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Realm of Algebra
Realm of Algebra
144 pages, Mass Market Paperback
First published January 1, 1961
15 people are currently reading
197 people want to read
About the author
Isaac Asimov
4,674 books27.3k followersWorks of prolific Russian-American writer Isaac Asimov include popular explanations of scientific principles,
The Foundation Trilogy
(1951-1953), and other volumes of fiction.
Isaac Asimov, a professor of biochemistry, wrote as a highly successful author, best known for his books.
Asimov, professor, generally considered of all time, edited more than five hundred books and ninety thousand letters and postcards. He published in nine of the ten major categories of the Dewey decimal classification but lacked only an entry in the category of philosophy (100).
People widely considered Asimov, a master of the genre alongside Robert Anson Heinlein and Arthur Charles Clarke as the "big three" during his lifetime. He later tied Galactic Empire and the Robot into the same universe as his most famous series to create a unified "future history" for his stories much like those that Heinlein pioneered and Cordwainer Smith and Poul Anderson previously produced. He penned "Nightfall," voted in 1964 as the best short story of all time; many persons still honor this title. He also produced well mysteries, fantasy, and a great quantity of nonfiction. Asimov used Paul French, the pen name, for the Lucky Starr, series of juvenile novels.
Most books of Asimov in a historical way go as far back to a time with possible question or concept at its simplest stage. He often provides and mentions well nationalities, birth, and death dates for persons and etymologies and pronunciation guides for technical terms. Guide to Science, the tripartite set Understanding Physics, and Chronology of Science and Discovery exemplify these books.
Asimov, a long-time member, reluctantly served as vice president of Mensa international and described some members of that organization as "brain-proud and aggressive about their IQs." He took more pleasure as president of the humanist association. The asteroid 5020 Asimov, the magazine Asimov's Science Fiction, an elementary school in Brooklyn in New York, and two different awards honor his name.
http://en.wikipedia.org/wiki/Isaac_As...
Isaac Asimov, a professor of biochemistry, wrote as a highly successful author, best known for his books.
Asimov, professor, generally considered of all time, edited more than five hundred books and ninety thousand letters and postcards. He published in nine of the ten major categories of the Dewey decimal classification but lacked only an entry in the category of philosophy (100).
People widely considered Asimov, a master of the genre alongside Robert Anson Heinlein and Arthur Charles Clarke as the "big three" during his lifetime. He later tied Galactic Empire and the Robot into the same universe as his most famous series to create a unified "future history" for his stories much like those that Heinlein pioneered and Cordwainer Smith and Poul Anderson previously produced. He penned "Nightfall," voted in 1964 as the best short story of all time; many persons still honor this title. He also produced well mysteries, fantasy, and a great quantity of nonfiction. Asimov used Paul French, the pen name, for the Lucky Starr, series of juvenile novels.
Most books of Asimov in a historical way go as far back to a time with possible question or concept at its simplest stage. He often provides and mentions well nationalities, birth, and death dates for persons and etymologies and pronunciation guides for technical terms. Guide to Science, the tripartite set Understanding Physics, and Chronology of Science and Discovery exemplify these books.
Asimov, a long-time member, reluctantly served as vice president of Mensa international and described some members of that organization as "brain-proud and aggressive about their IQs." He took more pleasure as president of the humanist association. The asteroid 5020 Asimov, the magazine Asimov's Science Fiction, an elementary school in Brooklyn in New York, and two different awards honor his name.
http://en.wikipedia.org/wiki/Isaac_As...
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Displaying 1 - 15 of 15 reviews
March 16, 2013
My grasp of algebra and the logical interpretation of mathematics has been greatly improved through Mr. Asimov's superb intelligence. Realm of Algebra explains the orders of operations all the way through quadratic equations and I've now realized the complications I've faced with mathematics is in part due to bad teaching.
May 2, 2018
I remember reading this book under a tree at the lake when I was in my early 20’s. I went outside to focus all my attention on the famous subject of those curious x’s and y’s. My greatest excitement about this book was brought forth because I was going to start college at the time and wanted to pass the math portion of the entry-level assessment test. I had known Asimov for a couple years already as the greatest nonfiction science writer of the last 50 years so I knew this book would be a delight from the start. My pondering was right. I found myself fascinated and overjoyed by this book that explained all those simple things I never understood in high school. It’s simply a great little book that explains why you’re doing what you’re doing and how it came about. Coming from someone who wasn’t born until 1991 I found this book relevant and very helpful. It was one of those books that also instilled in me a growing infatuation with mathematics.
