Order Matters: Intro to Pure Mathematics Module

[matqkks]

I want to produce a resource that has a narrative and includes the following topics:
Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation.
It is in aid as an introduction to a number theory module.
How should I order these so that the end document has a narrative and is coherent, not just disjoint set of topics?

 

[lofgran]

I would suggest organizing the resource in a way that builds upon each topic and creates a logical flow for the reader. Here is a possible order that could be used:

1. Introduction to Sets: Start by introducing the concept of sets and their properties. This will provide a foundation for understanding the other topics.

2. Logic and Proofs: Next, introduce the basics of logic and proofs, including the use of symbols and logical operators. This will help readers understand the importance of reasoning and proof in mathematics.

3. Numbers: After establishing the basics, move on to discussing different types of numbers, such as irrational, integers, and rational numbers. This will allow readers to understand the different properties and characteristics of each type of number.

4. Binomial Theorem: Once the concept of numbers is established, introduce the binomial theorem and its applications. This will help readers understand the relationship between numbers and algebraic expressions.

5. Geometric Series: Building upon the concept of binomial theorem, introduce geometric series and their properties. This will allow readers to understand the connection between series and geometric patterns.

6. Inequalities: After discussing series, introduce the concept of inequalities and how they relate to numbers and equations. This will provide readers with a deeper understanding of mathematical relationships.

7. Identity, Polynomial, and Symmetry: These topics can be grouped together as they all relate to algebraic expressions and their properties. Introduce the definitions and properties of these terms and how they relate to each other.

8. Sigma and Product Notation: Finally, introduce sigma and product notation and their use in mathematical expressions. This will tie together the previous topics and show readers how these concepts can be used in real-life situations.

By following this order, the resource will have a clear narrative and will build upon each topic in a logical manner. This will help readers understand the connections between the different topics and how they relate to each other. Additionally, it will provide a solid foundation for readers to further explore number theory in the future.