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Supplemental Mathematics for the Curious
These books are written for the student with exceptional abilities. Their focus is conceptual development, and they are written for the self-learner.
The emphasis is not on covering new material or learning additional facts. While some material will be new to the student, much will be familiar. Instead, the emphasis is on the role of definitions, proofs, and developing mathematical ideas. It is therefore important for the student to pay attention to the narrative and spend sufficient mental energy to understand it. A student who simply skims the narrative and reads the examples in order to work the exercises will miss the point of the book!
Dr Bryan Dawson is Professor of Mathematics at Union University, Jackson, TN. Read more about Dr Dawson.
These books are written for the student with exceptional abilities. Their focus is conceptual development, and they are written for the self-learner.
The emphasis is not on covering new material or learning additional facts. While some material will be new to the student, much will be familiar. Instead, the emphasis is on the role of definitions, proofs, and developing mathematical ideas. It is therefore important for the student to pay attention to the narrative and spend sufficient mental energy to understand it. A student who simply skims the narrative and reads the examples in order to work the exercises will miss the point of the book!
Dr Bryan Dawson is Professor of Mathematics at Union University, Jackson, TN. Read more about Dr Dawson.
Supplemental Mathematics for the Curious: Number Theory
- Author:
- Dawson, Bryan PhD
- Subjects:
- Mathematics; Number theory
- Grade:
- 7, 8, 9, 10, 11, 12
- Order code:
- 4311
- Price:
- $25.00
- Online Price:
- $15.00
Designed for the gifted self-learner who has completed Algebra I, this supplemental high school text is ideal for summertime or other independent study. Careful exposition of the topics and well-developed examples with ample comments guide the student’s thinking, while answers to odd-numbered exercises provide feedback on the student’s progress.
The topics chosen form an introduction to the rich field of number theory. Among others, they include: divisibility, the Euclidean algorithm, prime numbers, figurate numbers, recursively-defined numbers such as Fibonacci and Lucas numbers, modular arithmetic, the Chinese Remainder Theorem, and an appendix on sets.
Applications are made to calendar systems, UPC and ISBN codes, and more. Side notes are provided to spark further interest or exploration on such topics as digital signals, the history of mathematical symbols, and numerology.
Throughout the text, students are guided to think carefully about mathematics itself, including learning the roles of definitions and proof. Such study can be an invaluable aid in maximizing a student’s understanding of high school geometry.
Sample pages: (pdf files) Page 2 | page 21 | page 31| page 62
Designed for the gifted self-learner who has completed Algebra I, this supplemental high school text is ideal for summertime or other independent study. Careful exposition of the topics and well-developed examples with ample comments guide the student’s thinking, while answers to odd-numbered exercises provide feedback on the student’s progress.
The topics chosen form an introduction to the rich field of number theory. Among others, they include: divisibility, the Euclidean algorithm, prime numbers, figurate numbers, recursively-defined numbers such as Fibonacci and Lucas numbers, modular arithmetic, the Chinese Remainder Theorem, and an appendix on sets.
Applications are made to calendar systems, UPC and ISBN codes, and more. Side notes are provided to spark further interest or exploration on such topics as digital signals, the history of mathematical symbols, and numerology.
Throughout the text, students are guided to think carefully about mathematics itself, including learning the roles of definitions and proof. Such study can be an invaluable aid in maximizing a student’s understanding of high school geometry.
Sample pages: (pdf files) Page 2 | page 21 | page 31| page 62
Supplemental Mathematics for the Curious: Number Systems
- Author:
- Dawson, Bryan PhD
- Subjects:
- Mathematics; Number systems
- Order code:
- 4328
- Price:
- $25.00
- Online Price:
- $15.00
Designed for the self-learner who has completed the traditional high school mathematics curriculum through trigonometry, this supplemental text is ideal for summertime or other independent study.
Careful exposition of the topics and well-developed examples with ample comments guide the student’s thinking, while answers to odd-numbered exercises provide feedback on the student’s progress.
Beginning with new ways to think about such familiar number systems as natural and rational numbers, the text progresses through algebraic numbers, real numbers, complex numbers, quaternions and infinitesimals, with treatment of the infinite along the way. Historical and philosophical side notes are included.
Throughout the text, students are guided to think carefully about mathematics itself, learning not just what is true but why it is true. Students who take the time to think through the ideas of this text will have the tools necessary for a deeper understanding of calculus.
Go to the top of the page for a description of the series.
Sample pages: (pdf files) Contents Page | Page 4 | Page 15 | page 23
Designed for the self-learner who has completed the traditional high school mathematics curriculum through trigonometry, this supplemental text is ideal for summertime or other independent study.
Careful exposition of the topics and well-developed examples with ample comments guide the student’s thinking, while answers to odd-numbered exercises provide feedback on the student’s progress.
Beginning with new ways to think about such familiar number systems as natural and rational numbers, the text progresses through algebraic numbers, real numbers, complex numbers, quaternions and infinitesimals, with treatment of the infinite along the way. Historical and philosophical side notes are included.
Throughout the text, students are guided to think carefully about mathematics itself, learning not just what is true but why it is true. Students who take the time to think through the ideas of this text will have the tools necessary for a deeper understanding of calculus.
Go to the top of the page for a description of the series.
Sample pages: (pdf files) Contents Page | Page 4 | Page 15 | page 23
