Math 311w - Concepts of Discrete Mathematics

Final grades are now posted. I am in my office Friday, 1-3 pm if you want to pick up your exam before break. Otherwise, you are welcome to pick it up after break.

This is the web page for section 4 of Math 311w taught by Tim Reluga in the autumn of 2017.

This course introduces students to the use of mathematics as language. Using a theorem-proof framework much like that used in Euclid’s geometry textbook millenia ago, we will study elementary number theory advances from ancient times to our current technological age. Theories of modular arithmetic, set theory, formal logic, groups, and other discrete-math topics will be covered, with applications to encryption and digital information encoding. The course will include several writing assignments to help students develop their communications skills.

Course syllabus, including class data, contact information, office hours, and grading policies (subject to change)

Textbook and partial solutions courtesy of Gary Mullen.

Essays

Information on our weekly essays

Homework

• For 8/21 – Read Section 1.1.
• For 8/28 – Read Section 1.2.
• Practice homework: Section 1.2, problems 1-5,8,9,11,12
• Online pratice: A, B
• For 9/6 – Read Section 1.3
• For 9/11 – Read Section 1.4.
• Practice homework: Section 1.4, problems 1,2,3,5,6,7
• Extra problems for Section 1.4: A
• For 9/18 – Read Section 1.5.
• Practice homework: Section 1.5, problems 1-5
• For 9/25 – Read section 1.6.
• 9/29 - Exam 1, in-class
• For 10/4
• For 10/6 – Read section 3.1
• Practice homework: Section 3.1, problems 1,2,3,4
• Online pratice: A, B, C
• More pratice: Making truth-tables, Translating truth-tables
• A handout on common logic rules.
• Use deduction to prove (p → r) ∧ (q → r) = (p ∨ q) → r .
• Use deduction to prove ((p → q) ∧ (q → r)) → (p → r) . (A solution)
• For 10/9 – Read section 3.2
• Practice homework: Section 3.2, all problems
• For 10/13 – Read section 2.1
• Practice homework: Section 2.1, problems 1,2,3,5,6,7,8,9.
• Extra problems A and B
• For 10/18 – Read section 2.2
• Practice homework: Section 2.2, problems 1,2,4,5,6,7,8,9.
• Extra problems A
• For 10/23 – Read section 2.3
• Practice homework: Section 2.3, problems 1,2,3,4,6,7,9
• these extra problems, updated to include partial answers.
• 11/3, second midterm in class
• For 11/10 – Read section 4.3, Groups
• Practice homework: Section 4.3, problems 1-8
• Practice completing group multiplication tables and answers
• Practice counting objects based on symmetries.
• Practice recognizing symmetry transformations.
• For 11/17 – Read section 5.1 on subgroups and order
• Practice homework: Section 5.1, problems 1, 3, 6-10
• For 12/1 – Read section 5.2 on Cosets, orbits, and Lagrange’s theorem
• Practice homework: Section 5.2, problems 1, 2, 3
• 12/12(Tuesday), 8 am - 9:50, final exam will be in Willard room 73.