Math 645: A Survey of Mathematical Problems I
Frank Sottile

• A cornerstone of mathematics is our notion of mathematical truth and our method to arrive at it via formal mathematical proof. This has had an enormous influence on most fields of human inquiry (for example, the understanding that blood flows in our bodies involved a deductive proof.) Our book begins with simple logic, and continues to a discussion of mathematical induction, which is a framework for many proofs. Our readings reflect on nature of mathematical proof.
      In the excerpt from René Descartes, he lays out what is a mathematical proof, and how he is using that method of inquiry as basis for his further studies. It is a bit hard to read, as he writes very complicated sentences.
      Proofs without words express very eloquently another aspect of mathematical proof.
• Reading:
  • Dr. Geller's Lecture 1.
  • Chapter 1 of A Survey of Mathematical Problems Do not bother with the Readings listed in Section 1.2.
  • René Descartes: Discourse on the method.... Read this, starting from: "Among the branches of Philosophy:"
  • Look up some of the material on "Proof without words" on line (there is a lot).
• Assignment: Due Monday 3 September by Midnight. (HW1) It is OK to discuss this among yourselves. We all have something to learn from each other.
  To hand in: Email a .pdf to Taylor Brysiewicz tbrysiewicz@math.tamu.edu.
  1. Write a brief paragraph on what constitutes a proof. (Do not be too concerned about this; a goal of our course is to understand this notion better. The purpose of this question is for you to reflect on what you now know.)
  2. Exercises 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, and Problems 1.3 and 1.5 of A Survey of Mathematical Problems
     If you need a primer on mathematical induction, please start a discussion on Piazza.