Lecture Notes: Typesetting with LaTeX

Preliminaries

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Course Content

Review

Question: Imagine a classroom has 4 tables and 11 students. What is the minimum number of students at the most crowded table?

Solution: Three students. \( \mid S \mid = 11 \), \( \mid T \mid = 4 \) and \( f: S \rightarrow T \) maps students to tables.
\( \mid S \mid > 1 \cdot \mid T \mid \),
\( \mid S \mid > 2 \cdot \mid T \mid \),
\( \mid S \mid \not> 3 \cdot \mid T \mid \).

Question: Using a basic calculator, find the prime decomposition of 13,475.

Solution:

• Attempt division by increasing numbers: 2, 3, 4, 5
• 5 works, so divide until it doesn’t:
  • 13,475/5 = 2,695
  • 2,695/5 = 539
• Attempt division by increasing numbers: 6, 7
• 7 works, so divide until it doesn’t:
  • 539/7 = 77
  • 77/7 = 11
• Attempt division by increasing numbers: 8, 9, 10, 11
• Only 11 worked, so 11 is prime.

Prime decomposition: \( 13475 = 5^2 \cdot 7^2 \cdot 11 \)

Finish Pigeonhole Principle

Finish the pigeonhole principle lecture.

LaTeX Overview

• All written assignments must be submitted as PDFs typeset with LaTeX
• I highly recommend that you hand write your solutions first, before typesetting, because it is easier to think when hand writing.
• I require LaTeX because it ensures your submission is legible. Other courses also require LaTeX. Learning LaTeX is a valuable learning goal: LaTeX is essential for communicating mathematics digitally.
• Slides

Activity

• Guide students through opening the written assignment on Overleaf
• For the remainder of class, typeset your solutions to the first written assignment