 
 
ITEM  DETAILS  
AUTHOR  Russell Jay Hendel  
AFFILIATION  Towson University, Towon, Md 21252  
TITLE  CONVERTING LECTURE PREPS TO POLISHED WEB  
PRESENTED AT  ICTCM 15, 11102, 10:2010:35  
ICTCM15 SECTION  INTERNET / DISTANCE LEARNING TECHNOLOGIES  
EMAIL ADDRESS #1  RJHendel@Juno.Com  
EMAIL ADDRESS #2  RHendel@Towson.Edu  
ICTCM15 CODE  FriC1A 
 
The GOAL of this presentation is to enable instructors to produce, without extratimeresources, a webbasedcourse supplement that has...  
ITEM  DETAILS  
A Syllabus  A traditional 1215 week syllabus with  
(Sub)Topics  Indication of Major and minor syllabus topics and  
Slides  A fully developed set of slides for the course 
 
This presentation is targeted to the following AUDIENCE Instructors with the characteristics below can benefit from the ideas presented here*1. We assume that the instructor is...  
ITEMS  DETAILS  
TEACHING COURSES  
...using syllabii  The syllabus has about a dozen major course topics  
    
MAKING PREPARATIONS  
...with Problems  The instuctor already prepares class & HW problems  
...New concepts  The instructor prepares points introducing new ideas  
    
MAKING USEFUL POINTS  
For example,  The instructor points out useful CONTRASTS  
For example,  The instructor points out useful ANALOGIES  
For example,  The instructor points out useful OVERVIEWS  
For example,  The instructor points out useful DISTINCTIONS  


*1 To recap, the goal of this presentation is to show how to convert this type of lecture preps to a webbasedcourse resource without requiring extra time. 
 
The 2 key points in quickly converting lecturepreps to web slides are using a special...  
ITEMS  DETAILS  
TABLE FORMAT  This TABLE FORMAT is discussed in detail below*1  
PERL SCRIPT  A Perl script converts the text file to slides*2  


*1 The instructor must write out the lecture preps, that (s)he is already making, in a special TABLE FORMAT. This TABLE FORMAT is discussed in detail below The instructor must write out his/her lecture preps electronically Acclimating oneself to writing in this format isnt difficult The TABLE FORMAT is flexible and allows up to 6 table features *2 The instructor then uses a perl script or visual basic script to convert the electronic TABLE FORMATS to color coded slides*10  


*10 Since the perl or visual basic script executes instantly and since usage of the TABLE FORMAT requires no extra time requirements on the instructor it is immediately seen that the above setup enables conversion of the lecture preps to a collection of HTML slides. 
 
I first experimented with this idea in 1995 when I was visiting the University of Louisville. While teaching a routine Calculus I course, using Anton, I found I could type my lecture preps in etext files about as fast as I could scribble them on paper. However the etext files could be emailed to my students. Student feedback was positive Here are some of the positive aspects of using etext preps:  
ADVANTAGE  DETAILS  
More time  Students spend more time listening vs writing  
Absences  Efiles are invaluable when a student misses a class  
NoteTaking  Students print out enotes & add their own comments 
 
I began actively reexperimenting with this setup when I began lecturing at Towson University (1999) which encourages webbasedcourse material. During this period I have developed the following items:  
ITEM  WHAT WAS ACCOMPLISHED  
Table Format  I developed a TABLE FORMAT with up to 6 features  
Perl Scripts  Ive written vb scripts which convert txt to html  
8 Slide types  The rest of the paper presents these slide types  
 
