# Math 311w - Concepts of Discrete Mathematics

## Final exam

• Our final exam is Tuesday, 12:20 - 2:10 pm in Chemistry 102.
• Here are some extra practice problems
• I will have a question/answer session (where you are also welcome to work on problems) Sunday 1:30 - 3:30 in Sackett 107.
• I will have office hours Monday, 1:30 - 3:30.

## Introduction

This is the web page for section 5 of Math 311w taught by Tim Reluga in the autumn of 2018.

This course introduces students to the use of mathematics as a formal 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.

## Homework

• For 8/20 – Read Section 1.1.
• For 8/27 – Read Section 1.2.
• Practice homework: Section 1.2, problems 1-5,8,9,11,12
• Online pratice: A, B
• For 9/5 – Read Section 1.3
• For 9/10 – Read Section 1.4.
• Practice homework: Section 1.4, problems 1,2,3,5,6,7
• Extra problems for Section 1.4: A
• For 9/17 – Read Section 1.5.
• Practice homework: Section 1.5, problems 1-5
• For 9/24 – Read section 1.6.
• For 9/28
• 10/1 - Exam 1, in-class
• For 10/5 – 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 10/8 – Read section 3.2
• Practice homework: Section 3.2, all problems
• For 10/12 – Read section 2.1
• Practice homework: Section 2.1, problems 1,2,3,5,6,7,8,9.
• Extra problems A and B
• Show that the conjecture $$(a \cap b) \cup c = a \cap (b \cup c)$$ is true in general.
• Prove that $$A \cap (B \backslash C) = (A \backslash C ) \cap B$$.
• Prove that $$(A \cup B) \backslash C = (A \backslash C ) \cup (B \backslash C)$$.
• For 10/17 – Read section 2.2
• Practice homework: Section 2.2, problems 1,2,4,5,6,7,8,9.
• Extra problems A
• Using induction, prove that for any partition $$P$$ of a finite set $$S$$, the cardinality of $$S$$ is equal to the sum of the cardinalities of the elements of $$P$$.
• For 10/22 – 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.
• Sochi medal counts and retroactive update
• Construct an adjacency matrix for Pell’s relation, $$x \sim y$$ if and only if $$y^2 | (x^4 - 1)$$, on the positive integers up to 10 using a calculator.
• 11/2, second midterm in class
• For 11/9 – 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. solutions.
• Practice recognizing symmetry transformations.
• For 11/16 – Read section 5.1 on subgroups and order
• Practice homework: Section 5.1, problems 1, 3, 6-10
• For 11/30 – Read section 5.2 on Cosets, orbits, and Lagrange’s theorem
• Practice homework: Section 5.2, problems 1, 2, 3
• Our final exam is offered on Tuesday, December 11th, 12:20 - 2:10 in Chemistry 102.

## Essays

Information on our essays will be posted here.

## Past quizes

Past quizes, posted with their answers.