jeremy9959 / 2020-fall-2710w-math Goto Github PK

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

• 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

• Contrapositive Proof (Ch5.1)
• Congruence of Integers (Ch5.2a)
• Congruence (Ch5.2b)

Chapter 6: Contradiction

• Proof by Contradiction (Ch6.1a)
• Proof by Contradiction (Ch6.1b)

Chapter 7: Non-Conditional Statements

• 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

• 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

• Counterexamples (Ch9.1a)
• Proof of non-existence (Ch9.1bc)
• Disproof by contradiction (Ch9.2-3)

Chapter 10: Induction

• 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

• 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

• 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

Shield:

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