Introduction to Discrete Mathematics

Course Description and Grading Breakdown

The material covered in this term will include an introduction to mathematical logic, including propositional and predicate (or first-order) calculus.  We will discuss the syntax and semantics of formal languages, formal proofs, and the Gödel Completeness and Incompleteness Theorems.

There are no prerequisites for this course.

There will be no final exams. The grade will be based on 6 written assignments consisting of three questions each. Each question is worth 10 points.

Course Meeting Time and Location
Tuesday and Thursday
1:00 - 2:25 pm
B122 Gates Chemical Laboratory (GCL, Building #26)

Course Instructor Contact Information and Office Hours
210-1 Math Building (Building 15)

TA Contact Information and Office Hours
1-G Math Building
Office hours: Sundays 4 - 5 PM in 107 Downs Laboratory (Building 47)

Course Schedule and Textbook

There will be no official textbook.  The lectures will follow notes that will be posted here.

 April 3, 2018    
 April 5, 2018   
 April 10, 2018     
 April 12, 2018
 April 17, 2018  
 April 19, 2018    
 April 24, 2018
 April 26, 2018
 May 1, 2018
 May 3, 2018
 May 8, 2018 
 May 10, 2018 
 May 15, 2018 
 May 17, 2018
 May 22, 2018

Interested students can consult the following books:

Enderton, A mathematical introduction to logic. Second Edition (2001)

Shoenfield, Mathematical logic. Second Edition (2001)

Manin, A course in mathematical logic for mathematicians. Second Edition (2010)

The following is a book containing a wealth of examples of proofs by induction taken from a variety of mathematical subjects, and aimed at undergraduate students:

David Gunderson, Handbook of Mathematical Induction, CRC Press, 2011

Course Policies

  • Please staple a blank page containing only your name at the front of the assignment.
  • You are encouraged to work in groups on the assignments. However, you are required to write your solution on your own and not to look at written solutions of other students.

 Date PostedAssignment Due Date  Solutions
   April 6
 April 23
  April 17 April 30       
  May 1
 May 14
  May 8
 May 21
 May 22 May 28
 May 22 June 4

Midterm and Final Exam

Collaboration Table
You may consult: 
Course textbook (including answers in the back)YES
Other booksYES
Solution manualsNO
Your notes (taken in class)YES
Class notes of othersYES
Your hand copies of class notes of othersYES
Photocopies of class notes of othersYES
Electronic copies of class notes of othersYES
Course handoutsYES
Your returned homework / examsYES
Solutions to homework / exams (posted on webpage)YES
Homework / exams of previous yearsNO
Solutions to homework / exams of previous yearsNO
Emails from TAsYES
You may:
Discuss problems with othersYES
Look at communal materials while writing up solutionsYES
Look at individual written work of othersNO
Post about problems onlineNO
For computational aids, you may use:

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.