What do you think?
Rate this book
An Adventurer's Guide to Number Theory
Written for readers with an understanding of arithmetic and beginning algebra, this book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.
In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory , dealing with properties of numbers and with numbers as abstract concepts. Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects
Moreover, the author has included a number of unusual features to challenge and stimulate
Also included is a Table of Theorems grouped into categories according to subject, and an Index of Mathematicians . Readers with a mathematical bent will enjoy and benefit from these entertaining and thought-provoking adventures in the fascinating realm of number theory. Mr. Friedberg is a theoretical physicist who has contributed to a wide variety of problems in mathematics and physics, including mathematical logic, number theory, solid state physics, general relativity, particle physics, quantum optics, genome research, and the foundations of quantum physics.
Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen ( Set Theory and the Continuum Hypothesis ), Alfred Tarski ( Undecidable Theories ), Gary Chartrand ( Introductory Graph Theory ), Hermann Weyl ( The Concept of a Riemann Surface ), Shlomo Sternberg ( Dynamical Systems ), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.
In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory , dealing with properties of numbers and with numbers as abstract concepts. Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects
Moreover, the author has included a number of unusual features to challenge and stimulate
Also included is a Table of Theorems grouped into categories according to subject, and an Index of Mathematicians . Readers with a mathematical bent will enjoy and benefit from these entertaining and thought-provoking adventures in the fascinating realm of number theory. Mr. Friedberg is a theoretical physicist who has contributed to a wide variety of problems in mathematics and physics, including mathematical logic, number theory, solid state physics, general relativity, particle physics, quantum optics, genome research, and the foundations of quantum physics.
Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen ( Set Theory and the Continuum Hypothesis ), Alfred Tarski ( Undecidable Theories ), Gary Chartrand ( Introductory Graph Theory ), Hermann Weyl ( The Concept of a Riemann Surface ), Shlomo Sternberg ( Dynamical Systems ), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.
- GenresMathematicsNonfiction
240 pages, Paperback
First published January 9, 1995
26 people are currently reading
102 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 4 of 4 reviews
December 19, 2020
A wonderful introduction to number theory and proof construction using a story format from one of the chief mathematics researchers of the 20th century, Richard Friedberg. Friedberg takes us on a well-planned journey of mathematics, with the goal of helping the reader understand what exactly is number theory, where it originated, how it has evolved and most importantly, why it matters.
In this age of common core, as a teacher myself going through the teaching certification process, I see how the core has componentized math, and other subjects such as science, entirely stripping subjects of its story. This leaves each teacher in a mad dash to cover mathematics as if it were a checklist of properties and things to know, without providing the context, reasons and connections – and fun and wit - to why all of these things matter so much. We wonder why our students lack the deeper understanding of math and are devoid of finding math enjoyable. Read Friedberg and you can see a way for how mathematics could be taught.
Friedberg wrote this book a bit ago, and I suspect the same problems existed in mathematics education back then, and Friedberg recognized this. Friedberg is actually a researcher with an exhaustive list of significant published research, and to think he took time away from his research to explain to us the importance of Number Theory, well I have nothing but gratitude.
Friedberg starts with a story to help us understand what exactly is a theorem vs. a theory, and uses highly accessibly analogies to help us get there. He walks us through the important aspects of number theory in chapters from “On a clear day you can count forever” to “Proofs of a pudding”, using wit, interesting stories, history, supporting proofs and engaging problems throughout. He shares popular stories, such as Gauss’ childhood brilliance in Number Theory on summing 1 to 100 plus lesser known important events.
The problems are engaging, relevant and accessible. For example, Friedberg shares a problem his college mates came up with – what does this extraneous sequence represent: 14, 23, 28, 33, 42, 49, 59, 66, 77, 86, 96, 103… I had an advantage on this one, having lived at 33rd Street and Park Avenue in NYC for a number of years. I’ll lead you to purchase the book if you need the answer.
As others have mentioned, where Friedberg perhaps skims, is too brief and lacks detail, is in his descriptions of real world proofs. As one noted, you truly do need to pause, with pencil and paper, or should I say an Apple pen and Notability, to walk through the proofs and fill in the details for yourself. These are simple problems, (e.g. how to prove a number is even), but if you are unfamiliar with how to turn a theory into a theorem, Friedberg just doesn’t fully give enough details and perhaps adds to that feeling of this being above me. My recommendation is, to get the most out of this book, is to commit the extra time to understanding the proofs. It helps to look online to fill in any questions you may have as you are trying the proofs out for yourselves.