June 9, 2015
I have had a bit too much math education to really enjoy it but Asimov's writing style is very clear. If you know someone that is intimidated or having trouble with algebra, this is a good book to help them through it.
April 1, 2024
I read this because I was curious to see what Asimov's non-fiction was like. The answer is: clear, easy to follow, logical, and helpful. To someone already familiar with the material, it will be a pleasant read; to someone struggling to understand the concepts being discussed, it will likely be a great help.
An excerpt from the end of the book: "Thus Cavendish, by means of a careful experiment involving small balls, plus the techniques of algebra, had succeeded in weighing the earth."
I'm looking forward to reading some of Asimov's other non-fiction books.
An excerpt from the end of the book: "Thus Cavendish, by means of a careful experiment involving small balls, plus the techniques of algebra, had succeeded in weighing the earth."
I'm looking forward to reading some of Asimov's other non-fiction books.
September 11, 2012
better than any textbook i've read on the subject. it's only missing equation drills. it's a shame this is still out of print.
April 2, 2014
My mother gave me this book for Christmas when I was 15. Thirty some odd years later, I still think this is an awesome book for understanding Algebra.
August 9, 2019
Realm of Algebra, Isaac Asimov, 1961, 144pp. paperback, ISBN 0449243982
Asimov clearly, simply, conversationally, starting from arithmetic, explains the basics of algebra, including: factoring polynomials; deriving the quadratic formula; how in principle to solve N linear equations in N unknowns; imaginary and complex numbers. He tells us who came up with the ideas, and when and where. No matrices. No graphs. No exercises for the reader. No e^(iθ) notation.
The Kindle edition omits and misprints buckets of symbols, especially in the equations, but even in the text. Some places, there’s no way to know what the author was saying. Unfortunately, kindle is the only edition still in print. Get it on paper if you can. 459 worldcat libraries have a copy, as of 2019: https://www.worldcat.org/title/realm-...
The 1961 original printings were a 230-page hardcover, and a paperback, 143pp. plus 1-page index. The paperback was reprinted in 1982. The very-badly-typeset kindle edition came out in 2019.
ALGEBRA: OPERATIONS
Algebra is a variety of arithmetic. When we use “literal” symbols (letters such as x), we’re in the realm of algebra.
In all of algebra, there are only 3 pairs of operations:
addition and subtraction
multiplication and division
powers (involution) and roots (evolution)
INVERSE OPERATIONS
Subtraction gives rise to negative numbers.
Division gives rise to fractions.
Roots give rise to imaginary and complex numbers:
For example, the cube root of (+1) is:
+1, or,
−1/2 + (1/2)sqrt(3)i, or,
−1/2 − (1/2)sqrt(3)i
where i is the square root of minus 1. (pp. 92, 96)
(Asimov asks us to trust him on this. He doesn’t prove it. This book doesn’t get into e^(iθ) notation, which makes it easy.)
IDENTITIES
1/(b/a) ≡ a/b
a(b + c) ≡ ab + ac
(ab)^n ≡ (a^n)(b^n)
(a^m)(a^n) ≡ a^(m + n)
(a^m)/(a^n) ≡ a^(m − n)
a^0 ≡ 1, a ≠ 0
a^(−n) ≡ 1/(a^n)
(a^m)^n ≡ a^(mn)
If a^n = b then a is the nth root of b.
a^(1/2) is the square root of a.
a^(1/n) is the nth root of a.
a^(m/n) is the nth root of (a^m)
DEFINITIONS
Each item being added or subtracted is a “term.”
An expression with 2 terms is a “binomial.”
An expression with more than 1 term is a “polynomial.”
RULES FOR EQUATIONS
You can add or subtract the same thing from each side.
Multiply or divide each side by the same number. (Don’t divide by 0.)
Raise each side to the same power, or take the same root of each side.
