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Secondary Mathematics for Mathematicians and Educators: A View from Above [Pehme köide]

(The University of Michigan, USA)
  • Formaat: Paperback / softback, 324 pages, kõrgus x laius: 254x178 mm, kaal: 557 g, 3 Tables, black and white; 43 Line drawings, black and white; 4 Halftones, black and white; 47 Illustrations, black and white
  • Ilmumisaeg: 06-Oct-2020
  • Kirjastus: Routledge
  • ISBN-10: 1138294675
  • ISBN-13: 9781138294677
Teised raamatud teemal:
Secondary Mathematics for Mathematicians and Educators: A View from AboveSuurem pilt
  • Formaat: Paperback / softback, 324 pages, kõrgus x laius: 254x178 mm, kaal: 557 g, 3 Tables, black and white; 43 Line drawings, black and white; 4 Halftones, black and white; 47 Illustrations, black and white
  • Ilmumisaeg: 06-Oct-2020
  • Kirjastus: Routledge
  • ISBN-10: 1138294675
  • ISBN-13: 9781138294677
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138294677.html
Märksõnad:
In this engaging text, Michael Weiss offers an advanced view of the secondary mathematics curriculum through the prism of theory, analysis, and history, aiming to take an intellectually and mathematically mature perspective on the content normally taught in high school mathematics courses. Rather than a secondary mathematics textbook, Weiss presents here a textbook about the secondary mathematics curriculum, written for mathematics educators and mathematicians and presenting a long-overdue modern-day integration of the disparate topics and methods of secondary mathematics into a coherent mathematical theory.

Areas covered include:











Polynomials and polynomial functions;





Geometry, graphs, and symmetry;





Abstract algebra, linear algebra, and solving equations;





Exponential and logarithmic functions;





Complex numbers;





The historical development of the secondary mathematics curriculum.

Written using precise definitions and proofs throughout on a foundation of advanced content knowledge, Weiss offers a compelling and timely investigation into the secondary mathematics curriculum, relevant for preservice secondary teachers as well as graduate students and scholars in both mathematics and mathematics education.
Acknowledgments vii
Introduction 1(11)
0.1 Who This Book is For
1(1)
0.2 Preservice Secondary Teachers
2(2)
0.3 Mathematics Graduate Students
4(1)
0.4 Mathematics Education Doctoral Students
5(1)
0.5 Thinking Like a Mathematician
6(1)
0.6 The Theory-Building Disposition
7(3)
0.7 Structure of the Book
10(2)
1 Numbers and Number Systems
12(64)
1.1 Old and New Math
12(3)
1.2 Back to Basics
15(3)
1.3 What are Real Numbers?
18(3)
1.4 Characterizing the Reals
21(2)
1.5 Groups
23(5)
1.6 Fields and Rings
28(6)
1.7 Important Examples
34(4)
1.8 Order Properties and Ordered Fields
38(5)
1.9 Examples (and Non-Examples) of Ordered Fields
43(2)
1.10 Rational Subfields and the Completeness Property
45(7)
1.11 The Real Number Characterization Theorem, At Last
52(5)
1.12 Existence of a Complete Ordered Field
57(6)
1.13 Decimal Representations
63(7)
1.14 Recommended Reading
70(6)
2 Polynomials and Polynomial Functions
76(41)
2.1 Polynomials in the Secondary Curriculum
76(1)
2.2 Just What is a Polynomial?
77(2)
2.3 Functions
79(5)
2.4 Constant Functions and Polynomial Functions
84(5)
2.5 Formal Polynomials
89(6)
2.6 Interpreting Polynomials as Functions
95(11)
2.7 Polynomials over Finite Rings
106(8)
2.8 Recommended Reading
114(3)
3 Solving Equations
117(33)
3.1 "Equivalence" in the Secondary Curriculum
117(3)
3.2 Strings and Algebraic Strings
120(4)
3.3 Algebraic Equivalence
124(2)
3.4 Equations, Strong and Weak Equivalence, and Solutions
126(9)
3.5 A Complete (?) Algorithm for Solving Polynomial Equations in High School
135(2)
3.6 Equations in Two Variables
137(9)
3.7 Recommended Reading
146(4)
4 Geometry, Graphs and Symmetry
150(74)
4.1 Euclidean Geometry in the Secondary Curriculum
150(3)
4.2 Compass-and-Straightedge Constructions in the Euclidean Plane
153(6)
4.3 Measuring Ratios in the Plane
159(6)
4.4 From Geometry to Algebra: Coordinatizing Lines and the Plane
165(10)
4.5 Coordinate Systems, Lines and 1st-Degree Equations
175(10)
4.6 Non-Orthonormal Coordinate Systems
185(6)
4.7 Transformations and Symmetry
191(13)
4.8 Groups of Transformations
204(9)
4.9 Operations on Functions
213(6)
4.10 Recommended Reading
219(5)
5 Exponential and Logarithmic Functions
224(65)
5.7 What We Talk About when We Talk About Logs
224(6)
5.2 Exponential Functions, Roots, and the AM-GM Inequality
230(16)
5.3 Exponential Equations and Logarithmic Functions
246(12)
5.4 Logarithm-Like and Exponential-Like Functions
258(12)
5.5 Exponentials and Logarithms in Other Fields and Rings
270(9)
5.6 Applications to Cryptography
279(5)
5.7 Recommended Reading
284(5)
6 Complex Numbers
289(30)
6.1 A World of Pure Imagination?
289(3)
6.2 Hamilton's Construction
292(4)
6.3 Building a Multiplicative Structure from Scratch
296(5)
6.4 The Field Criterion
301(2)
6.5 The Complex Criterion
303(2)
6.6 The Case μ2 + 4λ ≥ 0
305(4)
6.7 Quadratic Polynomials, Factoring and Completing the Square
309(3)
6.8 Quotient Rings and Abstract Algebra
312(4)
6.9 Recommended Reading
316(3)
Index 319
Michael Weiss is currently a member of the faculty at the Department of Mathematics at the University of Michigan, USA. His background is in mathematics education and pure mathematics, and he was formerly a high school mathematics teacher in the United States.