We can distinguish different types of slides based on the FUNCTION and purpose of the slide. We have identified 8 distinct slide FUNCTIONS. These 8 slide types are listed below and will be discussed in the remainder of the paper This presentation was, in particular, based on material developed for an introductory Statistics course, taught at Towson University in Fall 2002. The URL is contained in footnote *1 Here are the 8 slide types and their FUNCTIONS  
TYPE OF SLIDE  Brief description of the slides FUNCTION  
DISTINCTION slides  Distinguish between TWO similar items  
DICTIONARY slides  eg Map VERBAL concepts to ARITHMETIC formulae  
LISTCONTRAST slides  LIST all possible techniques;hilight CONTRASTS  
OVERVIEW SLIDES  Revu several course topics with similar methods  
CONCEPT slides  Introduce a new courseconcept  
HW slides  Revu HW problems: Emphasize KEY points  
PROCEDURE slides  Problems whose solution requires MANY STEPS  
SPREADSHEET slides  Problems which are best solved using SPREADSHEETS  


*1 The URL is http://www.Towson.edu/~rhendel/m231f02.htm This URL contains complete information on the course including the name of the text, syllabus, and linked slides. However, this presentation is self contained and understandable without reference to this site. 
 
The course used for illustration is a traditional introductory stat course with 3 main COMPONENTS:  Descriptive Statistics,  Distributions,  Sampling inferences & Linear regression. The syllabus is divided into  3 COMPONENTS*1,  12 TOPICS*2,  A variety of SUBTOPICS*3,  Several SLIDES on each SUBTOPIC. The table below summarizes this terminology  
EACH  IS DIVIDED INTO  FOR EXAMPLE  
SYLLABUS  3 COMPONENTS*1  DISTRIBUTIONS  
COMPONENT  Topics*2  BINOMIAL, NORMAL*4  
TOPIC  SUBTOPICS*3  Exp,Variance,Word problems...*5  
SUBTOPIC  Slides  The 8 slide type examples given below  


*1 COMPONENTS correspond to exam units *2 TOPICS correspond to chapters *3 Subtopics correspond to chapter subsections *4 That is: BINOMIAL, NORMAL are TOPICS belonging to the DISTRIBUTION component. In most texts there are separate chapters to the BINOMIAL AND NORMAL distributions. *5 The BINOMIAL TOPIC (Chapter) has SUBTOPICS of  Expectation  Variance  Word problems etc Each of these subtopics corresponds to a subsection 
 
At the beginning of the semester I create a 5 column Syllabus The syllabus column headings are  DATE,  CHAPTER,  TOPIC,  SUBTOPICS,  SLIDES  Each subtopic is listed on a separate line.  The slides corresponding to each topic are listed on the same line.  Here is a sample syllabus segment  
DATE  Chapter  TOPIC  SUBTOPICS  SLIDES*1  
10/3/02  6  Binomial  Discrete RV  71  
10/3/02  6  Binomial  ExpVar  72,73,74 75  
10/8/02  6  Binomial  Bin Dist  76,77  
10/10/02  6  Binomial  Word problems  78,79,80,81,82  


*1  The numbered slides are hyperlinked to actual slides.  Each slide corresponds to 1 html page  Each slide performs one of the 8 slide FUNCTIONS developed in the remainder of this paper The above is the main web design. Various other links are added as needed and desired. For example  a COURSEINFO page or  a PROBLEMSDONE page listing problems reviewed in class 
 
The rest of this presentation will present...  
ITEM  SECTION IN PAPER  
... the anatomy of a slide  Section VIII  
... the 8 slide types with examples  Section IX  
... An extended example  Section X  
... summary and future developments  Section XI 
 
The slide after this one reproduces an actual course slide*1 This slide was part of a lecture on basic descriptive statistics. The purpose of this slide is to MOTIVATE the need for VARIANCE besides AVERAGE as a basic descriptive statistic. This slide below has 4 sections:*3 *10  
#  SLIDE COMPONENT  COMPONENT CONTENT  
VIIIa)  THE SLIDE TITLE:  Avg vs DISPERSION  
VIIIb)  THE SLIDE DESCRIPTION:  Why isnt average enough? etc  
VIIIc)  THE TABLE FIELDS:  DATA, AVG, DISPERSION  
VIIId)  THE TABLE DATA:  eg Temperature data:60 70...  
VIIId)  THE NOTE SECTION:  Notes are indicated by asterisks followed by # (*3)  
VIIId)  THE LONGER FOOTNOTE SECTION:  Notes are indicated by asterisks followed by # (*3)  
*1 http://www.towson.edu/~rhendel/math231f02/slide44.htm *2 The slide makes the point that in the situation of the first rowaverage temperature of 70 with little variationyou would only eg need to buy one set of clothes while in the situation of the 2nd rowaverage temperatures of 50 in winter and 90 in summer you would need to purchase two sets of clothes. This distinction hilights the need for a measure of DISPERSION besides the traditional AVERAGE measure *3 2 further slide components allowing explanatory footnotes (or longer footnotes) are not illustrated in the slide below as these features arent traditionally used in every slide  


