The New Mathematics by Irving Adler (PDF)

Description

The stock cover-photo shown with this issue may not match the actual book cover. Clean, bright used copy with tight binding. NEVER a library book./jl

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In the 1950s and 1960s, there was a movement in American schools to teach children to understand arithmetic, not just do rote calculation. This failed for a number of reasons: Parents didn’t understand it, teachers didn’t understand it, and it took time away from learning how to do rote calculations. The movement died in the 1970s.Perhaps things would have turned out differently if parents and teachers had had this book.For those few of us who actually like mathematics, this is a great book. Irving Adler wrote a great number of “popular” science and math books, which are still good reads, though of course the science ones are rather out of date.So this is a book about understanding arithmetic, at a much deeper level than most people do. If you want a really good book about doing arithmetic, see instead “The Trachtenberg Speed System of Basic Mathematics.”

⭐This mathematics publication is arranged and explained in a logical manner. It was a favorite of mine for many years. I had an original copy back in the early 60’s. My grandmother purchased it for me on a grocery shopping trip we were on together. I was about 9 or 10 years old.And I always treasured that book. Many years later when I moved to a new home, I had to recycle and get rid of many books that I no longer could keep. For most I found a good home. I had to part with my copy. But realized recently that I would purchase another copy to have in my book collection.

⭐Irving Adler was one of the most prestigious and prolific Mathematicians of the 20th century. All of his books and ‘The New Mathematics’ in particular, should be required reading for serious students at the High School, College and Graduate levels. I have read this book four times since I purchased my first copy in 1968.

⭐Best intro to the foundations of mathematics. I have ordered this books many times and given it away as gifts to students and friends. It opened my eyes to the wonderful world of abstract mathematics.

⭐John Stillwell has written many books showing the connections between old and new mathematics. But, they always miss the unified viewpoint of Irving Adler’s “The New Mathematics”.He’ll say that mathematics begins with the Pythagorean theorem which is easily false. It begins, well, with geometry. Or, does it begin with time? Numbers would be easily derivable from counting the time of day. Geometry could come about simply by taking each individual segment and combining them in various ways. We’ll never know! These things go back tens of thousands of years. Still, the filling of the number line . . . the combining of numbers with just the geometric line . . . proves to be a great introduction to the growth of the number concept. And, Irving Adler shows how the major abstract algebraic concepts relate to this growth. The Pythagorean theorem comes in . . . later.The relationship and how today’s non-standard everything . . . Greek algebra/geometry . . . comes out of the Greek problems can be tackled by reading John Stillwell’s books. Let me just point out that John Stillwell shows how group theory and Galois theory comes out of trying to find higher closed form solutions to algebraic equations(kind of like quadratic formula for higher degree equations). Ring theory comes out of number theory. Groups, fields, and rings are the initial major abstract algebras. They combine in David Hilbert’s work in Algebraic Number Fields. They also combine in Emmy Noether’s (non)commutative algebra. But, John Stillwell misses how to combine all this with the growth of the number concept as presented in Irving Adler’s book here, which I’m obviously a little disappointed.Irving Adler’s valuable little book ends with Frederick Gauss’s “Fundamental theory of Algebra.” John Stillwell once again fails to show the full implications and connections between this piece of mathematics and the rest of mathematics. He mentions some, but he misses the connection between the Fundamental theory of Algebra and algebraic varieties and then to algebraic geometry. With the remarkable connections between Algebraic geometry and algebraic number fields, and even Riemann surfaces and Elliptic functions, that’s one of the grand central stations of modern mathematics even today.Of course, Irving Adler doesn’t make those connections because those things are well beyond the goal of his little book. But, if you want to go beyond this book, I’d recommend John Stillwell’s works with some understanding that he doesn’t make all the connections in the world.

⭐I can’t believe this is out of print. I read this book first when I was about 13 or 14 and found it fascinating.I reread it many years later and it was still interesting. The book presents an argument for why we need all those kinds of numbers (integers, reals, imaginary, complex…) and does so in a straightforward and elegant way. Make no mistake, it is NOT a mathematics textbook – there are no systematic proofs – but it presents solid reasons for adding different kinds of numbers.The book starts with the counting numbers, then shows why we need zero, negative numbers, fractions (rational numbers), irrational numbers, imaginary numbers and complex numbers.Hopefully it will be reprinted someday… I’ll certainly buy a copy.

⭐When the phrase, new math, was all the rage. Good for learning the vocabulary.To add to the first review, my memory of the book is that it added elementary introductions to set theory, group theory, matrix algebra (I think; I also had a semester of M.A. in high school) and associated concepts such as commutivity, etc. It was very well-written, clear. I tried to look up someting in my copy today on groups and couldn’t find it. Which is why I’m here.I highly reccommend the book.

Keywords

Free Download The New Mathematics in PDF format
The New Mathematics PDF Free Download
Download The New Mathematics 1964 PDF Free
The New Mathematics 1964 PDF Free Download
Download The New Mathematics PDF
Free Download Ebook The New Mathematics