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# mean deviation formula for ungrouped data

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Search. So, standard deviation of the given data is 4.69. Standard Deviation Formula for Ungrouped Data: Standard deviation is normally represented by the symbol known as sigma or letter ‘σ’. Range and Mean Deviation. Question 2 : Calculate the standard deviation of the following data x 3 8 13 18 23 f 7 10 15 10 8 . Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number. Examples: Median Formula. Mean absolute deviation from mean for grouped and ungrouped data can be calculated by using the formulas: Similarly mean absolute deviation from median can be calculated by using the formulas: Mean deviation or average deviation is the arithmetic mean of the absolute deviations. 1 mo 12. For that, let us arrange the given data in ascending order. Find the variance and standard deviation. The average mean of this set is 16.4 now, out this mean in the formula of standard deviation as shown below. Covers frequency distribution tables with ungrouped data. Mean Deviation is used to determine how far the data values are dispersed from the mean value. Learn the definition, formula, and solved examples at BYJU’S. •Mode is the value that has the highest frequency in a data set. Know how to calculate the Mean Deviation for Grouped Data and Continuous Frequency Distribution. variance and standard deviation, variance calculator, variance formula, variance examples, standard deviation, standard deviation formula, standard deviation calculator, standard … 3) Find the mean of those distances. Two of our most-viewed posts deal with Mode and Median of Grouped Data: how to calculate these statistics for data that is supplied in the form of frequencies for classes of data (bins), rather than the individual data values.Here we’ll complete that topic with a look at the less troublesome cases of Mean and Standard Deviation, including some issues that arise in the grouping process itself. Click Create Assignment to assign this modality to your LMS. This video explains how to find out the mean & mean deviation about mean for ungrouped frequency data !! Example 1 : Find the coefficient of variation of 24, 26, 33, 37, 29, 31. MA TH Definition: The MEAN DEVIATION, or average deviation, is the dispersion of the data about the mean of these data. Mean Deviation -The mean of the distances of each value from their mean. The steps to calculate mean & standard deviation are: 1) Process the data. But a major problem is that mean deviation ignores the signs of deviation, otherwise they would add up to zero.To overcome this limitation variance and standard deviation came into the picture. Three steps on finding the mean: 1) Find the mean of all values. This indicates … To calculate mean deviation for ungrouped data, we have to find absolute deviation for every observation of central tendency and evaluate the mean about the given observation. Therefore in order to keep all the values positive, absolute deviations are used to find the mean of deviations called mean absolute deviation. Finding weighted mean by hand or using the TI calculator % Progress . Mean deviation in statistics is defined as the mean of the distances of each value from their mean. •For grouped data, class mode (or, modal class) is the class with the highest frequency. Here is the simplified formula of mean for your consideration. It is also referred to as mean absolute deviation. The following formulas are applied: Here below you can check out the median formula for the grouped data. In applying this method first of all we compute the arithmetic mean of the given data, either ungrouped or grouped. Find the standard deviation of the first n natural numbers. WELCOMEMATH 3. Skip navigation Sign in. 2) Calculate mean by formula. Below are the numerical examples with step by step guide solution on variance and standard deviation for ungrouped data. For ungrouped data, sort and tabulate the data in a table. MA TH MEAN DEVIATION (for ungrouped data) 4. Variance and standard deviation (ungrouped data) Introduction In this leaﬂet we introduce variance and standard deviation as measures of spread. While computing standard deviation, arranging data in ascending order is not mandatory. 19.5.3. •To find mode for grouped data, use the following formula: ⎛⎞ ⎜⎟ ⎝⎠ Mode. Mean Formula. Median of an Ungrouped Data Set The median refers to the middle data point of an ordered data set at the 50% percentile.If a data set has an odd number of observations, then the median is the middle value. If it has an even number of observations, the median is the average of the two middle values. 