Softcover ISBN:  9781470456771 
Product Code:  MBK/133 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
eBook ISBN:  9781470460068 
Product Code:  MBK/133.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9781470456771 
eBook: ISBN:  9781470460068 
Product Code:  MBK/133.B 
List Price:  $100.00 $75.00 
MAA Member Price:  $90.00 $67.50 
AMS Member Price:  $80.00 $60.00 
Softcover ISBN:  9781470456771 
Product Code:  MBK/133 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
eBook ISBN:  9781470460068 
Product Code:  MBK/133.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9781470456771 
eBook ISBN:  9781470460068 
Product Code:  MBK/133.B 
List Price:  $100.00 $75.00 
MAA Member Price:  $90.00 $67.50 
AMS Member Price:  $80.00 $60.00 

Book Details2020; 417 ppMSC: Primary 97; 00
This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and gradelevel appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject.
This volume distinguishes itself from others of the same genre in getting the mathematics right. In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles. It also provides details for extending the domain of definition of sine and cosine to all real numbers. It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians.
In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs. An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator. This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture.
This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.
ReadershipTeachers of middle school mathematics; students and professionals interested in mathematical education.

Table of Contents

Chapters

Trigonometry

The concept of limit

The decimal expansion of a number

Length and area

3Dimensional geometry and volume

Derivatives and integrals

Exponents and logarithms, revisited

Appendix: Facts from the companion volumes


Additional Material

Reviews

As in the previous volumes of this series, on each topic the author provides the reader with numerous illuminating activities and an excellent choice of a wide range of exercises.
António de Bivar Weinholtz (University of Lisbon), European Mathematical Society


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This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and gradelevel appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject.
This volume distinguishes itself from others of the same genre in getting the mathematics right. In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles. It also provides details for extending the domain of definition of sine and cosine to all real numbers. It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians.
In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs. An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator. This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture.
This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.
Teachers of middle school mathematics; students and professionals interested in mathematical education.

Chapters

Trigonometry

The concept of limit

The decimal expansion of a number

Length and area

3Dimensional geometry and volume

Derivatives and integrals

Exponents and logarithms, revisited

Appendix: Facts from the companion volumes

As in the previous volumes of this series, on each topic the author provides the reader with numerous illuminating activities and an excellent choice of a wide range of exercises.
António de Bivar Weinholtz (University of Lisbon), European Mathematical Society