MTH 181-01 (1PM) Discrete Mathematics Fall 2022
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(EP), 49, 52 |
2.2 Conditional Statements | 4, 13, 17, 20bceg, 22bceg, 23bceg, 21(EP), 38, 40, 45 |
2.3 Valid and Invalid Arguments | 2, 9, 11, 28, 30, 32, 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(EP) |
4.8 Indirect Argument: Two Famous Theorem | 7, 13, 25,32 |
6.1 Set Theory: Introduction | 1, 4, 10, 12, 16(upload scan), 23(upload scan), 27, 30, 35(upload scan) |
6.2 Properties of Sets | 2, 4, 6, 13, 18, 24(upload scan), 26, 31, 35 |
6.3 Sequences | 2, 8, 13(upload scan), 20, 24, 29, 32, 42, 46(EP) |
5.1 Sequences | 7, 13, 21, 28(EP), 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, 17EP(upload scan), 19(upload scan), 22, 23, 29 |
9.2 Possibility Trees and the Multiplication Rule | 5, 7, 10, 15EP, 17, 22, 25(upload scan), 32NVA, 37, 38, 40 |
9.3 Counting Elements of Disjoint Sets: The Addition Rule | 5, 7, 9, 12.NVA, 17, 19, 21(EP), 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: Rules Of Inference Handout PDF
- Chapters 2-4: Mathematical Conventions for Writing Proofs
- Chapters 2-4: Proof Tips
- Chapter 5: Formats for Mathematical Induction
- Chapter 5: Tromino Puzzle Solver
- Chapter 6: Elementwise Set Proofs Handout V2 PDF
- Chapter 6: Sample Power Set App
- Final (Tuesday, 12/13/2022, 3:00 PM– 6:00 PM):
LaTeX
- The LaTeX Project Site
- Modern Algebra LaTeX CheatSheet
- User Created LaTeX Commands
- Michelle Krummel's video LaTeX Videos Tutorials:
- 5. Text and Document Formatting 6. Packages, Macros and Graphics
- 7. Errors and Debugging 8. Texmaker Tips
- 9. Calculus Notation 10. How to Format a Math Paper
- 11. Beamer Slide Presentation
- Overleaf:An on line editor with free individual accounts The editors below require you to install a LaTeX distribution (see LaTeX Distributions)
- Texmaker: Open-source, Cross-platform
- TexStudio: Open-source, Cross-platform (based on Texmaker)
- TexShop: Open-source, Mac Only
- LyX: Open-source,Cross-platform
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.