Finite Lessons at Notre Dame

Go on to page two for Lesson 16 Nov 18 Click Here

Sept 25 Lesson 1

Openning introductory remarks with procedures and expectations
Permutations, Ordered Samples, Fundamental Principle of Counting, & Rule of Sum
Determining the sample space S(n) of various situations.
Sampling with and without replacement.
Sampling events that consist of or have repeats
The Factorial
Development of a P(n,r) formula and its use in permutation problems
Remember that the formula will not handle all situations directly but must be tempered with some common sense.
No assigned work; texts not available but make sure you can get one on Monday

Sept 30 Lesson 2

Permutations of distinct objects; selecting a given number of objects from a group in which order of selection is important. Objects arranged in a circle.
Algebraically working with the permutation formula.
Introduction to Venn diagrams and Set Theory
Homework:
1. Page 8 #1
2. Page 9 # 2, 4, 5, 7, 8
3. Page 10 #11, 14
4. Page 12 # 2, 3 a, c, d
5. Page 13 # 6, 7, 8

Oct 2 Lesson 3

More Venn digrams
Combinations: how are they different from permutations.
The combination formula C(n,r) or nCr
Examples and problems involving combinations
Homework: Permutations
1. Page 18 # 3, 4, 8, 10
2. Page 19 # 12, 14, 15
3. Page 22 & 23 # 4, 5, 8, 12, 13
4. Page 25 & 26 # 7, 8, 11, 14
Homework: Set Theory & Venn Diagrams
1. Page 39, 40 & 41 # 4, 7, 11, 12, 15
2. Page 59, 60 & 61 #1, 4, 7, 8, 9, 11
Homework: Combinations
1. Page 46, 47 & 48 # 3 (a, c, g, h, k), 6, 8, 12, 14, 16, 19, 20, 23
2. Page 52, 53, & 54 # 5, 7, 8, 10, 14, 15, 18, 24, 25

In class work diligently without wasting time on these questions.

Test on these first two chapter will be next Wednesday Oct 9
If you can do the above questions you should have no trouble!

Oct 7 Lesson 4

Makin' sure you are ready for Wednesday's test
Ask for help for any required question
Introduction to Pascal's Triangle and the Binomial Theorem

Homework based on Pascal's Triangle

Page 80 to 83 # 2, 3, 6, 8, 9, 11, 15
Page 89 to 91 # 1, 2, 6, 7, 8

Oct 9 Lesson 5

Test on chapters 1 & 2 Should take about ½ the period. Binomial Theorem to follow the test.
Homework based on the Binomial Theorem
Introduction to sigma notation and series, how to convert a series into sigma notation and visa versa. JUst started this, more to follow.

Page 95, 96 # 1, 2, 3, 4, these are very introductory
#5 a, e, 6 a, d, 8 a, 9, 13
Page 99 & 100 # 1, 2, 4, 5 a, d, e, f, 8, 9

Oct 15 Lesson 6

Independent study day; homework assignment provide; see below
Bring you questions one Wednesday

Page 105 # 5, 7
Page 106; the review exercise
# 2, 6, 7, 8, 12, 14, 15, 20, 22, 24, 27

Oct 16 Lesson 7

Next test is on chapters 3 & 4 only, coming up within a week. I'm lookin' at Oct 23
Sigma notation and numerical series.
Introduction to Finite Series : Arithmetic and Geometric
You must be able to deal with

sigma notation & its accompanying algebra (Page 120 to 124)
Arithmetic Series Page 126
Geometric Series Page 129
The combination; Arithmetic-geometric series Page 132
The Infinite Geometric Series Page 135
Problem Solving using series Page 140
Telescoping Sums Page 145

The theorey of these topics is short and sweet; its being able to do the problems thats the real issue
I wish to cover all of this today with some serious review next day before the test

Page 124, 125 & 126 # 2, 4d, 5b, 5d, 6 a,b,c,g,h,i, 7, 9, 15
Page 131 etc: # 2, 3, 4, 6, 7, 8, 9, 13
Page 134 # 1, 2, 3
Page 138 # 3, 4, 11
Page 143 etc # 1, 4, 5
Page 148 # 1, 2, 3,

Oct 21 Lesson 8

Review & take up assigned problems
If this becomes a waste of time then its on the Chapter Five ==> Probability
Introduction to Probability Page 168
Event space versus total sample space ==> the key to probability
Definition terms discussed; Venn diagrams and sample space versus event space, intersection and union sets

Problems assigned from text as must be able to do

Oct 23 Lesson 9

Study and prepare for test #2 Chapters 3 & 4; Binomial theorem, Pascal's triangle with its associated patterns and Series, don't forget sigma notation
Probability continued;

Counting the Outcomes: the tree digram
permutation or combination?
Mutually exlusive events

Probability questions, Chapter 5

Page 173 etc # 1, 3, 6, 7, 8, 9
Page 180 etc # 2, 3, 5, 7, 10, 12, 13, 15
Page 187 etc # 1, 2, 3, 4

Oct 28 Lesson 10

Second test; at the start of the period, then continuation of Probability
Conditional probability

Page 193 # 1, 2, 3, 4, 6

Oct 30 Lesson 11

Independent Events
Odds and wagering
Stochastic process

Page 197 etc #1, 2, 3, 4, 6, 7, 9, 11
Page 203 etc #1, 2, 3, 6, 7, 9, 10, 15
Page 211 etc #1, 2, 3, 6, 7

Nov 4 Lesson 12

Introduction to Probaility Models: Probility distributions
Discrete random variables, expected value, expectation
Uniform distributions
Binomial distribution and Bernoulli trails

Page 228 etc #1, 2, 4, 5, 7, 8, 9, 12
Page 233 etc # 1, 3, 6, 8
Page 240 etc #1, 3, 4, 5, 10, 11, 13

Nov 6 Lesson 13

Waiting tmes and Geometric distributions Hypergeometric distributions and expectation of a hypergemotric distribution

Page 245 etc # 2, 3, 4, 5, 10, 11
Page 252 etc # 1, 3, 4, 5, 6, 7, 10, 12, 13, 15

This is the end of this unit. Test should be two lessons hence or Nov 13

Nov 11 Lesson 14

Review of the different types of binomial distributions
Hypergeometric was not covered on Wednesday,hence it is done today
Review question may be found on

Page 254 etc # 1, 2, 3, 4, 5, 8, 9, 10

Test Wednesday of Monday, your call!

Nov 13 Lesson 15

Half way there, folks! Test # 3 Probability and Probability Distributions
Start of Statistics; Chapter 7. Remember, this is short unit, only one chapter

Page 275 etc # 2(ii), 5,

Measures of Central Tendency: mean, mode, median, weighted mean, and mean for grouped data

Page 286 etc # 1, 3, 4, 7

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