Topic Outline

• Preliminaries: Quadratics, Inqualities, and Numbers

• Sets, Functions, and the Field Axioms

• Logic and Proof Strategies

• Mathematical Induction

• Bijections and Cardinality

• Relations

• (If time permitted) Integers and Divisibility

Tentative Class schedule

Lecture 1 (08/07/2023): Syllabus, quadratic Formula, proof-based mathematics, inequalities (Lecture Notes) 

Lecture 2 (08/08/2023): More on inequalities, group discussion (Lecture Notes, Discussion Notes)

Lecture 3 (08/09/2023): Type of numbers and operations on numbers, set notations and set operations (Lecture Summary, Homework (corrected version)) 

Lecture 4 (08/11/2023): Set identies and functions (Lecture Summary, Discussion Notes)

Lecture 5 (08/14/2023): Functions, fields axioms and examples (Lecture Summary)

Lecture 6 (08/15/2023): Logic and building blocks of mathematical statements (Lecture Summary, Discussion Notes) 

Lecture 7 (08/16/2023): Truth tables, logical equivalences and proof strategies (Lecture Summary, Homework (corrected version))

Lecture 8 (08/18/2023): Negations, Quiz 1 (Quiz Solutions)

Lecture 9 (08/21/2023): Natural numbers, PMI (Lecture Summary)