Spring 2025
MATH 312: Proofs in Elementary Analysis

Branko Ćurgus

Wednesday, March 26, 2025

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• The information sheet
• In this class we present a rigorous approach to basic theorems in calculus. Since rigorous reasoning in Mathematics is based on Mathematical Logic, we will start with a Brief Review of Mathematical Logic. This is Chapter Two in the class lecture notes.
• Most, if not all mathematical statements, involve quantifiers. In the class lecture notes the quantifiers are presented in Section 2.3. Examples are given in Section 2.4. For additional examples, you can read my webpage Mathematical Rigor in the Context of Quadratic Functions.
• Some useful Wikipedia links:
  • Mathematical proof
  • Set
  • The number 1
  • The number 0
  • Integers
  • Natural numbers
  • Rational numbers
  • Real numbers
  • Intervals
  • Sign function
  • Floor and ceiling
• My one-page on the Power of Math. This page is a part of Chapter One in the class lecture notes.
• My one-page on Rigorous Reasoning. This page is a part of Chapter One in the class lecture notes.

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