*10 Again: A fundamental assumption of this presentation is that an instructor could acclimate him/herself to preparing this slide electronically on say notepad in about the same time that they could prepare such a slide on pencil and paper. 
 
Why isnt average enough? Why do we need a second measure? The example below illustrates  
TEMPERATURE DATA  AVG  DISPERSION  
60 70 70 70 80  70  Buy clothes for 70 weather  
40 50 60 80 90 100  70  Need 2 sets of clothes 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The first slide type is the DISTINCTION SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide44.htm  
FUNCTION  Use a punchy distinction to motivate a point  
CONTENT  Motivate need for a VARIANCE besides AVERAGE 
(C) Dr Hendel, Sep02  
Why isnt average enough? Why do we need a second measure? The example below illustrates  
TEMPERATURE DATA  AVG  DISPERSION  
60 70 70 70 80  70  By clothes for 70 weather  
40 50 60 80 90 100  70  Need 2 sets of clothes 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the url for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 2nd slide type is the DICTIONARY SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide88.htm  
FUNCTION  Create a MAPPING of 2 disparate domains(eg Algebra & Geometry)  
CONTENT  Probability formulae for keywords AT LEAST,AT MOST... 
(C) Dr Hendel, Sep02  
We redo the word problems for the normal distribution*10 Again we relate KEY PROBLEM WORDS to CUMULATIVE PROBABILITIES*11 (Added 102902 Compare slide79Binomial word problems)  
WORD PROBLEM TYPE  RELATIONSHIP TO CUMULATIVE PROBABILITY  
AT MOST*1  P(At most h) = P(H<=h)  
AT LEAST*2  P(At least h) = 1P(H<=h)*3  
BETWEEN  P(Between a & b) = P(H<=b) P(H<=a)*3  
EXACT  P(EXACTLY h) = P(H<=h+.5)P(H<=h.5)*4  


*1 STUDENT QUESTION (CORRECTED 102902) MORE THAN h is the same, for BINOMIAL, as AT LEAST h+1 MORE THAN h is the same, for NORMAL, as AT LEAST h h or LESS is the same as AT MOST h for BINOMIAL or NORMAL *2 STUDENT QUESTION (CORRECTED 102902) LESS THAN h is the same, for BINOMIAL, as AT MOST h1 LESS THAN h is the same, for NORMAL, as AT MOST h h or more is the same as AT LEAST h for BINOMIAL or NORMAL *3 In the BINOMIAL word problems we use h1 and a1 The minus 1 is not present in the normal problems Also in the normal problems it does not make a big difference if you use the LESS THAN vs LESS THAN OR EQUAL*10 *4 This is called the CONTINUITY correction. It takes a long time till students get this correct. I am therefore not covering it on tests since students expressed a desire for further practice on the other items  


