# Course Notes

We will not be using a textbook this semester, but rather a theorem-sequence adopted for inquiry-based learning (IBL) and the Moore method for teaching mathematics. The theorem-sequence that we are using is an adaptation of notes written by Stan Yoshinobu of Cal Poly and Matthew Jones of California State University, Dominguez Hills. The authors have been gracious enough to grant me access to the source of these notes, so that we can modify and tweak for our needs if necessary. Every attempt will be made on my part to maintain the integrity of these notes. Any new errors introduced are no one's fault but my own. In this vein, if you think you see an error, please inform me, so that it can be remedied.

In addition to working the problems in the notes, I expect you to be *reading* them. I will not be covering every detail of the notes and the only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the content of the notes whenever necessary by asking questions in class or posting questions to the course forum.

You can find the course notes below. I reserve the right to modify them as we go, but I will always inform you of any significant changes. The notes will be released incrementally.

- Elements of Style of Proofs (PDF)
- Chapter 0: Foundations of Higher Mathematics (PDF)
- Chapter 1: Introduction to Mathematics
- Section 1.1: A Taste of Number Theory (1.1-1.15) (PDF)
- Section 1.2: Logic, Negation, and Contrapositive (1.16-1.42) (PDF)
- Section 1.3: Negating Implications and Proof by Contradiction (1.43-1.54) (PDF)
- Section 1.4: Introduction to Quantification (1.55-1.66) (PDF)
- Section 1.5: More on Quantification (1.67-1.80) (PDF)
- Section 1.6: And Even More on Quantification (1.81-1.92) (PDF)
- Chapter 2: Set Theory and Topology
- Section 2.1: Sets (2.1-2.27) (PDF)
- Section 2.2: Power Sets (2.28-2.43) (PDF)
- Section 2.3: Indexing Sets (2.44-2.58) (PDF)
- Section 2.4: Basic Topology of $\mathbb{R}$ (2.59-2.99) (PDF)
- Chapter 3: Relations and Functions
- Section 3.1: Relations (3.1-3.27) (PDF)
- Section 3.2: Equivalence Relations (3.28-3.46) (PDF)
- Section 3.3: Partitions (3.47-3.66) (PDF)
- Section 3.4: Introduction to Functions (3.67-3.90) (PDF)
- Section 3.5: Composition and Inverses (3.91-3.107) (PDF)
- Chapter 4: Induction