**Math 2710W: Transition to Higher Mathematics**

**University of Connecticut**

**Instructor**

Professor Jeremy Teitelbaum

homepage: https://teitelbaum.math.uconn.edu and https://jeremy9959.net

This is a hybrid synchronous/asynchronous online course. The materials for this course consist of:

- The textbook, Richard Hammack’s Book of Proof
- A set of video “mini-lectures” (linked to below)
- A set of course notes/slides (available below as they are developed)
- Periodic assessments and writing prompts (available to UConn students through the HuskyCT LMS)

**Chapter 1: Sets**

The video lectures for Chapter 1 are available here.

- Introduction to Sets (Ch1.1a)
- Introduction to Sets (Ch1.1b)
- Cartesian Product (Ch1.2)
- Subsets (Ch1.3a)
- Subsets (Ch1.3b)
- Subsets (Ch1.3c)
- Subsets (Ch1.3d)
- Power Sets (Ch1.4)
- Union, Intersection, Difference (Ch1.5)
- Complement (Ch1.6)
- Venn Diagrams (Ch1.7)
- Indexed Sets (Ch1.8)
- Russell’s Paradox (Ch1.10)

**Chapter 2: Logic**

The video lectures for Chapter 2 are available here.

- Statements (Ch2.1)
- And, Or, Not (Ch2.2)
- Conditional Statements (Ch2.3a)
- Conditional Statements (Ch2.3b)
- Biconditionals (Ch2.4)
- Truth Tables (Ch2.5)
- Logical Equivalence (Ch2.6)
- Quantifiers (Ch2.7a)
- Quantifiers (Ch2.7b)
- More on Conditionals(Ch2.8)
- Comparing Colloquial English and Logic (ch2.9)
- Negations (Ch2.10)
- Inference (Ch2.11)

**Chapter 4: Direct Proof**

The video lectures for chapter 4 are available here

- Theorems (Ch4.1)
- Definitions (Ch4.2)
- Direct Proof (Ch4.3a)
- Direct Proof (Ch4.3b)
- Direct Proof (Ch4.3c)
- Direct Proof (Ch4.3d)
- Direct Proof (Ch4.3e)
- Cases (Ch4.4)

**Chapter 5: Contrapositive Proof**

The video lectures for Chapter 5 are available here.

**Chapter 6: Contradiction**

The video lectures for Chapter 6 are available here.

**Chapter 7: Non-Conditional Statements**

The video lectures for Chapter 7 are available here

- If and only if proofs (Ch7.1)
- Existence, and Existence and Uniqueness Proofs (Ch7.3a)
- Existence/Uniqueness Proofs (Ch7.3b)
- Existence/Uniqueness Proofs (Ch7.3c)
- Existence/Uniqueness Proofs (Ch7.3d)
- Constructive vs non-constructive proofs (Ch7.4)

**Chapter 8: Set Proofs**

The video lectures for Chapter 8 are available here

- Proving x is an element of a set A (Ch8.1)
- Proving A is a subset of B (Ch8.2)
- Proving set A equals set B (Ch8.3)

**Chapter 9: Disproofs**

The video lectures for Chapter 9 are available here

**Chapter 10: Induction**

The video lectures for Chapter 10 are available here )

- Mathematical Induction (Ch10.1a)
- Mathematical Induction (Ch10.1b)
- Mathematical Induction (Ch10.1c)
- Strong Induction (Ch10.2)
- Minimal counterexample/well-ordering (Ch10.3)
- Fundamental Theorem of Arithmetic (Ch10.4)
- Fibonacci Numbers (Ch10.5)
- FibSumsOfSquares
- nthFibonacci
- RedBluePtsProblem

**Chapter 3: Counting**

The video lectures for Chapter 3 are available here.

- Lists (Ch3.1a)
- Lists (Ch3.1b)
- Lists (Ch3.1c)
- Multiplication Principle (Ch3.2)
- Errata to previous video (Ch3.2.Example5Redo)
- Addition and subtraction principle (Ch3.3)
- Factorials and Permutations (Ch3.4)
- Counting subsets (Ch3.5)

**Chapter 11: Relations**

The video lectures for Chapter 11 are available here.

- Relations (Ch11.1)
- Properties of Relations (Ch11.2)
- Equivalence Relatons (Ch11.3a)
- Equivalence Relations (Ch11.3b)
- Equivalence Classes (Ch11.4)
- Integers mod N (Ch11.5)
- Relations between sets (Ch11.6)

**Chapter 12: Functions**

The video lectures for Chapter 12 are available here.

- Functions (Ch12.1a)
- Functions (Ch12.1b)
- Injective and surjective functions (Ch12.2a)
- Injective and surjective functions (Ch12.2b)
- Pigeonhole principle (Ch12.3)
- Composition of functions (Ch12.4)
- Inverse functions (Ch12.5a)
- Inverse functions (Ch12.5b)
- Image and preimage (Ch12.6
- Problem12.2.10

This work is licensed under a Creative Commons Attribution 4.0 International License.