## Before the Lecture

• Carefully read our Course Web Site.
• Check the course areas in Blackboard. Please subscribe to all Forums: Course Structure, Math Related, Computer Related and Feedback.
• Create an account at SageMathCloud. You should have received an invitation to collaborate in the "Math 506 - Summer 2015" project that I've created. You don't need to worry much about it for now, but watch the videos I've posted to see how it works.
• Watch the videos on:
• Introduction to SageMathCloud: here I show a little about LaTeX and the use of SageMathCloud.
• Optional (but recommended): You can watch these videos on What is Algebra?, where I give a brief answer to the question, and on Algebraic Structures (made for Math 457), which goes over a few topics we will cover, but many others that we won't. I think these make a good introduction to our course.
• Quickly check sections 1.1, 1.2 and 2.1 from the book. (You can leave 2.1 for later, perhaps.) You basically have to remember the basics of: complex numbers (Section 1.2), matrices (see, for instance, the Wikipedia entry), induction (see Section 1.1), binomial theorem (see Section 1.1) and functions (including one-to-one, onto and invertibles functions -- Section 2.1). Don't spend too much time here! You can always come back as you need it.
• On induction, you can check this lecture from my 504 course. In particular, you can watch some videos with examples.
• Write down all questions about the above topics to bring to our (online) lecture. You can also type them, ahead of time, in the file "Questions.tex" (a LaTeX file) in SageMathCloud (under the "Math 506 - Summer 2015" project). You might see others questions in there (everyone will use the same file).
• Check if you are prepared for our lecture with Blackboard Collaborate.
• Optional: Post an introduction on Blackboard.

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## Related Problems

• None!

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## In Class

In class:

• We will get used to Blackboard Collaborate interface and functionality.
• I will discuss the use of SageMathCloud.
• I will answer any other questions.
• We will talk a little about LaTeX.

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## Outcomes

After the assignment (before class) and class:

• You should understand how the course will be run.
• You should be (mostly) comfortable with Blackboard Learn (where you post feedback, answer surveys, etc.) and Collaborate (where we have our lectures and office hours).
• You should (from the reading):
• Know how to compute with complex numbers and matrices.
• Know basic concepts of functions, such as one-to-one, onto, invertible and inverses.
• Know the formula (and how to use it) from the Binomial Theorem: $(a+b)^n = \sum_{i=0}^n \binom{n}{i} a^i b^{n-i}.$
• Know how to do simple proofs with induction.

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