## MTH 181-02 (Noon) Discrete Mathematics Fall 2021

### Syllabus

### Assignments

Chapter Section | Suggested Problems |
---|---|

1.1 Variables | 2,4,6,11,13 |

1.2 The Language of Sets | 4,5,8,9,12,15 |

2.1 Logical Form and Logical Equivalence | 5,8,9,15,17,26,35,43,45,49,52 |

2.2 Conditional Statements | 4, 13, 17, 20bceg, 22bceg, 23bceg, 21, 38, 40, 45,48 |

2.3 Valid and Invalid Arguments | 2, 9, 11, 28, 30, 32, 38, 40, 42 |

3.1 Predicates and Quantified Statements I | 4, 5, 10, 16, 18, 22, 29 |

3.2 Predicates and Quantified Statements II | 4,8,12,15, 17, 27, 38, 42, 46 |

3.3 Arguments with Quantified Statements | 4,10,12,17,20,23,30,36,38 |

3.4 Arguments with Quantified Statements | 4,6,14,17,22,26,29,32 |

4.1 Direct Proof and Counterexamples I: Introduction | 2,4,7,11,15,16,24 |

4.2 Direct Proof and Counterexamples II: Writing Advice | 5,13,18,27,29,35 |

4.3 Proof and Counterexamples III: Rational Numbers | 1,2,3,5,7,8,14,17,22,25,30,38 |

4.7 Indirect Argument: Contradiction and Contraposition | 4,6,11,18,24,27, 30,32,34 |

4.8 Indirect Argument: Two Famous Theorem | 7, 13, 25,32 |

6.1 The Principle of Mathematical Induction | 8,13,17,19,20 |

6.2 Additional Examlples of Induction Proofs | 2,4,6,13,18,24,26,31,35 |

6.3 Sequences | 2,8,13,20,24,29,32,42,46 |

5.1 Sequences | 7,13,21,28,36,38,44,57,63,67 |

5.2 Mathematical Induction I: Proving Formulas | 7,12,14,23,26,31,35 |

5.3 Mathematical Induction II: Applications | 5,9,12,20,30,39,46 |

5.6 Defining Sequences Recursively | 6,8,10,16,21,24,32,36,40 |

9.1 Introduction to Probability | 6,10,11,17,19,22,23,29 |

9.2 Possibility Trees and the Multiplication Rule | 5,7,10,11,15,17,22,25,32,37,38,40 |

9.3 Counting Elements of Disjoint Sets: The Addition Rule | 5,7,9,12,17,19,21,22,24,34,36 |

9.4 The Pigeonhole Principle | 4,6,11,13,15,18,21,28,30,36 |

9.7 Pascal's Formula and the Binomial Theorem | 4,7,24,30,32,39,44,46,50 |

### Handouts

- Chapter 0: Worksheet 0: Recognizing Common Algebra Errors PDF Solution
- Chapter 1: Logic Puzzle Worksheet V1
- Chapter 1: Rules Of Inference Handout PDF
- Chapter 1: Online Logic Quizzes and Puzzles
- Value of a Logical Expression Quiz Truth Table Quiz
- To run the Wolfram demo apps below, you must either use the FireFox browser or download the corresponding "CDF" file and open it with Wolfram's CDF player or Mathematica. If you do not have the CDF player/plugin, you will be prompted to download and install it!

- Chapters 2-4: Worksheet 03: Quantifiers V1
- Chapters 2-4: Mathematical Conventions for Writing Proofs
- Chapters 2-4: Proof Tips
- Chapters 2-4: Worksheet 04: Methods of Proof V1
- Chapter 5: Formats for Mathematical Induction
- Chapter 5: Worksheet 05: Mathematical Induction V2
- Chapter 5: Tromino Puzzle Solver
- Chapter 6: Elementwise Set Proofs Handout V2 PDF
- Chapter 6: Sample Power Set App
- Chapter 6: Online Venn Diagram Puzzles and Games:
- Chapter 6: Partitions and Bell Numbers
- Quiz Solutions
- Exam Review Sheets and Solutions:
- Final (Monday, 12/13/2021, 11:30 AM – 2:30 PM):

### LaTeX

- The LaTeX Project Site
- Modern Algebra LaTeX CheatSheet
- User Created LaTeX Commands
- Michelle Krummel's video LaTeX Videos Tutorials:
- LaTeX Editors:
- Overleaf:An on line editor with free individual accounts
- Texmaker: Open-source, Cross-platform
- TexStudio: Open-source, Cross-platform (based on Texmaker)
- TexShop: Open-source, Mac Only
- LyX: Open-source,Cross-platform

**The editors below require you to install a LaTeX distribution (see LaTeX Distributions)** - LaTeX Distributions: Open-source distributions of LaTeX

### Markdown

- Markdown Guide
- Typora: Free cross-platform markdown editor
- MacDown: Open-source Mac markdown editor
- Remarkable: Open-source Linux-Windows markdown editor

### Mobile Scanning Apps

- Apple Notes iOS App: How to scan documents on iPhones and iPads
- Turboscan App: Michelle Krummel's Turboscan Video for iPhone, iPad
- Google Drive App How to SCAN documents to PDF Video for Android
- MS Office with Lens App: How to Scan a Document to your iPhone or Android phone

### Resources

### Logic Extras

- The home of Logisim: A free graphical tool for simulating logic circuits.
- The home of SWI-Prolog: A language used for developing expert systems and artificial intelligence applications.

### Number Theory

### Graph Theory Extras

- GeoGebra: A general open-source geometry program that can be used to crete graphs.
- A Gentle Introduction To Graph Theory

### Scientific Computation

- The home of Sage: An python-based open source computer algebra system that can also be used for numerical computing.
- The home of the Python: A programming language for scientific computation.
- Anaconda Python Distribution: Free distributions of Python with the necessary packages for scientific computation.
- The home of Visual Python: A free software package for creating 3D simulations using the Python. Note: The most recent version of Visual Python is now able to run in a Jupyter notebook which are part of the Anaconda 3.5 distribution.
- The home of Glowscript: Based on Visual Python, it is a cloud-based IDE for creating 3D simulations that can run in browsers.
- The home of of Julia: A new high performance open source programming language designed for scientific computing. It's execution speed is close to that of C with a python-like syntax. It has features that make it easer to write code for multiple processors, GPU's and clusters.
- The home of the R Project for Statistical Computing: The most widely used open source application and language for statistical computing.