#### Multiple Choice Portion

To assist in your studying for the multiple choice portion of the waiver exam please focus on the following.
Unless otherwise specified all references are to

**How to Think Like a Mathematician: A Companion to Undergraduate Mathematics** by Dr Kevin Houston.

**Supplementary PDF**
- CH01: Sets and Functions
- CH06: Making a Statement
- CH07: Implications
- CH08: Finer Points Concerning Implications
- CH09: Converse and Equivalence
- CH10: Quantifies - For All and There Exists
- CH11: Complexity and Negation of Quantifiers
- CH12: Examples and Counterexamples
- CH20: Techniques of Proof I: Direct Method
- CH22: Techniques of Proof II: Proof by Cases
- CH23: Techniques of Proof III: Contradiction
- CH24: Techniques of Proof IV: Inductions
- CH25: More Sophisticated Induction Techniques
- CH26: Techniques of Proof V: Contrapositive Method
- CH27: Divisors
- CH28: The Euclidean Algorithm
- CH29: Modular Arithmetic
- CH30: Injective, Surjective, Bijective - And a Bit About Infinity
- CH31: Equivalence Relations

#### Written Portion

In addition to knowing the facts related to the multiple choice portion above for the written portion it is important that you
can convey your ideas clearly and concisely.
To assist in your studying for the written portion of the waiver exam please focus additionally on the following topics.
Unless otherwise specified all references are to

**How to Think Like a Mathematician: A Companion to Undergraduate Mathematics** by Dr Kevin Houston.

- CH03: Writing Mathematics I
- CH04: Writing Mathematics II
- CH05: How to Solve Problems
- CH14: Definitions, Theorems, and Proofs
- CH15: How to Read a Definition
- CH16: How to Read a Theorem
- CH17: Proof
- CH18: How to Read a Proof