The first midterm will cover the content from Lecture 1 until Lecture 12. Please see the lecture notes here.
This corresponds to the following chapters and sections of the book

D’Angelo/West, Mathematical Thinking, Second Edition

Chapter 1: Numbers, Sets, and Functions

– Set-theoretic concepts and operations
– Functions: Formal definition and basic concepts (graph, image set, bounded function, decreasing/increasing function)
– Triangle and AGM inequalities

Chapter 2: Language and Proof

– Logical statements, conditionals, quantifiers
– Methods of proof (direct, contraposition, contradiction)

Chapter 3: Induction

– Induction and strong induction
– Well-ordering principle
– Applications

For the part of ‘Language and Proof’, you can also check the first chapter of the book

Kenneth H. Rosen: Discrete Mathematics and Its Applications, McGraw-Hill, 7th edition