See 1 question about Topics in Algebra…. Lists with This Book. Community Reviews. Showing Rating details. More filters. Sort order. Jul 12, David rated it really liked it. Truth be told, I always considered myself more of an analysis guy than an algebraist in college. So why is it that, of the various texts I had as an undergraduate, this is one of the handful I've never managed to get rid of? Because group theory rocks, in its own buttoned-down, hidden-depths, body-of-an-accountant-soul-of-a-poet fashion.
Herstein's slightly desiccated prose is oddly appropriate for its subject matter, though it's hard to love. You have to read between the lines to discover the u Truth be told, I always considered myself more of an analysis guy than an algebraist in college. You have to read between the lines to discover the underlying beauty. But then again, Stewart is an impossible act to follow. View 1 comment.
Aug 28, Becky rated it it was ok. One of my math professors gave this book to me when I was in school. I've been thinking about going back and getting my Masters in math. I just wanted to see how much I remembered or could comprehend. I got through five pages in one lunch hour. But I understood it! This one will be on the "Currently Reading" shelf for a while. View all 3 comments. May 29, Daniel Kelleher rated it really liked it.
One of the great classics in mathematics literature. Herstein's mathematical writing is some of the best, at times a pleasure to read. I recommend this book, especially for self study or a supplement to an algebra course. This book is worth a skim even for its historical value as an example of who to construct a mathematical text.
That being said, a would be user should be warned of a few of the books quirks. First the book is old, and a bit antiquated. Second, this book was not actually designed One of the great classics in mathematics literature. Second, this book was not actually designed for a graduate-level course, but instead based on and advanced undergraduate curriculum. So, the material falls short of a standard North American graduate course in algebra.
Mar 08, Ankush Sharma rated it it was amazing Shelves: math.
One of the most beautiful books on pure mathematics that I've read. Its a pity that it wasn't even part of the course! It was so damn good that I spent most of my time studying this in the library for months instead of cramming and preparing for my entrance exams. Jan 21, Imran Qureshi rated it it was amazing. Fantastic book on algebraic structures. Made me love the subject. Babak rated it really liked it May 29, Susan rated it really liked it Nov 15, Nathan Hunsaker rated it liked it Feb 06, Evan rated it really liked it Dec 24, Christopher Burgess rated it really liked it May 01, Nicole Deyerl rated it really liked it Aug 16, Stephen rated it really liked it Mar 08, Srikanth S rated it it was amazing Jul 17, Ruitu Xu rated it really liked it Jun 06, The later Greeks, Hindus and Nemorarius Jordanus, a German born mathematician, expressed addition by juxtaposition.
The Italian algebraists eventually began to use the initial letter P or p , sometimes with a line drawn through it for plus. The practice, however, was not uniform. Some mathematicians denoted plus by , and sometimes by e , and the mathematician Niccolo Tartaglia commonly used.
Subtraction was indicated by the Greek mathematician by an inverted and truncated or.
The Hindus used a dot while the Italian algebraists denoted minus by M or m, sometimes with a line drawn through the letter or sometimes by. The German and English algebraists introduced the present symbol - and described it as "signum subtractorum. The English mathematician William Oughtred, in , first used the symbol x for multiplication, while Thomas Harriot used a dot. The German Mathematician Gottfried Wilhelm Leibnitz used a period to indicate the operation and French mathematician Rene Descartes used juxtaposition in In Leibnitz used the sign to denote multiplication and to denote division.
Leibnitz used the colon : in the form of a ratio a:b. The current symbol for division , which is a combination of the - symbol and the : symbol, was used by Johann Heinrich Rahn at Zurich in and by John Pell in London in But for the most part, the word was written at length until the year Rafaello Bombelli is credited with the earliest symbolic notation for exponential notation in He represented the unknown quantity by , its square by , its cube by , and so on. In , simon Stevinus used , , , etc.
