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18.200 | Spring 2024 | Undergraduate

# Principles of Discrete Applied Mathematics

REC # | RECITATIONS
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1 | Math Topics: Strategies for becoming unstuck when proving something. Writing Topics: The role of proof, norms of proof writing, proof generation strategies. Description: For the statements in Homework 1 Problem 1, practice choosing a proof strategy and generating a proof. Recitation begins with a summary of the role of proof in the doing of mathematics, illustrated by the Mathematics Reasoning Diagram (PDF).
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: Precision, Rigor, & Formality Description: Discuss the proof in the pre‐recitation assignment and how it breaks down, with emphasis on the importance of independence and how the proof obscures whether the events are independent. Practice with additional wrong proofs (PDF).
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: None Writing Topics: Using Known-to-New structure to craft text that flows well Description: Learn how to order information to help readers follow the flow of logic, practicing on a sample proof whose flow can be improved. Known-to-New Structure (PDF)
Pre-Recitation Assignment Do Pre-recitation Assignment 3 (PDF) | Post-Recitation Assignment Revise lecture notes: Do Problem 1 of using these additional files , ,
4 | Math Topics: None Writing Topics: Genre/Rhetorical analysis Description: Learn how to write in a new genre by analyzing its features, such as citations. Practice on the article and lecture note from the pre-recitation assignment, comparing them. Known-to-New Structure (PDF)
Pre-Recitation Assignment Carefully read Sections 1 and 2 of the lecture notes | Post-Recitation Assignment Do using these additional files
5 | Math Topics: Quiz review Writing Topics: None Description: Review math topics that will be on the quiz and practice quiz problems, based on student preferences.
Pre-Recitation Assignment Carefully | Post-Recitation Assignment Do using these additional files
6 | Math Topics: Probabalistic method and Chernoff bound Writing Topics: Meaning guiding text, global Known-to-New structure, and revising for economy Description: Learn to write text that meaningfully guides readers through logic, while helping them to see connections across the text; and learn to revise drafts for economy. Practice on the proof assigned for the homework. Economical Guiding Text (PDF)
Pre-Recitation Assignment None | Post-Recitation Assignment Work on : Term paper assignment
7 | Math Topics: Chernoff bound Writing Topics: Drawing the logic of a proof to better understand it at a detail level; drafting guiding text to better understand the proof at a higher level, choosing how to order logic when writing up a proof. Description: After identifying points of confusion in the pre-recitation assignment lecture notes, draw the logic of the Chernoff bound proof, labeling the arrows with guiding text explaining the logic, including at the identified points of confusion. Discuss how the structure of the drawing relates to the structure of the written proof.
Pre-Recitation Assignment Do : Writing for your Audience | Post-Recitation Assignment Do : Write an MIT News style article
8 | Math Topics: Linear Programming Writing Topics: Drawing to learn Description: Prove that the given linear program yields the shortest bath between two nodes of a graph, and draw a figure to understand why. Write the dual linear program and prove that it too finds the shortest path.
Pre-Recitation Assignment Before recitation, go over Section 4 (Dual) of the 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 | Math Topics: Quiz review Writing Topics: None Description: Review problems in Practice Quiz (PDF).
Pre-Recitation Assignment None | Post-Recitation Assignment Revise the term paper as described in Problem 1 of
10 | Math Topics: Post-quiz review Writing Topics: None Description: Address student questions about any material so far, including questions they had trouble with on Quiz 2 (PDF).
Pre-Recitation Assignment None | Post-Recitation Assignment Revise the term paper as described in Problem 1 of
11 | Math Topics: Huffman Coding Writing Topics: Figure Design and Creation Description: Learn when figures are useful and visual design choices for crafting effective figures. These choices depend on the purpose of the figure. Practice by designing a figure to communicate Huffman Coding, and a proof of the Kraft Inequality. Learn tools for creating figures and how to integrate figures with text. Designing Figures for Communicating in Mathematics (PDF)
Pre-Recitation Assignment None | Post-Recitation Assignment None
12 | Math Topics: Term paper problems Writing Topics: Peer review Description: After a brief discussion of giving effective peer review and acknowledging help from peers with sample acknowledgements (PDF), students provide in-person feedback to each other on their drafts.
Pre-Recitation Assignment Critique the term papers of two classmates as described in | Post-Recitation Assignment Revise the term paper in part based on the peer critique, as described in
13 | Math Topics: Quiz review Writing Topics: None Description: Review math topics that will be on the quiz and practice quiz problems, based on student preferences.
Pre-Recitation Assignment Critique the term papers of two classmates as described in | Post-Recitation Assignment Revise the term paper in part based on the peer critique, as described in

## Course Info

##### Instructors

- Prof. Ankur Moitra
- Prof. Peter Shor
- Susan Ruff

##### Departments

- Mathematics

##### As Taught In

Spring 2024

##### Level

Undergraduate

##### Topics

- Mathematics
  - Applied Mathematics
  - Discrete Mathematics
  - Probability and Statistics
- Social Science
  - Communication

##### Learning Resource Types

theaters Lecture Videos
notes Lecture Notes
assignment Problem Sets
Editable Files

Browse Resources

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