*10 STUDENT QUESTION  Recall the BINOMIAL RV is DISCRETE (Possible values:0,1,2,.. By contrast the NORMAL RV is CONTINUOUS( eg height=6.1111) In a discrete rv,eg MORE THAN 10 means 11 or more(AT MOST 11) In a continuous rv, MORE THAN 10 means 10 OR MORE The point is that the probability of EXACTLY being 10 feet tall is 0 (eg you might be 10.001 or 9.999) So we  dont have to add the minus 1  dont have to worry about less than or equals Nevertheless purists can use or omit the equality sign *11 STUDENT QUESTION  This table is not in the book. But it is not something to MEMORIZE rather it is something to UNDERSTAND. All the slides are logical. For example to analyze  MORE THAN 11  we ask if 10 is an example of more than 11 (NO) we ask if 11 is an example of more than 11 (NO) we ask if 12 is an example of more than 11 (YES) we ask if 13 is an example of more than 11 (YES) we ask if 11.0001 is an example of more than 11 (YES) It emerges that MORE THAN 11 is equivalant to AT LEAST 11 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 3rd slide type is the LISTCONTRAST SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide63.htm  
FUNCTION  LIST all techniques of a domain & hilight CONTRASTS  
CONTENT  We list:a)4 Boolean connectives b)notation c)Probability formulae  


*1 This slide uses HAT data from class. The data was as follows  There were 14 students in class(4 wore hats,10 did not)  There were 7 males and 7 females  3 students were MALE and had HATS 
(C) Dr Hendel, Sep02  
We summarize 4 ways of COMBINING EVENTS And how this affects probability Again we use the class hat data  
METHOD OF CONNECTION  SYMBOL  Arithmetic symbol  RULE  COMPUTATION  
Complement NOT  Hbar  minus  P(Hbar)=1P(H)  P(Hbar)=110/14  
Conjunction AND  Juxtaposition  *  P(HM) = #(H and M)/#S  P(HM)=3/14  
Disjunction OR  u  +  P(H u M)=P(H)+P(M)P(HM)  P(H u M)=4/14+7/143/14=8/14  
Conditioning*1 IF  /  P(MH) =P(MH)/P(H)=3/4  P(M  H)=P(MH)/P(H)=3/4  


*1 We will discuss thoroughly CONDITIONING in the next slide 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 4th slide type is the NEW CONCEPT SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide59.htm  
FUNCTION  Expose students to the issues in a new course concept  
CONTENT  We introduce the concept of probability by a simple example  


*1 This simple example exposes students to 4 concepts  The EXPERIMENT  The POSSIBLE OUTCOMES  The SPACE (of all possible outcomes)  The EVENT The probability measure can then be illustrated using these 4 basic introductory concepts 
(C) Dr Hendel, Sep02  
4 basic items related to the definition of PROBABILITY  
ITEM  VALUE OR APPLICATION  
EXPERIMENT  Tossing a die one time  
POSSIBLE OUTCOMES  1,2,3...  
SPACE(all possible outcomes)  {1,2,3,4,5,6}  
The EVENT  EVEN #<>{2,4,6}*1  
The PROBABILITY MEASURE  Counting  
The PROBABILITY  P(Even)=#Even/#S=3/6*2  


*1 There is alot of confusion here Math textbooks tend to identify the above two descriptions  EVEN  {2,4,6} Actually they are distinct.  EVEN is the UNDERLYING ATTRIBUTE of the outcomes  {2,4,6} is the set of events in the space ASSOCIATED with this attribute To form this set simply go thru all points in the space and see which ones are even. *2 The probability is usually based on COUNTING 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 5th slide type is the PROCEDURE SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide56.htm  
FUNCTION  List the several steps in a procedure  
CONTENT  We present a 4step procedure to compute percentiles 
(C) Dr Hendel, Sep02  
How do you compute the pth percentile We will illustrate with the 75th Percentile, Q3*1  
STEP  WHAT TO DO  THE RESULT  75th percentile  
0  Data set  80,70,90,85,80  
1  Sort it  70,80,80,85,90  
2  n=# Items  n=5  
3  Lp=(n+1)p/100  Lp=(5+1)p/100=  L75=3/4*6=4.5  
4  Q3 at Lpth place  Look up value*2  4.5th item=85*3  


