The first question from the class was concerning the topics that will be covered on the test. I told the class that they should expect the following three broad areas to be on the exam:
- Graph theory
- Cryptography
- Modular arithmetic and congruences
Students asked to go through examples for cryptography first. I said that simple ciphering may be included and more difficult problems would delve into the Diffie-Hellman exchange. We walked through a Diffie-Hellman exchange and I provided examples of what might be asked on the exam.
Next we dove into modular arithmetic and congruences. I told the class I would expect students to be able to determine if two integers were congruent mod a given value. I also thought students should be able to write congruence statements for a word problem. More difficult problems would involve solving a system of linear congruences or proving relationships. For modular arithmetic, I might ask them to construct an addition and multiplication table, perform arithmetic for values, or correct a table of addition and multiplication that contained mistakes.
For graph theory, students are expected to be able to draw simple graphs for given criteria (number of edges, vertices, and degrees of vertices), determine if an Euler path or Euler circuit exists for a graph, and prove certain simple properties.
Students felt comfortable with the topic coverage. I allow students to use notes and told the class they should spend some time before the exam going through their notes and making sure they are in good order.
Visit the class summary for a student's perspective and to view the lesson slide.
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