5. MEMORY METER. Mean Deviation for Grouped Data Calculator. Harmonic Mean (H.M.) Harmonic Mean is defined as the reciprocal of the arithmetic mean of reciprocals of the observations. Example 7 Calculate the mean deviation about median for the following data : Median = + 2 −  ×ℎ Where, = lower limits of median class N = sum of frequencies = frequency of median class C = Cumulative frequency of class before median class Here, = 20, N = Mean Deviation tells us how far, on average, all values are from the middle. The age (in years) of 6 randomly selected students from a class are. This method is already defined above. Δ =L + i. Δ + Δ. Mode – Grouped Data Question: Find the variance for the following set of data representing trees heights in feet: 3, 21, 98, 203, 17, 9 Solution: Step 1: Add up the numbers in your given data set. 2) Find the distance of each value from that mean. The calculation of this entity can be found by using a formula called, standard deviation formula, which is used by mathematicians or statisticians. Standard deviation for ungrouped data. We can evaluate the variance of a set of data from the mean that is, how far the observations deviate from the mean. 6. For grouped data, obtain the mid-value of each intervals. 22,25,24,23,24,20. Let x 1, x 2, ..., x n be the n observations then the harmonic mean is defined as . Solution : First let us find the standard deviation for the given data. Formula for Mean Deviation: (ungrouped data) MD Where, μ = mean x n x = each value N = number of values 6. Sample mean is represented by the symbol $\bar{x}$. 3 + 21 + 98 + 203 + 17 + 9 = 351. Solution : Let us use actual mean method to find standard deviation. Now, first of all we have to figure out the median class and for that we will apply the following formula … The data in a tabular form which indicates the frequency is known as a frequency distribution. Then we take the deviation from the actual mean. ! The data has to be arranged in ascending order and then the quartile formula for ungrouped data is applied to calculate the values of Q 1,, Q 2 ,and Q 3 Solved Examples For Quartile Formula Below you can see solved examples for quartile formulas which will clear your concepts of quartile formulas … 3) Calculate standard deviation in two steps We have studied mean deviation as a good measure of dispersion. 7. (a) H.M. for Ungrouped data . MA TH Definition: The MEAN DEVIATION is a measure of variation that makes use of all the scores of the distribution. The sample mean is the average and is calculated as the addition of all the observed outcomes from the sample divided by the total number of events. For a given series of data, statistics aims at analysis and drawing conclusions.The various measures of central tendency – mean, median and mode represent the values in a series. Watch Queue Queue. Mean Deviation 1. 4. mean absolute deviation, mean absolute deviation formula, mean absolute deviation calculator, mean absolute deviation calculator, mean absolute deviation for ungrouped data 6. skewness meaning, skewness in statistics, skewness formula, skewness coefficient, pearson coefficient of skewness for ungrouped data Standard deviation for ungrouped data. Step 2: Square your answer: 351 × 351 = 123201 …and divide by the number of items. Example Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14 The mean of the data is 10.222 Subtracting the mean individually from each of the numbers given and square the result. A man travels from Jaipur to Agra by a car and takes 4 hours to cover the whole distance. If you are interested in calculating this function manually by your hands then the best way of doing this is to prepare a table by the data set you are having like, for example, we are having 5,12,16,21,28 data. Need for Variance and Standard Deviation. Calculate the mean deviation about the mean of the set of first n natural numbers when n is an even number. H9018 x, H9018 x. Also Check: Standard Deviation Formula Variance Formula Example Question. 3.2 Measures of Dispersion for Ungrouped Data 95 H17011 Two Observations Calculating the population variance and standard deviation for ungrouped data. Mean and Standard Deviation Formula. Example 5.11. However, we can further implement this analytical claim of statistics, by measuring the scattering and dispersion of data around these measures of central tendency. Here is an example (using the same data as on the Standard Deviation page): Example: You and your friends have just measured the heights of your dogs (in millimeters): In Mathematical terms, sample mean formula is given as: $\bar{x}$= 1/n $\sum_{i=1}^{n}x$ Loading... Close. Because the data in this example are on earnings of all employees of this company, we use the population formula to … Variance and Standard deviation of ungrouped data Example 1. Solution MATH 2. This video is unavailable. The standard deviation is given by the formula: s means 'standard deviation' m is the mean N is the number of values. 5. ... Ungrouped Data to Find the Mean. Formula for mean deviation for ungrouped data or an individual series is given from BMA 2202 at Mount Kenya University Namaste to all Friends, This Video Lecture Series presented By VEDAM Institute of Mathematics is Useful to all students of Class 11th & 12th of … 351 × 351 = 123201 …and divide by the symbol \ [ {! Or, modal class ) is the mean of the distances of each value from their.!, on average, all values to keep all the scores of distribution. We take the deviation from the actual mean is a measure of that. Statistics is defined as of 24, 26, 33, 37, 29, 31 observations from... 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# Confuse the Word spell checker!

