Preface
- Page ID
- 7333
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)To those teaching this course:
Course Description:
This course explores elementary number theory, numeration systems, operations on integers and rational numbers, and elementary combinatorics, using both inductive and deductive methods. Emphasis will be placed on the development of clarity and understanding of mathematical processes and ideas, the application of these ideas to problem-solving and the communication of these ideas to other people.
This course is one of the required courses for the Minor in Mathematics for Elementary Education program at Mount Royal University (MRU) and was designed especially for elementary education students. The purpose of this course is to introduce future elementary (grades K-6) educators to elementary number theory. The relationship of concepts to the elementary mathematics curriculum is emphasized. We started offering this course in Winter 2014. I have been teaching this course since its inception. I have created these lecture notes to facilitate student learning. This course partially fulfills the need for mathematics to be taught as a language with reasoning and gives students number sense.
Course Learning Outcomes:
Upon successful completion of this course, students will be able to:
- show knowledge of fundamental concepts in mathematics,
- encourage mathematical investigations,
- demonstrate an understanding of elementary number theory,
- reflect major algebraic ideas such as algebra as a set of rules and procedures; algebra as the study of structures; algebra as the study of the relationship among quantities,
- do problem-solving by using number theory, and
- perform mathematical calculations that use modulo operations and different number bases.
Course topics and tentative schedule:
| Week | Chapter(s) |
| 1 | 1 |
| 2,3 | 2 |
| 3,4 | 3 |
| 4,5 | 4 |
| 7,8 | 5 |
| 9,10 | 6 |
| 11 | 7 |
| 12 | 8 |
To those taking this course:
A Note on Formatting:
Throughout this resource, practice exercises can be found at the end of each chapter. No answer key is provided. This is to encourage students to experience mathematics as a synthetic and creative field and also to attend class to ask questions. The "Thinking Out Loud" sections are to prompt discussion - take these up with your classmates and see if you can justify your position using what you know.
Acknowledgements:
The creation of this resource would not have been possible without significant help from a variety of sources. They are, in no particular order,
- Professor Delmar Larsen, LibreTexts, for his unconditional support,
- The Department of Mathematics and Computing, Mount Royal University,
- Faculty of Science and Technology, and
- Former students, who have taken this class in person, and who donated their class notes as reference material.
- Undergraduate research assistant Dallas Daniel.
- Undergraduate student James Bergeron.
Thank you all, so very much, for your help, insights, and resources.
Pamini Thangarajah, PhD
Calgary, Alberta
November 2017, edited in December 2019, April 2022
Contact:
If you find any error(s), please contact me via email: pthangarajah@mtroyal.ca.