Navigation
- Back to Main Page.
- Back to the Lectures.
- Before the Lecture
- Related Problems
- In Class
- Outcomes
Before the Lecture
- Read Section 1.3 up to (and including) Proposition 1.34 on
pg. 40:
- Division algorithm: review how to do it by hand and careful with negative numbers! (Remainder is always non-negative!)
- Definition of prime and composite numbers.
- Skip algorithm on top of pg 39.
- Definition of divisibility and GCD.
- Watch the videos related to this section (after reading it):
- Long division with negatives.
- Proof of the following Basic Lemma: Suppose that $d \mid a$. Then $d \mid (a+b)$ iff $d \mid b$.
- 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: 1.50. |
| Extra Problems: 1.46(i) to (vii), 1.50. |
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:
- be able to perform long divisions (even with negatives);
- understand divisibility (Problem 1.46(i) to (v));
- be able to write simple proofs about divisibility (such as Problem 1.50);
- know what are prime and composite numbers and be able to distinguish them (for small numbers);
- know what the GCD is and how to compute it for small numbers (Problem 1.46(vi) and (vii)).