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

  1. Chapter 0: Worksheet 0: Recognizing Common Algebra Errors PDF    Solution
  2. Chapter 1: Logic Puzzle Worksheet V1  
  3. Chapter 1: Rules Of Inference Handout PDF
  4. Chapter 1: Online Logic Quizzes and Puzzles

  5. Chapters 2-4: Worksheet 03: Quantifiers V1  
  6. Chapters 2-4: Mathematical Conventions for Writing Proofs
  7. Chapters 2-4: Proof Tips
  8. Chapters 2-4: Worksheet 04: Methods of Proof V1    

  9. Chapter 5: Formats for Mathematical Induction
  10. Chapter 5: Worksheet 05: Mathematical Induction V2 
  11. Chapter 5: Tromino Puzzle Solver

  12. Chapter 6: Elementwise Set Proofs Handout V2 PDF
  13. Chapter 6: Sample Power Set App
  14. Chapter 6: Online Venn Diagram Puzzles and Games:
  15. Chapter 6: Partitions and Bell Numbers

  16. Quiz Solutions
  17. Exam Review Sheets and Solutions:
  18. Final (Monday, 12/13/2021, 11:30 AM – 2:30 PM):

LaTeX

Markdown

Mobile Scanning Apps

Resources

  1. Logic Extras

  2. Number Theory

  3. Graph Theory Extras

  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.