Handouts for Math 554 Spring 2025

* The symbol * means not handed out in class; however, you should read on the internet.

Writing Guidelines (WG)*

  1. Our Writing Guidelines  (details included)
  2. List of Our Writing Guideline  (the WG listed out)
  3. Sundstrom's Writing Guidelines  (from Sundstrom's Math 300 book, Appendix A)
  4. Hammack's Writing Guidelines  (from Hammack's Math 300 book)
  5. Symbolically Write Guidelines
  6. Math Induction (PMI) Writing Guidelines

Course Handouts

  1. 1.1. Set Operations: Unions, Intersection, Complement
  2. 1.1. Functions and Sets   (injective, surjective, (inverse) image)
  3. 1.2. Induction *   (Summary. Since covered in Math 300, we will not cover in Math 554.)
  4. 1.3. Countability: Finite and Infinite Sets   (lecture notes)
  5. Ch 2. A Rigorous Axiomatic Approach to the Real Numbers   (soln to charts)
  6. 3.1. Two color coded Sequences Limit proofs*   (bcs better in color, not distributed in class)
  7. 3.2. Sequences Limit Theorems

Findable from URL: http://people.math.sc.edu/girardi/