*1 The following notation is used Q1=25th percentile Q2=50th percentile Q3=75th percentile *2 So L_p is the LOCATION of the pth percentile But the pth percentile is the VALUE in the L_pth row *3 Either of these answers is correct  the 4.5 th item on the list 70,80,80,85,90 is the 4th item:85  the 4.5 th item on the list 70,80,80,85,90 is the 5th item:90  the 4.5 th item on the list 70,80,80,85,90 is the average of the 4th and 5th item: (85+90)/2=87.5 This last method is call LINEAR INTERPOLATION(You are NOT responsible for it) Excel uses a totally different formulae (and gets different answers) to compute the pth percentile. Since there is so much disagreement any of the above answers is ok 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 6th slide type is the SPREADSHEET SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide47.htm  
FUNCTION  Present a spreadsheet method for solving a problem*1  
CONTENT  We present a spreadsheet for computing Population SD  


*1 It is debatable whether the FORMULA or SPREADSHEET approach is superior. One can hide the SPREADSHEET by simply presenting the formula and then going over the subcomputations in the formula. 
(C) Dr Hendel, Sep02  
We use the same Data as in the Mean Deviation slides We use the same columns with occasional modifications We derive two useful measures: The Population Variance indicated by the Greek SIGMA2 The population Standard Deviation indicated by Greek Sigma  
C1Data  c2Average  c3=C1c2=Distance from avg  c4=c3^2  c5=Avg(c4)*4  c6=Sqrt(c5)  
38  28*1  10*2  100*3  534/5=106.8  10.33*5  
26  28  2*2  4  
13  15  225  
41  13  169  
22  6  36  


*1 Average = Sum of C1 over # Items in C1 = 140/5=28 *2 c3=c1c2. So 3828=10. 2628=2. *3 c4=c3^2. eg 10^2=100. Note how the definition of c4 is different for the SD vs the MD *4 c5 = Average (C4) = Sum(C4)/# Items= 534/5=106.8 c5 is called the POPULATION VARIANCE It is denoted by the Greek letter sigma^2 *5 c6 = Sqrt(c5). Sqrt(106.8)=10.33 c6 is called the POPULATION SD (Standard deviation) It is denoted by the Greek sigma 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 7th slide type is the OVERVIEW SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide49.htm  
FUNCTION  Compare several similar course problemshilight differences  
CONTENT  We compare the POPULATION SD,SAMPLE SD and MEAN DEVIATION  


*1 The emphasis here is on comparing several similar COMPLEX problems. Thus in this example we compare the POPULATION SD, the SAMPLE SD etc Each of these concepts are COURSE CONCEPTS IN THEIR OWN RIGHT. Hence the purpose of the OVERVIEW slide is to compare course items that have a great deal of similarlity 
(C) Dr Hendel, Sep02  
We compare the column definitions for MD, Population SD & Sample SD  
Column  Mean Deviation  Population SD  Sample SD  
c1  data  data  data  
c2  average c1  average c1  average c1  
c3  c3=c1c2  c3=c1c2  c3=c1c2  
c4  c3 with + sign  c4=c3^2  c4=c3^2  
c5  Sum(C4)/n*1  Sum(c4)/n  Sum(c4)/(n1)  
c6    c6=Sqrt(c5)  c6=Sqrt(c5)  


*1 n=# Of data items (Thoughout the course) 
 
In this section we present the 8 slide types. Each slide type corresponds to a distinct slide FUNCTION Each slide is preceded by a slide describing  the URL for the reproduced slide  the FUNCTION of the slide  Key points & CONTENT of the slide The 8th slide type is the HOMEWORK SLIDE  
ITEM  DETAILS  
url  http://www.towson.edu/~rhendel/math231f02/slide101.htm  
FUNCTION  Examine HomeWork Problemsemphasize subtle distinctions  
CONTENT  Review sample mean problems: Two issues are studied*1  
ISSUE 1  What justifies using the NORMAL distribution for sample means?  
ISSUE 2  How does a student RECOGNIZE that this is a SAMPLE MEAN problem?  


