Lecture 3

Navigation

• Back to Main Page.
• Back to the Lectures.
• Before the Lecture
• Related Problems
• In Class
• Outcomes

Before the Lecture

• Read the rest of Section 1.3:
  • Euclid's Lemma (Theorem 1.38).
  • Skip Proposition 1.42.
  • $\sqrt{2}$ is irrational.
  • Extended Euclidean Algorithm.
  • Skip Proposition 1.46.
  • $b$-adic digits (representation on base $b$) and applications on divisibility criteria.
• Watch the videos related to this section (after reading it):
  • Euclid's Lemma.
  • Example of the Extended Euclidean Algorithm.
  • \(b\)-adic representation (1.53 with \(b=4\)).
  • Problems: 1.46(ix), (x), 1.60.
  • A few words about Example 1.49.
  • Computations in Sage.
• Write down all questions about the above topics to bring to our (online) lecture. (You can also type them in the file "Questions.tex" in SageMathCloud.) Comments about the videos are welcome!
• Work on the assigned problems for these sections. (See Related Problems below.) You don't need to finish them, but try to work on as many as you can and the bring your questions to class.

 

Related Problems

The "turn in" problems are due on 06/09 by 11:59pm.

Section 1.3:	Turn in: 1.46(vii), 1.53 with $b=3$, 1.55(i).
	Extra Problems: 1.46(viii) to (x), 1.52, 1.53, 1.55, 1.57.

 

In Class

In class:

• We will discuss the reading and pace.
• I will discuss the main points.
• I will answer questions about the sections covered.
• I will answer any other questions.
• We can work on the HW problems.

 

Outcomes

After the assignment (reading and videos before class) and class, you should:

• know how to compute GCD of large numbers and how to write it as linear combination of the given numbers (Extended Euclidean Algorithm or Bezout's Theorem - Problem 1.55);
• be able to use the fact that the GCD is a linear combination of the numbers in simple proofs (Problem 1.57);
• know how to express numbers in different bases (Problem 1.53) and use it (Problem 1.52).