Illinois State University Mathematics Department

MAT 409: Topics in Algebra and Combinatorics for K-8 Teachers

Dr. Roger Day (day@ilstu.edu)





Session 1 (actual): 16 January 2018



Combinatorics in the Real World
  • Acquaintances?
  • A high school teacher's discovery (text: p 6)
  • Testing Positive . . . What Does That Mean?
    • Three Facts to Consider
      • Approximately one-half of 1% of the US population ages 13 and older is HIV infected.    
      • One version of an HIV test yields 1.5% false positives (test is positive, but in reality the person tested is not HIV infected) and 0.3% false negatives (test is negative, but in reality the person tested is  HIV infected)
    • A person from the general US population tests positive for HIV infection. What's the probability the person actually is HIV infected?


The Pigeonhole Principle
  • An Initial Problem
  • Generalizing the Principle
  • A Concluding Problem


Course Information



Assignment #1

Read

  • Preface (pp 1-4)
  • Chapter 1 (pp 6-12)
  • Chapter 2 Section 1 (pp 15-20)
  • Learning from Others (pp 23-25)
  • Chapter 2 Section 2 (pp 26-27)
  • Chapter 2 Section 3 (pp 30-34)

Problems

  • Chapter 2 Section 1 (pp 20-22): 2,4,6,8,10,12,one of 15-17

Early Send-Ins

  • By 9:32 pm next Sunday night (Sun 1/21/18), email to me (day@ilstu.edu; write MAT 409 Assignment #1 as subject line) your responses to:
    • Ch 2 Section 1 (pp 20-21): one of 2, 4, or 6; one of 8 or 10
    • Ch 2 Section 1 Learning From Others (pp 23-25): Provide responses for three prompts, including for Solutions #1-#4 (prompt on p 23), for Solution #5 (prompt on p 24), and for Solution #6 (prompt on p 25)