With the assistance of Jason Brasel
Softcover ISBN:  9781470472474 
Product Code:  MBK/148 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470474263 
Product Code:  MBK/148.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Softcover ISBN:  9781470472474 
eBook: ISBN:  9781470474263 
Product Code:  MBK/148.B 
List Price:  $178.00 $133.50 
MAA Member Price:  $160.20 $120.15 
AMS Member Price:  $142.40 $106.80 
With the assistance of Jason Brasel
Softcover ISBN:  9781470472474 
Product Code:  MBK/148 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470474263 
Product Code:  MBK/148.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Softcover ISBN:  9781470472474 
eBook ISBN:  9781470474263 
Product Code:  MBK/148.B 
List Price:  $178.00 $133.50 
MAA Member Price:  $160.20 $120.15 
AMS Member Price:  $142.40 $106.80 

Book Details2023; 339 ppMSC: Primary 00; 05; 11; 20; 97
The Mathematical Neighborhoods of School Mathematics visits regions beyond, but proximal to and accessible from school mathematics. Its aim is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but, most importantly, its interconnections and overall coherence, a perspective not easily available from the school curriculum. This aim entailed assembling a variety of substantial mathematical domains that do not typically cohabit the same volume. The book begins with an indepth treatment of topics in the school curriculum, often with novel approaches and connections. A unifying thread is the group theoretic study of addition and multiplication in the various number systems of school mathematics. The exposition is mathematically rigorous, including proofs of many fundamental theorems not otherwise easily available in mathematically accessible form.
The Mathematical Neighborhoods of School Mathematics is intended to be a conceptual contribution to mathematics education. It will be a valuable resource in professional development of mathematics teachers, and in mathematical enrichment programs, for both students and teachers. In this regard, many of the chapters are relatively selfcontained. It could also serve as a text for undergraduate mathematics majors with an interest in teaching. The exceptional Chapter 11 presents some novel instructional designs for problemsolving activities meant to cultivate “connectionoriented mathematical thinking.”
Hyman Bass is the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education at the University of Michigan. He is a member of the National Academy of Sciences and of the National Academy of Education.
Jason Brasel, a former high school mathematics teacher, is a mathematics educator and researcher in secondary mathematics, who works at TeachingWorks, University of Michigan.
ReadershipPreservice and inservice secondary teachers (and faculty who teach them) interested in expanding their knowledge of the deeper mathematics underlying what they teach.

Table of Contents

Chapters

Basic notation and background

Division with remainder, place value, and order of magnitude

Modular congruence and base$B$ expansions of rational numbers

Discrete real additive groups

Primes and factorization

Group theory and Euclidean isometry groups

Rings and fields

Polynomials

Combinatorics

Discrete calculus

Complex numbers

Mathematical connections


Additional Material

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The Mathematical Neighborhoods of School Mathematics visits regions beyond, but proximal to and accessible from school mathematics. Its aim is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but, most importantly, its interconnections and overall coherence, a perspective not easily available from the school curriculum. This aim entailed assembling a variety of substantial mathematical domains that do not typically cohabit the same volume. The book begins with an indepth treatment of topics in the school curriculum, often with novel approaches and connections. A unifying thread is the group theoretic study of addition and multiplication in the various number systems of school mathematics. The exposition is mathematically rigorous, including proofs of many fundamental theorems not otherwise easily available in mathematically accessible form.
The Mathematical Neighborhoods of School Mathematics is intended to be a conceptual contribution to mathematics education. It will be a valuable resource in professional development of mathematics teachers, and in mathematical enrichment programs, for both students and teachers. In this regard, many of the chapters are relatively selfcontained. It could also serve as a text for undergraduate mathematics majors with an interest in teaching. The exceptional Chapter 11 presents some novel instructional designs for problemsolving activities meant to cultivate “connectionoriented mathematical thinking.”
Hyman Bass is the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education at the University of Michigan. He is a member of the National Academy of Sciences and of the National Academy of Education.
Jason Brasel, a former high school mathematics teacher, is a mathematics educator and researcher in secondary mathematics, who works at TeachingWorks, University of Michigan.
Preservice and inservice secondary teachers (and faculty who teach them) interested in expanding their knowledge of the deeper mathematics underlying what they teach.

Chapters

Basic notation and background

Division with remainder, place value, and order of magnitude

Modular congruence and base$B$ expansions of rational numbers

Discrete real additive groups

Primes and factorization

Group theory and Euclidean isometry groups

Rings and fields

Polynomials

Combinatorics

Discrete calculus

Complex numbers

Mathematical connections