Your task is to make a program that will take an input of a word of any length, in the Calibri font. This word will be made out of letter characters that are found on a normal QWERTY keyboard. There will be no accents or any other characters (i.e punctuation, numbers etc).

So, the original characters are:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The program will then scramble it to change the characters so they look similar or exactly the same, which would probably confuse a spell checker by flagging it, but it would confuse me as it looks the same as the normal word, with the unchanged character.

An example of this is the Unicode character U+0430, Cyrillic small letter a ("а"), can look identical to Unicode character U+0061, Latin small letter a, ("a") which is the lowercase "a" used in English.

Another example is the Russian letters а, с, е, о, р, х and у have optical counterparts in the basic Latin alphabet and look close or identical to a, c, e, o, p, x and y.

Rules:

1. The program has to work out similar characters. This means that they cannot be stored in any form. This means that Unicode value or the character itself.
2. This is a code golf - the shortest answer wins!
3. You have to post the ungolfed version too to avoid cheating that can't be detected when its golfed!
4. You can use any function or program to do this, as long as words are not stored there either.
5. You must use UTF-8. Other inputs and outputs are banned. This is so that I am actually able to read what you are outputting, and what I am inputting, so I do not have a random mass of squares, question marks and ❮ther rand❮m punctuati❮n!
6. It has to work with any word that I input.

A working example (Copy and paste this into word and insert a space after, it should flag the second one and not the first one.)

Halim
Hаlim

Some helpful info is here

Good Luck! Begin

• I think this is a great candidate for code-golf instead of popularity-contest. – ProgrammerDan Apr 1 '14 at 17:23
• @ProgrammerDan the question with this as code-golf is, how many characters have to be replaced and how dissimilar are they allowed to look for an answer to be valid? – Martin Ender Apr 1 '14 at 17:58
• In either case, a definition of "confuse the spell checker" would be nice. Which spell checker? Also, what is our input alphabet? Output alphabet? I recommend that you specify a popular online spell checking tool, and specify an encoding, such as UTF-8. – Rainbolt Apr 1 '14 at 18:03
• I've taken your comments on board and changed a few things - thanks for the advice :) – George Apr 1 '14 at 18:11
• This would have been a great April Fools' prank if I had asked this a few days ago! – George Apr 1 '14 at 18:52

## JavaScript, 71 characters

function f(s){return "\u202E"+s.split("").reverse().join("")+"\u202C";}

Try it out on JSFiddle.

