MTH 181-02 (Noon) Discrete Mathematics Fall 2022

• Syllabus
• Assignments
• Handouts
• Home

• LaTeX
• Markdown
• Scanning Apps
• Resources

Syllabus

• Download Tentative Syllabus V2 (PDF)

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

1. Chapter 0: Worksheet 0: Recognizing Common Algebra Errors PDF   
2. Chapter 1: Rules Of Inference Handout PDF


3. Chapters 2-4: Mathematical Conventions for Writing Proofs
4. Chapters 2-4: Proof Tips
 

5. Chapter 5: Formats for Mathematical Induction
6. Chapter 5: Tromino Puzzle Solver


7. Chapter 6: Elementwise Set Proofs Handout V2 PDF
8. Chapter 6: Sample Power Set App
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9. Final (Wednesday, 12/14/2022, 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:
  • 1. Creating a LaTeX Document    2. Common Mathematical Notation
  • 3. Brackets, Tables, and Arrays    4. Creating Lists
  • 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
• LaTeX Editors:
  • 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
• LaTeX Distributions: Open-source distributions of LaTeX
  • Mac MacTex-TexLive:   Windows MikTex:    Linux TeXLive:

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

1. 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.

2. Number Theory

   • The Math Forum: Prime Numbers
   • The Prime Pages
   • New Twin Primes Found! 9/14/2016
   • The Great Internet Mersenne Prime Search (GIMPS)
   • The Twin Prime Conjecture    Recent Progress!
   • Summary of RSA Encryption    Details of RSA Encryption
   • Fermat's Last THeorem
   • The Riemann Hypothesis

3. Graph Theory Extras

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

4. 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.