In mathematical writings published in , P. Herigonus wrote a , a2 , a3 , Rene Descartes presentd the idea for the modern day notation of using exponents to mark the power to which a quantity was raised. English mathematician John Wallis explained the meaning of negative and fractional exponents in and first employed the symbol for infinity in References: Ball, W. A Short Account of the History of Mathematics. Bowen, J. Early English Algebra [On-line]. The Origins of Algebra [On-line]. Mathematical Symbols. Microsoft R Encarta Encyclopedia Dauben, J.
The predecessor to symbolic logic was classical logic more commonly referred to as Aristotelian logic. Aristotle's B. The principle of contradiction: no proposition can be both true and false. Aristotelian logic dominated scientific reasoning in the Western world for years. In the English mathematician and logician George Boole demonstrated in his Mathematical Analysis of Logic that a system of algebra can be used to express logical relations.
Originally devised Gullberg, as a system for logical reasoning, Boole developed symbolic logic as a means of clarifying difficult Aristotelian logic. His system has been used as a tool to help sound reasoning. We refer to it today as Boolean Algebra or symbolic logic. Boolean algebra Gullberg, is concerned with ideas or objects that have only two possible stable states - e. Although it was devised by Boole in In the late 17 th century the foundation for symbolic logic was made by the German mathematician and philosopher G.
Gottlob Frege from Germany, founder of modern symbolic logic, in constructed an elaborate logico-mathematical system, Gullberg, now known as predicate logic. He was not interested in higher mathematics but, was rather interested in philosophy, logic, and law which were the bases of his career as a diplomat. His goal was to reduce all truths of reason to a simple system of arithmetic lead into infinitesimal calculus. Together with Alfred North Whitehead tried to derive mathematics from self-evident logical principles.
They did not reach their goal.
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Kurt Godel a Czech-Austrian-American mathematician and logician published his famous incompleteness theorem that states any consistent formal system adequate to describe arithmetic must contain statements which can either be proved nor disproved within this system. He showed that there is no systematic way to list the true statements in arithmetic. Boolean algebra symbolic logic remained dormant until the middle of the 20 th century.
Symbolic logic is used not only in genuinely logical or mathematical domains but also in the natural sciences, and in disciplines such as linguistics, law, and computer technology. Today Boolean algebra is used everyday to help people when doing searches on the Internet. It is more commonly referred to as a Boolean search. The three Boolean operators used today are as follows: AND, OR, NOT When you search the internet for specific words you will get many, often thousands of hits for the words your typed in and still your frustrated because it isn't what you want.
Since OR is the default it is assuming you want either lesson or plans not lesson plans. To modify your search to be more specific use AND between words if you are interested in dyslexia in teens type: dyslexia AND teens. This will give you sites that have both words in their titles. You will type: radiation NOT nuclear and it will give you just the radiation sites. References: Bergamini, David. Choose a positive integer.
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If your number is even, divide it by two. If your number is odd, multiply it by three and add 1. Take your new number as the starting number, and repeat until you can't go any farther. The process sounds easy enough, but how to predict what will happen may be less obvious.
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Welcome to hailstones. Hailstone numbers are generated by the simple mathematical process described above. A small integer value of n can demonstrate the process. To compare hailstone sequences from different starting numbers, it is useful to note both the largest value attained, and the number of computations needed to reach 1.
To compare, change n by a small amount and note what happens to the sequence. Here the largest value is again 16, but the number of steps is 8.
How high will hailstone numbers go? And just how many steps are needed? Some larger examples may show greater variation attained in hailstone number sequences. The pattern is 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Here the maximum value is 88, and the length is This is where the surprises of hailstone numbers become more obvious. The sequence is 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The maximum value is 40, and the number of computations only The sequence has a maximum value of 9,, and takes computations to reach 1!
So far, it appears that the maximum values and numbers of computations needed are in some way related to the size of the starting number. Perhaps more notable is the contrast between even and odd starting numbers. There is, as yet, no complete understanding of the apparently chaotic nature of the sequences produced by this simple procedure.
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Also, another puzzling question remains. Will any starting number used for a hailstone sequence eventually reach 1? From the examples above, it would appear so.