My recommendation is – if you are an aspiring elementary or high school mathematics teacher, or a middle school or high school student looking to understand this foundational area of mathematics called Number Theory – “An Adventurer’s Guide to Number Theory” is the only book out there that will give you its true essence and further feed your love for mathematics.
In this age of common core, as a teacher myself going through the teaching certification process, I see how the core has componentized math, and other subjects such as science, entirely stripping subjects of its story. This leaves each teacher in a mad dash to cover mathematics as if it were a checklist of properties and things to know, without providing the context, reasons and connections – and fun and wit - to why all of these things matter so much. We wonder why our students lack the deeper understanding of math and are devoid of finding math enjoyable. Read Friedberg and you can see a way for how mathematics could be taught.
Friedberg wrote this book a bit ago, and I suspect the same problems existed in mathematics education back then, and Friedberg recognized this. Friedberg is actually a researcher with an exhaustive list of significant published research, and to think he took time away from his research to explain to us the importance of Number Theory, well I have nothing but gratitude.
Friedberg starts with a story to help us understand what exactly is a theorem vs. a theory, and uses highly accessibly analogies to help us get there. He walks us through the important aspects of number theory in chapters from “On a clear day you can count forever” to “Proofs of a pudding”, using wit, interesting stories, history, supporting proofs and engaging problems throughout. He shares popular stories, such as Gauss’ childhood brilliance in Number Theory on summing 1 to 100 plus lesser known important events.
The problems are engaging, relevant and accessible. For example, Friedberg shares a problem his college mates came up with – what does this extraneous sequence represent: 14, 23, 28, 33, 42, 49, 59, 66, 77, 86, 96, 103… I had an advantage on this one, having lived at 33rd Street and Park Avenue in NYC for a number of years. I’ll lead you to purchase the book if you need the answer.
As others have mentioned, where Friedberg perhaps skims, is too brief and lacks detail, is in his descriptions of real world proofs. As one noted, you truly do need to pause, with pencil and paper, or should I say an Apple pen and Notability, to walk through the proofs and fill in the details for yourself. These are simple problems, (e.g. how to prove a number is even), but if you are unfamiliar with how to turn a theory into a theorem, Friedberg just doesn’t fully give enough details and perhaps adds to that feeling of this being above me. My recommendation is, to get the most out of this book, is to commit the extra time to understanding the proofs. It helps to look online to fill in any questions you may have as you are trying the proofs out for yourselves.
My recommendation is – if you are an aspiring elementary or high school mathematics teacher, or a middle school or high school student looking to understand this foundational area of mathematics called Number Theory – “An Adventurer’s Guide to Number Theory” is the only book out there that will give you its true essence and further feed your love for mathematics.
January 30, 2018
I thought the book was an enjoyable excursion through numbers. Unfortunately, I didn't read the book as one should (by which I mean, with pencil and paper out), but simply to read through the mathematics. Therefore, despite being mathematically inclined, it was difficult to follow some points.
I also thought it was odd to include pictures in the book, since they didn't really add to it. The chapters were relatively short, making them easy to digest as well. Overall, I thought the book was interesting, but I didn't love it.
I also thought it was odd to include pictures in the book, since they didn't really add to it. The chapters were relatively short, making them easy to digest as well. Overall, I thought the book was interesting, but I didn't love it.
Read
August 7, 2017Finally found a book that teaches Number theory the way i wanted it to be told.
Number theory (for me) is full of puzzles, if we don't know the stories behind their formation and solutions then it always seemed incomplete.
Thanks for filling that void.
Number theory (for me) is full of puzzles, if we don't know the stories behind their formation and solutions then it always seemed incomplete.
Thanks for filling that void.
March 5, 2022
This is a really good book on number theory. It helped me understand many issues around prime numbers, properties of numbers, residue arithmetic (helped me formulate a vague understanding about positional number systems). I have to admit, I didn’t understand the last two chapters, but that was my fault!
Displaying 1 - 4 of 4 reviews