Principles of Discrete Applied Mathematics

Recitations

REC #	RECITATIONS
1	Math Topics: Probability: Sample Spaces Writing Topics: Precision, Rigor, Formality Description: Work through the process of generating a rigorous proof of Problem 1 of Homework 1 (below) with emphasis on choosing an appropriate sample space.
	Pre-Recitation Assignment Read the Probability Theory (PDF) lecture notes Do Pre-recitation Assignment 1 (PDF)	Post-Recitation Assignment Write a proof: Do Problem 1 of Homework 1 (PDF)
2	Math Topics: Probability: Independence & Multiplication Writing Topics: Proof Rigor & Level of Detail Description: Discuss the proof in the pre‐recitation assignment and how it breaks down, with emphasis on the importance of independence and how the choice of notation obscures whether the events are independent.
	Pre-Recitation Assignment Do Problem 1(a) of Homework 2 (PDF)	Post-Recitation Assignment Correct the wrong proof: Do Problem 1(b) of Homework 2 (PDF)
3	Math Topics: Chernoff Bound Writing Topics: Explanatory and Guiding Text Description: Draw the logic of the proof of Chernoff bound, both to demonstrate that the flow of text may or may not match the flow of the underlying logic and to ensure understanding of the proof. Then discuss where the Chernoff bound lecture notes would benefit from additional guiding or explanatory text. “Guiding text” helps readers see the structure of the text or of the logic, while “explanatory text” helps readers understand or elaborates upon the logical argument.
	Pre-Recitation Assignment Do Pre-recitation Assignment 3 (PDF)	Post-Recitation Assignment Revise lecture notes: Do Problem 1 of Homework 3 (PDF) using these additional files chernoff.tex (TEX), ulem.sty (STY), xcolor.sty (STY)
4	Math Topics: None Writing Topics: Information Order and Connectivity (Cohesion) Description: Briefly summarize “The Science of Scientific Writing” by Gopen and Swan and use the worksheet (below) to solidify the ideas. Analyze Sample Proofs 1 and 2 (below), which are modified from the lecture notes to show how connectivity (cohesion) can be created by starting sentences with “old information that links backward” and using it to introduce the sentence’s important new information. Sketch the proof’s logic to demonstrate that although text is one-dimensional, it must communicate logic that is multidimensional. A sketch of the logic can provide ideas for how to approach this challenge. Worksheet: Improving Information Order and Connectivity (PDF) Sample Proofs 1 and 2 (PDF) Sketch of the Logic (PDF)
	Pre-Recitation Assignment Carefully read Sections 1 and 2 of the Generating Functions (PDF) lecture notes	Post-Recitation Assignment Do Homework 5 (PDF) using these additional files hw5.tex (TEX)
5	Review for Exam 1: Work through Practice Exam 1 (PDF)
6	Math Topics: Simplex and Linear Programming Practice Writing Topics: Although this recitation does not have an explicit communication topic, it models drawing-to-learn. Description: After reviewing some of the questions on the exam, work through a two-dimensional example of the simplex method while graphing each step to see how the simplex method can be understood visually.
	Pre-Recitation Assignment None	Post-Recitation Assignment Work on Homework 6 (PDF): Term paper assignment
7	Math Topics: None Writing Topics: Audiences, Explaining a Topic to an Informal Audience Description: Discuss how communication is affected by context, not only for MIT News articles, but in other contexts as well, including journal articles. Discuss how to explain generating functions, union bound, and the max flow / min cut theorem to a nontechnical audience.
	Pre-Recitation Assignment Do Pre-recitation Assignment 7 (PDF): Writing for your Audience	Post-Recitation Assignment Do Homework 7 (PDF): Write an MIT News style article
8	Math Topics: Linear Programming Duality Writing Topics: Designing Visuals Description: Discuss the meaning of the figure in the Pre-Recitation Assignment, its purpose, and how it could be revised to communicate more effectively.
	Pre-Recitation Assignment Before recitation, go over Section 4 (Dual) of the Network Flows (PDF) notes and observe the figure on page 6, which represents a dual solution to a maximum flow problem. Briefly, answer the following questions: - What is the purpose of the figure? - Why is this figure useful? What content does it convey effectively? - How could the figure be improved? What content does it fail to represent?	Post-Recitation Assignment None
9	Review for Exam 2: Work through Practice Exam 2 (PDF)
10	Math Topics: Euclid’s Algorithm & Number Theory Writing Topics: None Description: Work through Problems Related to Euclid’s Algorithm and Number Theory (PDF).
	Pre-Recitation Assignment None	Post-Recitation Assignment Revise the term paper as described in Problem 1 of Homework 9 (PDF)
11	Math Topics: Primality Testing & RSA Writing Topics: None Description: Work through problems related to fast modular exponentiation, primality testing, and Carmichael numbers.
	Pre-Recitation Assignment None	Post-Recitation Assignment None
12	Math Topics: None Writing Topics: Peer Critique Description: In small groups, students discuss their papers.
	Pre-Recitation Assignment Critique the term papers of two classmates as described in Homework 10 (PDF)	Post-Recitation Assignment Revise the term paper in part based on the peer critique, as described in Homework 6 (PDF)
13	Review for Exam 3: Work through Practice Exam 3 (PDF)