Quantitative Literacy Math 102 Fall 2004

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Quantitative Literacy Math 102Fall 2004

• Introduction
• Wednesday, August 25

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Contact Information

• Instructor Henjin Chi
• Office RO A-150
• Phone [phone]
• E-mail mathchi_at_isugw.indstate.edu
• Webpage math.indstate.edu/chi/ma102

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Textbook

• Mathematical Excursions, By Aufmann, Lockwood,
  Nation and Clegg.
• Houghton Mifflin Company.

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Syllabus

• We will cover the following sections from the
  textbook 1.1, 1.2, 1.3 2.1, 2.2, 2.3, 2.4, 2.5
  4.2, 4.3 5.2, 5.3 10.1, 10.2, 10.3, 10.4 11.1,
  11.2, 11.3, 11.4, 11.5, 11.6 12.1, 12.2, 12.3,
  12.4

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Exercises

• I will assign problems from the book (and maybe
  some additional ones) for each section we cover.
  These will be also posted on my website
  http//math.indstate.edu/chi/ma102. You are not
  expected to work all the exercises in the book,
  however you may wish to work these for additional
  practice. The assigned exercises should be worked
  after each class period.

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Grade

• Your overall grade will be based on a two-hour
  final exam, 3 one-hour exams, quizzes and
  Homeworks. The assigned point values are final
  200, exams 3 x 100, quizzes 10 pts each,
  homeworks 10 pts each. The overall grade should
  be approximately A90, B85, B80, C75,
  C70, D65, D60, F Below 60.

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Exams, quizzes and homeworks

• All the exams and quizzes will be taken during
  the recitations on Fridays. As a general rule,
  there will be a quiz each Friday, unless there is
  an exam scheduled. Exams date are 9/24, 10/22,
  and 12/3. Homework always due on Friday in
  recitation.

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Attendance

• You are expected to attend each class.
• If you happen to miss a class it is your
  responsibility to learn the material covered.
  Visit the website to learn what was covered in
  the class.

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Remember

• Make-Ups only given for the exams, under special
  circumstances, at a later date, and for
  verifiable emergencies.
• If you have questions you can always come to my
  office.
• Read through the material, prior to the class
  discussion.
• Do the assigned exercises the same day as the
  material is covered in class. Do at least the
  problems assigned. You can always ask me or your
  teaching assistant about the problems you could
  not solve.

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Assumed knowledge

• This is a general education course, i.e., this is
  a course designed for all ISU students. The
  students are not expected to be particularly
  mathematically skilled, but you should expect to
  be asked to do the following basic arithmetic
  operations, powers and square roots, work with
  fractions, use a scientific calculator.

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Chapter One

• Problem Solving

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1.1 Inductive and deductive reasoning

• Inductive reasoning is the process of reaching a
  general conclusion by examining specific
  examples. Example the sun will come out
  tomorrow
• Example Completing a sequence 3,6,9,12,15,
  
• 1,3,6,10,15,

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Inductive reasoning to make a conjecture

• Pick a number, multiply the number by 8, add 6 to
  the product, divide the sum by 2, and subtract
  3.
• 5, 8 x 5 40, 40 6 46, 46 / 2 23, 23 3
  20
• 6, 8 x 6 48, 48 6 54, 54 / 2 27, 27 3
  24
• 7, 8 x 7 56, 56 6 62, 62 / 2 31, 31 3
  28

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Conclusion based on inductive reasoning may be
incorrect!!!

• See the example involving the number of regions
  in a circle on page 6 on the textbook.

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Counterexample

• A statement is a true statement only if it is
  true in all cases. If you can find one case for
  which the statement is not true, it is called a
  counterexample, and the statement is not true.

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Find a counterexample

• x gt 0, for all numbers
• Square of x is always bigger than x itself.
• Square root of x squared is always equal to x.

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Solution

• x gt 0, for all numbers 2 gt 0, 4 gt 0, -4 gt
  0, but 0 0 which is not greater than 0.

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Solution

• Square of x is always bigger than x itself. 4
  squared is 16 gt 4, (-4) squared is 16 gt -4, but ½
  squared is 1/4 which is not bigger than ½.

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Find a counterexample

• square of 4 is 16, the square root of 16 is 4,
  but the square of -4 is 16 and the square root
  of 16 is 4 which is not equal to -4.

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Deductive reasoning

• Deductive reasoning is the process of reaching a
  conclusion by applying general assumptions,
  procedures, or principles.

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Example of deductive reasoning

• Pick a number, multiply by 8, add 6, divide by 2,
  subtract 3. Conjecture one will get a 4 multiple
  of the original number. Deductive reason n, 8n,
  8n6, (8n6)/2 4n3, (4n3) 3 4n So it will
  always be true!

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Homework for Section 1.1

• Page 12 1 10, 11, 13, 14, 15, 17 22, 25,
  27, 28, 31, 32, 33, 35, 37, 38, 41

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1.2 Problem solving with patterns

• Read the textbook on this section. You should
  learn the terms sequence, n-th term of a
  sequence, first differences, second differences,
  third differences, Fibonacci sequence.

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Exercises for Section 1.2

• Page 23 1, 2, 4, 7, 8, 10, 11, 13, 14, 17, 18,
  20, 21, 27, 28

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1.3 Polyas problem-solving strategy

• Understand the problem
• Devise a plan
• Carry out the plan
• Review the solution
• Read the detailed suggestions on pages 28 and 29,
  and read the solved Example 4 on page 32.

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End of chapter suggestions.

• Read your notes before your class on Friday
• Try the recommended exercises
• Prepare questions for your TA
• Try the review exercises on p. 43