CS311H Discrete Mathematics for Computer Science

Tuesday, August 25

Introduction to CS311H

Readings

• None

Videos

• None

Thursday, August 27

Propositional Logic

Readings

• Rosen Ch 1 Sections 1.1, 1.2

Videos

• Building Blocks of Boolean Logic
• Logical Operators
• Truth Tables
• Implication
• Necessary and Sufficient Conditions
• Biconditional Operator
• Precedence of Logical Operators

Postcondition

• the symbols
• the different ways these operators show up in the English language
• the truth tables
• operator precedence

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Tuesday, September 1

Propositional Logic and Proofs

Readings

• Rosen Ch 1 Sections 1.6.1 through 1.6.6

Videos

• What is a Proof?
• Proof Using Truth Tables
• Equivalence-Style Proofs
• Argument Form
• Rules of Inference
• Natural Deduction Proof (Proof using Rules of Inference)

Postcondition

After the readings/videos, you must know how to

• Prove a theorem using truth tables.
• Prove a theorem using equivalence-style proof.
• Prove a theorem using the rules of inference.
• operator precedence

Thursday, September 3

First-Order Logic

Readings

• Rosen Ch 1 Sections 1.4 and 1.5

Videos

• Predicates
• Quantifiers
• Universal Quantifier
• Existential Quantifier
• Exactly One

Tuesday, September 8

First-Order Logic Proofs

For this lecture, please go through both readings and videos. The videos talk about some nuances of quantifiers.

Readings

• FREGE by Elain Rich and Alan Cline.
  Chapter 5 pages 1-9 and 21-47.

Videos

• Logical Representation - Part I: Combining Quantifiers
• Logical Representation - Part II: More Practice
• Proof by Counterexample

Postcondition

After doing the readings and watching the videos, you must know

• when the order of nested quantifiers matter.
• why the order of nested quantifiers matter.
• how to use universal instatiation and generalization.
• how to use existential instatiation and generalization.
• how to use instantiate and generalize nested quantifiers.

Thursday, September 10

Proof Methods and Techniques

Readings

• The Book of Proofs Chapter 4

Videos

• None

Postcondition

Tuesday, September 15

Proof Methods and Techniques (contd.)

Readings

• The Book of Proofs Ch 5, 6, 7.
• (OR) Rosen Chapter 1.7, 1.8.

Videos

• No videos.

Postcondition

After doing either of the readings, you must know

• Develop a proof using indirect proof techniques such as proof by contrapositive and proof by contradiction.
• Recognize and develop a proof for theorems that are biconditional in nature.
• Recognize and develop a constructive existence proof.
• Recognize a non-constructive existence proof.
• Recognize and develop a uniqueness proof.

Thursday, September 17

Number Theory

Readings

Videos

Tuesday, September 22

Sets

Readings

• Rosen Ch 2 Sections 2.1 and 2.2

Videos

• Definition of Equal Sets, Empty Set, and Singleton Set
• Cardinality of a Set and Power Set
• Union of Sets
• Intersection of Sets
• Disjoint Sets
• Difference of Sets
• Complement of a Set
• Set Identities
• Generalized Union and Intersection of Sets

Postcondition

After doing the readings or watching the videos, you must be able to

• Identify sets.
• Represent sets in roster and set-builder form and convert between the two.
• Given specific sets, identify if a set is a subset (or proper subset) of another set.
• Differentiate the difference between a subset and proper subset.
• List the elements in the intersection of sets, union of sets, difference of sets, and the complement of a set.
• Construct a power set of a set.

Thursday, September 24

Sets

Readings

Videos