QUADRATIC FORMULA (pp. 109–113)
To solve a quadratic equation of the form
ax² + bx + c = 0
Divide by a
x² + (b/a)x + c/a = 0
Subtract c/a:
x² + (b/a)x = −c/a
Add (b/2a)²:
x² + 2(b/2a)x + (b/2a)² = b²/4a² − c/a
Factor the left side; give the right side a common denominator:
(x + b/2a)² = (b² − 4ac)/(4a²)
Take the square root:
x + b/2a = ±sqrt[(b² − 4ac)]/2a
Subtract b/2a:
x = −b/2a ± sqrt(b² − 4ac)/2a
Express as one fraction:
x = [−b ± sqrt(b² − 4ac)]/2a
This is the quadratic formula. It’s the general solution to
ax² + bx + c = 0
HISTORY
Decimal numbers, including zero, were first used in the 800s in India. (p. 6, chapter 1)
French mathematician François Vieta first used letters as symbols for unknowns, about 1590. He’s sometimes known as the “father of algebra.” (p. 10, chapter 1)
Mohammed ibn Musa al-Khowarizmi wrote a book, ilm al-jabr wa’l muqabalah, “the science of reduction and cancellation,” about 825 CE. These were his methods of dealing with equations—rules for algebra. “Algebra” is a mispronunciation of the second word in the title of his book. (p. 12, chapter 2)
Italian mathematician Geronimo Cardano first used negative numbers, around 1550. (p. 17. chapter 2)
Not until around 1900 were mathematicians careful to state the axioms (presumptions) they were starting from. The first to do so were Giuseppe Peano (Italian) and David Hilbert (German).
René Descartes in 1637 first used superscripts to indicate raising numbers to powers, as x² or x³.
Logarithms were developed around 1600 by Scottish mathematician John Napier.
Quiz questions:
https://www.goodreads.com/trivia/work...
Permalink:
https://www.worldcat.org/profiles/Tom...
Asimov clearly, simply, conversationally, starting from arithmetic, explains the basics of algebra, including: factoring polynomials; deriving the quadratic formula; how in principle to solve N linear equations in N unknowns; imaginary and complex numbers. He tells us who came up with the ideas, and when and where. No matrices. No graphs. No exercises for the reader. No e^(iθ) notation.
The Kindle edition omits and misprints buckets of symbols, especially in the equations, but even in the text. Some places, there’s no way to know what the author was saying. Unfortunately, kindle is the only edition still in print. Get it on paper if you can. 459 worldcat libraries have a copy, as of 2019: https://www.worldcat.org/title/realm-...
The 1961 original printings were a 230-page hardcover, and a paperback, 143pp. plus 1-page index. The paperback was reprinted in 1982. The very-badly-typeset kindle edition came out in 2019.
ALGEBRA: OPERATIONS
Algebra is a variety of arithmetic. When we use “literal” symbols (letters such as x), we’re in the realm of algebra.
In all of algebra, there are only 3 pairs of operations:
addition and subtraction
multiplication and division
powers (involution) and roots (evolution)
INVERSE OPERATIONS
Subtraction gives rise to negative numbers.
Division gives rise to fractions.
Roots give rise to imaginary and complex numbers:
For example, the cube root of (+1) is:
+1, or,
−1/2 + (1/2)sqrt(3)i, or,
−1/2 − (1/2)sqrt(3)i
where i is the square root of minus 1. (pp. 92, 96)
(Asimov asks us to trust him on this. He doesn’t prove it. This book doesn’t get into e^(iθ) notation, which makes it easy.)
IDENTITIES
1/(b/a) ≡ a/b
a(b + c) ≡ ab + ac
(ab)^n ≡ (a^n)(b^n)
(a^m)(a^n) ≡ a^(m + n)
(a^m)/(a^n) ≡ a^(m − n)
a^0 ≡ 1, a ≠ 0
a^(−n) ≡ 1/(a^n)
(a^m)^n ≡ a^(mn)
If a^n = b then a is the nth root of b.
a^(1/2) is the square root of a.
a^(1/n) is the nth root of a.
a^(m/n) is the nth root of (a^m)
DEFINITIONS
Each item being added or subtracted is a “term.”
An expression with 2 terms is a “binomial.”
An expression with more than 1 term is a “polynomial.”
RULES FOR EQUATIONS
You can add or subtract the same thing from each side.
Multiply or divide each side by the same number. (Don’t divide by 0.)
