Category: Lessons

Lesson 26 Handout – Strong Induction examples

Theorem NT 5.1: Every natural number n>1 is either prime or divisible by a prime.

Theorem NT 5.2: Suppose p is prime and a_{1}, a_{2}, a_{3}, \ldots, a_{n} are n integers, where n \geq 2. If p \mid a_{1} \cdot a_{2} \cdot a_{3} \cdot \ldots \cdot a_{n}, then p \mid a_{i} for at least one of the a_{i}(1 \leq i \leq n).

Theorem NT 5.3: If n is an integer greater than 1 then n can be written as a product of primes.
(HINT: Prove using strong induction. Consider two cases, when k+1 is prime, and when it is composite)

Lesson 8: Negating Statements, Counting Lists

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class.

Lesson 8: Negating Statements, Counting Lists

Topic. This lesson covers:

  1. Sec 2.10 Negating Statements
  2. Sec 3.1 Counting Lists
  3. Sec 3.2 Factorials

Learning Outcomes.

  • Apply rules for negating various types of statements, both in formal logic and natural language
  • Count collections of lists with various properties

Homework. There is one WeBWorK assignment on today’s material (Note: some of the material in this assignment will be covered in the next lesson):

  1. WeBWorK: WeBWorK Assignment5-Sec3.1-3.4

Lecture Notes:

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Lesson 4: Indexed Sets

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class.

Lesson 4: Indexed Sets

Topic. This lesson covers:

  • Sec 1.8: Indexed Sets

Learning Outcomes.

  • Take unions and intersections of collections of sets indexed by the natural numbers or other sets.

Homework. There is 1 written assignment on today’s material:

  1. Homework: Section 1.8 p.29: 3, 5, 6, 8

Lecture Notes:

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Lesson 2: Cartesian Products and Subsets

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class.

Lesson 2: Cartesian Products and Subsets

Topic. This lesson covers:

  • Sec 1.2: Cartesian Products
  • Sec 1.3: Subsets

Learning Outcomes.

  • Identify and manipulate ordered pairs and Cartesian products of sets.
  • Identify and manipulate subsets of sets.

WeBWorK. There is 1 WeBWorK assignment on today’s material:

  1. Assignment1-Sec1.2-1.3

Lecture Notes:

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