*1 This slide summarizes 8 problems on sample means done in class. The slide is a bit terse for someone not in class and needs further clarification for full understanding. These further details are provided in footnotes 2,3. *2 The 6th column entitled NORMAL? presents 3 possible justifications for using the Normal distribution(vs the t distribution) on the sample means  #1: The problem explicitly states that the POPULATION is NORMAL and the POPULATION SD is known  #2: The sample size n >=30 (The point being that a t distribution with n>=30 can be approximated by the normal distribution)  #3: The population standard deviation is given AND It is reasonable to ASSUME that the population is normally distributed *3 The 3rd column entitled WHY SAMPLE MEANWHAT KEYWORDS?, presents the phrase in the problem question that would enable the student to recognize that the problem is dealing with SAMPLE MEANS. This column was included in response to student inquiries: (How does a student know that the problem is a Sample mean problem vs a population mean problem). Such phrases as  WHAT PERCENT OF THE SAMPLE MEANS ARE...  FOR A RANDOM SAMPLE...WHAT IS THE PROBABILITY OF THE MEAN.... indicate that the problem is a SAMPLE MEAN (vs a POPULATION MEAN) problem. Note how several of these phrases more clearly indicate that it is a SAMPLE MEAN problem. 
(C) Dr Hendel, Sep02  
From page 293 in the book Notice the emphasis and contrast in the WHY SAMPLE MEANWHAT KEYWORDS column.  
#  Dist type  Why sample meanwhat keywords  u  sig  Normal?  SD Sample means  
29  Sample mean  What fraction of the samples  35  5.5  Known  5.5/sqrt(25)  
30  Sample mean  What Percent of sample means  135  8  Known  8/sqrt(16)  
              
31  Sample mean  likelihood of finding a sample mean  350  >=30  45/sqrt(40)  
32  Sample mean  likelihood of selecting sample mean  110000  >=30  40000/sqrt(50)  
              
34  Sample mean  likelihood that sample mean is..  18  3.5  Assume  3.5/Sqrt(15)  
36  Sample mean  Likelihood that the sample mean..  23.5  >=30  5/Sqrt(50)  
              
37  sample mean  random sample...prob..mean is..  947  205  >=30  205/Sqrt(60)  
33  Sample mean  For a random sample ..prob of mean  24.8  >=30  2.5/Sqrt(60) 
 
Let us use the theoretical slide types of section IX to show how to construct slides for the topic of COUNTING FUNCTIONS  combinations, permutations and powers. The table below compactly presents the items that are necessary to be presented.  
ITEM NEEDED  EXAMPLES  
name of function  Combination, Permutation  
notation  n_C_r  
simple numerical example  2_C_4=6  
rule for function  n!= n x (n1) x (n2)...  
special (initial) values  0!=1!=1  
nonsimple numerical examples  4! = 4 x 3 x 2 x 1 = 24  
Functionword problem map  SETScombinations;SEQUENCESpermutations  
Sets vs sequences  Does ORDER count? Are items REPEATED?  


*1 http://www.Towson.Edu/math231f02/slide66.htm http://www.Towson.Edu/math231f02/slide67.htm http://www.Towson.Edu/math231f02/slide68.htm http://www.Towson.Edu/math231f02/slide69.htm 
 
The above analysis naturally gives rise to 4 slides The 4 slide titles are presented below along with the slide field names. Footnotes indicate how each of these 4 slides are classified in the 8 slide types The actual 4 slides are presented immediately below.  
This slide does the following  Fields in the slide  
LIST 4 counting functions*1  English Name, Math Notation,simple examples  
LIST functionsRules*2  Function, Rule, special values, examples  
List word problemsfunctions*3  Function,Typical word problem, solution  
SEQUENCES vs SETS vs CODES*4  Does ORDER matter? Are items REPEATED?  


