The hardcover costs an extreme 9 times the $16.95 list price of the Dover paperback! $152 for this 304pg book is a whopping $0.50/pg. We could commercially photocopy that many pages about twice for this price. $152 for hardcover of this little book seems like unfair gouging of potential customers for it. In March 2012, Dover has re-reprinted 'Boolean Reasoning', so this super expensive hardcover will hopefully just go away now. Unfortunately it still hasn't gone away a year later in Mar 2013.

A RECOMMENDED MORE CLEAR AND LESS EXPENSIVE BOOK
If you are willing to spend more than $16.95 for a book on Boolean algebra, instead of hardcover 'BR', I would recommend the book 'Ones and Zeros' by John R. Gregg on IEEE Press/Wiley, about $56 and 296 pages from Amazon. 'Ones and Zeros' covers Boolean subjects very thoroughly, yet rather accessibly. It covers nearly all of what is in 'Boolean Reasoning' more clearly than in that book, plus it covers all the circuit elements stemming from Boolean logic. A very good paperback textbook. Here is a link to that book: Ones and Zeros: Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets (IEEE Press Understanding Science & Technology Series). Started reading the 'Ones and Zeros' textbook on Sat 9Mar13 afternoon. I'll keep a copy of the present Dover 'Boolean Reasoning' book around as a closely related reference to the more accessible yet thorough IEEE book. Ended reading the recommended book in final chapter 8 on Mon 8Apr13. In Apr2013 I have started some rereading of 'Boolean Reasoning', now that more Boolean knowledge from reading '1s and 0s' makes 'BR' a bit more understandable.

CORRELATION
On Thu 14Mar13 afternoon at my favorite coffee place in Dubuque, I spent about 2 hours with tables of contents and indexes of 'Ones and Zeros' and 'Boolean Reasoning', recording in detail what subjects are in both books on a sheet of graph paper. A lot of overlap as expected, with just items in chapters 5, 7, and 8 of '1s and 0s' corresponding to items in chapters 1-7 and the appendix of 'BR', which is more detailed in most items than '1s and 0s' is. 'BR' contains 10 regular chapters, while the recommended book contains 8 regulars. The two books are of nearly the same number of pages close to 300.
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2011-early 2012 / MOSTLY OBSOLETE VERY FIRST REVIEW

CANCELLATION OF THE BOOK BY DOVER / THEIR RE-REPRINTING OF THIS BOOK
At the time I was reading this interesting book to about mid Chapter 5, Dover pulled 'Boolean Reasoning' off of their Logic 1 page on 14Jan11 in their web book store, apparently taking it out of print. That is the first time I've seen Dover cancel a book with no warning in the 1.5 years since I've been buying books online directly from them. In Amazon on evening of 22Sep11, the page for this book shows Dover reprinting it again in May 2012. That would be nice for killing the $152 hardcover version's viability. See my paragraph above on that hyper expensive and mysterious occurrence. On Sat 17Mar12, I see on Dover's web store Logic 1 page that 'Boolean Reasoning' has been re-reprinted, selling for its same previous $16.95 list price.

MY READING OF THE DOVER PAPERBACK 'Boolean Reasoning' aka 'BR' IN JANUARY 2011
Short chapters 1, 'Introduction' and 2 'Fundamental Concepts' were quite interesting and straighforward. Then during good but increasingly difficult and long chapter 3, 'Boolean Algebras', the level of writing seemed high enough that reading a simpler book on Boolean subjects before this one would have been a good idea. Then Brown's chapter 4 on 'The Blake Canonical Form' was awful, mainly because of a useless circular definition of 'absorptive' on p.79, so that 'absorbed, absorption, unabsorbed', and so on were prominent undefined words used 15 times in the chapter. Context there was no help. Appendix A had the same circular definition, with 'absorptive' defined as not being absorbed yet again. On 23Jan I ended reading 'BR' at the end of section 5.6 in chapter 5 'Boolean Analysis', just before difficulty of this book would increase severely. The place of diminishing returns for me had been reached. The remaining chapters were 6 'Syllogistic Reasoning' / 7 'Solution of Boolean Equations'/ 8 'Functional Deduction' / 9 'Boolean Identification' / 10 'Combinational Circuits: Specification & Optimization' / Appendix A 'Syllogistic Formulas'.

My own overall take regarding 'Boolean Reasoning' after reading in Jan 2011 is that it is a difficult graduate level or near that level book, and not much of a well written one. Very poorly done chapter 4 and appendix A seem to call all of Brown's writing into question. Also, I am much more of a classical logician and so am not especially Boolean algebraic in outlook.
Jugami
Brown's book contains proofs of fundamental results that are only quoted in other books on the subject.
Boolean Reasoning: The Logic of Boolean Equations
Cesar
Great book
Dreladred
This book goes into detail about using Boolean algebra in reasoning. It is well written and contains many examples to illustrate the methods.
Bradeya
Boolean algebra is the bedrock of computing. So if you want to deepen your understanding of computing, Brown presents this exposition. Beware. It is a lot more abstruse than the way Boolean logic is often taught in computer science courses. It shows a depth and elegance far removed from those treatments. There is a beauty here in the Boolean expressions that is sadly not appreciated by enough programmers.

Along the way, Brown explains Karnaugh maps to good detail. He also ties this into programs that optimise Boolean expressions according to various criteria. So yes, there are actual code examples, just in case you think this is all too airy fairy.
Flash_back
I'd like to point out the following URL containing a complete review of the book

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