Raise each side to the same power, or take the same root of each side.
QUADRATIC FORMULA (pp. 109–113)
To solve a quadratic equation of the form
ax² + bx + c = 0
Divide by a
x² + (b/a)x + c/a = 0
Subtract c/a:
x² + (b/a)x = −c/a
Add (b/2a)²:
x² + 2(b/2a)x + (b/2a)² = b²/4a² − c/a
Factor the left side; give the right side a common denominator:
(x + b/2a)² = (b² − 4ac)/(4a²)
Take the square root:
x + b/2a = ±sqrt[(b² − 4ac)]/2a
Subtract b/2a:
x = −b/2a ± sqrt(b² − 4ac)/2a
Express as one fraction:
x = [−b ± sqrt(b² − 4ac)]/2a
This is the quadratic formula. It’s the general solution to
ax² + bx + c = 0
HISTORY
Decimal numbers, including zero, were first used in the 800s in India. (p. 6, chapter 1)
French mathematician François Vieta first used letters as symbols for unknowns, about 1590. He’s sometimes known as the “father of algebra.” (p. 10, chapter 1)
Mohammed ibn Musa al-Khowarizmi wrote a book, ilm al-jabr wa’l muqabalah, “the science of reduction and cancellation,” about 825 CE. These were his methods of dealing with equations—rules for algebra. “Algebra” is a mispronunciation of the second word in the title of his book. (p. 12, chapter 2)
Italian mathematician Geronimo Cardano first used negative numbers, around 1550. (p. 17. chapter 2)
Not until around 1900 were mathematicians careful to state the axioms (presumptions) they were starting from. The first to do so were Giuseppe Peano (Italian) and David Hilbert (German).
René Descartes in 1637 first used superscripts to indicate raising numbers to powers, as x² or x³.
Logarithms were developed around 1600 by Scottish mathematician John Napier.
Quiz questions:
https://www.goodreads.com/trivia/work...
Permalink:
https://www.worldcat.org/profiles/Tom...
September 16, 2016
Always be sure, then, that you are making sense in the first place and the rules of algebra will then take care of you. If you're not making sense to begin with, then nothing can take care of you, algebra least of all.
Ha!
I happen to love algebra, so this book was a good reminder of that. It is however a book about very basic algebra, so while it might provide clear, useful help for young students, it's not much more than a reminder for the rest of us. Though, as I said, a reminder of love as much as method...
Ha!
I happen to love algebra, so this book was a good reminder of that. It is however a book about very basic algebra, so while it might provide clear, useful help for young students, it's not much more than a reminder for the rest of us. Though, as I said, a reminder of love as much as method...
June 30, 2019
I learned Algebra from this book during summer break between 5th and 6th grades. Never found a more clear, straightforward explanation of the foundation and basic operations of Algebra during many subsequent years of math, science and engineering studies. I believe every student would benefit from reading this before, or perhaps instead of, taking the subject in school.
June 28, 2016
An insightful manual on the basic principles surrounding the curious world of algebra. To many, it may not hold any practical utility, yet it has allowed for the development of many of the worlds technological achievements.
February 28, 2010
A nice book. Read over the summer, it got me through high school algebra after I didn't make it through 6th grade math.
July 7, 2011
This was my first book on mathematics. Back when I was a wee lad, algebra seemed quite daunting, but my father and Asimov worked together to provide such a clear education in basic arithmetic.
November 20, 2016
No book can replace a good teacher in person but this one is very close to it.
Highly recommended to young learners of algebra.
Highly recommended to young learners of algebra.
April 14, 2024
There is not much to offer in this book if you have that Mathematical Maturity. You won't find anything new or interesting as in other Asimov's work
So better you skip it.
And if you are beginner, then too its No
Better if you study rigour textbook rather than this
You can visit this when you have some knowledge of Algebra, this is more type of "connecting the dots book". It would connect or refine your some already made concept.
So better you skip it.
And if you are beginner, then too its No
Better if you study rigour textbook rather than this
You can visit this when you have some knowledge of Algebra, this is more type of "connecting the dots book". It would connect or refine your some already made concept.
January 25, 2019
This is surely not one of his better works. Funny, that he was quite lost in mathematics. 5/10
Displaying 1 - 15 of 15 reviews