*1 This is a LIST CONTRAST slide (It lists all 4 counting functions relevant to COUNTING problems and contrasts their notations and names) *2 This is a LISTCONTRAST SLIDE (It lists the 4 counting functions and contrasts their algorithmic rules) *3 This is a DICTIONARY SLIDE (It shows the CORRESPONDENCE between WORD PROBLEMS (eg # sets, # sequences) and COUNTING FUNCTIONS *4 This is a DISTINCTION SLIDE (It distinguishes between SETS, SEQUENCES and CODES) 
(C) Dr Hendel, Sep02  
In this slide we introduce the NAMES & NOTATIONS for the 4 functions Future slides will indicate how to compute & what word problems they solve  
NAME OF FUNCTION  NOTATION  NUMERICAL EXAMPLES  
Factorial  n!  3! 4!  
Permutation  n_P_r  5_P_3 *1  
Combination  n_C_r  5_C_3 *1  
Power  n^r  5^3  


*1 Answer to student question: The BIGGER number is always on the left (5_P_3 is correct; 3_P_5 will not be used in this course) 
(C) Dr Hendel, Sep02  
How to compute with them  
FUNCTION  SPECIAL VALUES  RULE  EXAMPLE  
n!  0!=1 1!=1  n!=n*(n1)*(n2)...*1  4!=4*3*2*1=24  
n_P_r  n_P_0=1  n_P_r =n*(n1)...(nr+1) *1  7_P_3=7*6*5=210 *1  
n_C_r  n_C_0=1  n_C_r=n/1*(n1)/2*...*(nr+1)/r *2  7_C_3=7/1*6/2*5/3=35 *2  
n^r  n^0=1  n^r =n*n*n...n (r times)  4^3=4*4*4=64  


*1 The book uses the rule n_P_r= n!/r!. However the rule I give is simpler computationally   Multiply downward starting at n(left side number)  have r items in produce (r is right side number)  See *10 for an extended example SEE PROBLEMSDONE page for a list of book examples done *2 The book uses the rule n_C_r = n! / (r! (nr)!) However the rule I give is simpler computationally   multiply downward starting at n(Left side number)  let the denominators go upward starting at 1  stop when the denominator = r (Right side number)   


*10 So 7_P_3 is computed as follows  Start at 7 the left hand # in 7_P_3  Use 3 multiplicands (3 is the right hand #) EXAMPLE: 7_P_3 7 x 6 x 5 = 210 1st # 2nd # 3rd # In answer to student questions:  If you understand the above description then forget the abstract notation and simply learn the rule...To show work you can suffice with showing numerical work  *11 EXAMPLE: 7_C_3  Start numerator at 7 (Left hand #) on top  Start denominator at 1  Go upwards to 3 (Right hand #) 7 6 5  x  x  = 35 1 2 3 1st # 2nd # 3rd # 
(C) Dr Hendel, Sep02  
What word problems can be done with them  
FUNCTION  TYPICAL WORD PROBLEM  SOLUTION  
n!  NA  NA  
n_P_r  How many SEQUENCES of 3 items from 7  ANSWER: 7_P_3=210  
n_C_r  How many SETS of 3 items from 7  ANSWER: 7_C_3=35  
n^r  How many CODES of 3 items from 7  ANSWER:7^3=343 
(C) Dr Hendel, Sep02  
Differences between SEQUENCES, SETS, CODES (NOT IN BOOK but very helpful)  
ITEM  DO YOU CARE ABOUT ORDER?  DO YOU ALLOW REPETITION  EXAMPLE*1  
SEQUENCES  Yes  No  route 3 cities  
SETS  No  No  3 stat Profs  
CODES  Yes  Yes  Phone#  


*1 Many examples were done in class. Please see the PROBLEMSDONE page 
 
As indicated in the introduction the above methods have been particularly helpful in calculus and stat courses. I however have encountered resistance in upper level courses due to notational problems. For example, Students simply do not relate well to text substitutes for integral signs. Here is a brief description of courses where these methods worked. Footnotes indicate attempts to improve other courses.  
COURSE  DO SLIDES WORK?  WHY  
Calculus  Yes  Notepad=blackboard  
Statistics  Yes  Notepad=blackboard  
Upper level  No*1  Notation(Integral,quotients)  


*1 One student suggested that if problems are worked out in say mathematica and the appropriate exe files are on the system then a hyperlink to a worked out problem in mathematica would automatically open. This would solve the problem of presenting worked out problems. The description of theory and contrasts could probably still be accomplished in English. Hence future versions of this approach will focus on techniques relevant to upper level courses. 