Transition to Advanced Mathematics

Office Hours

Room 443, in the DMF Center for Science and Mathematics (near the Rondileau Campus Center).

• Monday 5:00-6:00, Tuesday 11:00-12:00, and Friday 3:00-4:00

You can also drop in and ask me a question: Any time you find me in my office (DMF 443)

Syllabus

• The Syllabus for Math 180. This is your source for course pacing, grading, and some helpful hints on group work and studying.
  
  
• You can access the online homework system via a link on the course page at http://blackboard.bridgew.edu.
  
  

Required Course Textbook:

• Book Of Proof, Second Edition, by Richard Hammack.
  Click Here to download a free PDF copy of the book.
  
  
• "A Semiformal Introduction to Formal Mathematics", by Dr. Ward Heilman.
  • Part 1: Logic

1. Statements, Truth Tables, and Logical Equivalence

• Worksheet - Exploring Statements
• Worksheet - Compount Sentences and Truth Tables and Solutions
• Worksheet - Introducing Implications
• Worksheet - Logical Equivalence and Solutions

You can also find a number of helpful videos at ProofSpace at SUNY Geneseo

• 1.1 - An Introduction to Logic and Proof
• 1.2 - Conditional Statements
• 1.4 - Logical Equivalences

2. Negating Statements

• Worksheet - Simplifying Negations and Solutions

3. Valid Arguments

• Worksheet - Valid Deductions and Solutions
• Flashcards - Syntactic Deductions

4. Quantifiers

You also can find a number of helpful videos at ProofSpace at SUNY Geneseo

• 1.5 - Quantifiers

5. Sets

• Worksheet - Introducing Sets and Solutions
• Flashcards - Set Notation
• Worksheet - Proofs about Subsets, Venn Diagrams, and Counting Sets and Solutions

6. Functions and Relations

• Worksheet - Relations and Solutions
• Worksheet - Functions

7. Proving Statements about Integers

• Worksheet - Mathematical Knowledge and Exploring Definitions
• Worksheet - Exploring versus Proving Implications and Solutions

8. Techniques of Proof

• Worksheet - Combining Proof Methods and Solutions
• Worksheet - Proof By Contradiction And Mixed Rules and Solutions
• Worksheet - Recursion and Induction and Solutions

Additional Resource: ProofSpace

You can find a large number of helpful videos at ProofSpace at SUNY Geneseo

• 1.1 - An Introduction to Logic and Proof
• 1.2 - Conditional Statements
• 1.4 - Logical Equivalences
• 1.5 - Quantifiers

• 2.1 - Direct Proofs
• 2.3 - Proof By Cases
• 2.2a - Proof By Contrapositive
• 2.2b - Proof By Contradiction
• 2.4 Proof By Induction

Reading for Further Exploration

• A Friendly Introduction to Mathematical Logic, Second Edition
  by Christopher C. Leary and Lars Kristiansen.
  
  In Math 180, we have focused on laying a practical foundation for mathematics and mathematical arguments.
  A Friendly Introduction to Mathematical Logic explores both the power and the limitations of this kind of formal mathematical thinking.