By the way, this would be a good bit shorter in CoffeeScript (53 characters)

f=(s)->"\u202E#{s.split('').reverse().join ''}\u202C"

EDIT: I just noticed that UTF-8 requirement. That's going to be tough in JavaScript. :-/

• Don't downvote this answer - its a good one, but it was posted before the rules changed slightly. You also have to input a word and it cant just be hardcoded in. Sorry. – George Apr 1 '14 at 18:44
• @GeorgeH well the function takes any arbitrary text (not just single words). It's just the JSFiddle that showcases the usage with one specific example. – Martin Ender Apr 1 '14 at 18:45
• Oh, Sorry, I've never used JSFiddle before! Its really confused Word now - It thinks George is Egret and other stuff! – George Apr 1 '14 at 18:48
• Hmm... I randomly picked some words to test your function but it doesn't work... The words I picked were level, rotor, racecar, refer and kayak. – ace Apr 1 '14 at 20:31
• @ace Touché. :P – Martin Ender Apr 1 '14 at 20:35

# Python3 - 51

print(''.join(chr(ord(c)+0xFEE0)for c in input()))

The lazy way!

Slightly ungolfed

r=''
for c in input():
r += chr(ord(c) - 0x20 + 0xFF00) # convert to fullwidth ASCII range
print(r)

• Please can you post an ungolfed version? Thanks! – George Apr 2 '14 at 21:28
• Done, it should be self explaining :) – LemonBoy Apr 2 '14 at 21:38
• If you use it in IDLE you can remove the print() - it'll print it out anyway – chill0r Jun 14 '14 at 16:35
• You can save one byte by changing the hexadecimal number FEE0 to a decimal number (65248). – 0WJYxW9FMN Apr 3 '17 at 8:59

# Common Lisp, 142

I have no font named Calibri, and most of my fonts lack these symbols, but DejaVu Sans has them. I replace letters with Mathematical Alphanumeric Symbols. The spell checker does not flag any errors. Instead, it fails to detect errors, even if words have obvious typos.

Golfed:

(ignore-errors(do(c)(())(setf c(char-code (read-char)))(write-char(code-char(cond((< 64 c 91)(+ c 120159))((< 96 c 123)(+ c 120153))(t c))))))

Ungolfed:

(ignore-errors      ; Ignore when (read-char) signals end of file.
(do (c) (())      ; Loop forever with variable c.
(setf c (char-code (read-char)))
(write-char
(code-char
(cond
;; Replace A to Z with U+1D5A0 to U+1D5B9.
((< 64 c 91) (+ c 120159))
;; Replace a to z with U+1D5BA to U+1D5D3.
((< 96 c 123) (+ c 120153))
;; Keep other characters.
(t c))))))

## Usage

• clisp asconfuse.lisp <in >out
• ecl -shell asconfuse.lisp <in >out
• sbcl --script asconfuse.lisp <in >out

I assume that your Lisp interpreter has Unicode support and your locale is UTF-8. Do not use abcl, because it has problems outside the Basic Multilingual Plane.

Unix clones: You can run locale in a terminal. If the line for LC_CTYPE does not mention UTF-8, try export LC_CTYPE=en_US.UTF-8.

## Example

I pasted some output into LibreOffice. My text has obvious spelling errors, but LibreOffice fails to detect them. It draws no red squiggles under the words, and the spell-check button only reports, "The spellcheck is complete."

The text is, "𝖭𝗈𝗐𝗐 𝗂𝗓 𝗍𝖾𝗁 𝗍𝗍𝗂𝗆𝖾 𝖿𝗈𝗈𝗋 𝖺𝗁𝗅 𝗀𝗎𝖽 𝗇𝖾𝗆 𝗍𝗍𝗈 𝖼𝗈𝖾𝗆 𝗍𝗍𝗈 𝗍𝖾𝗁 𝖺𝖾𝖽 𝗈𝗏 𝗍𝖾𝗋𝖾 𝖼𝗈𝗎𝗇𝗍𝗋𝖾𝖾." Firefox also finds no spelling errors in this text.

# Dyalog APL, 7 chars

∊''∘,¨

There is a U+FEFF (Zero Width No-Break Space, a.k.a Unicode BOM) between the quotes. This character occurs in in the Calibri font. The character '' is ∘ prepended , to each ¨ character in the argument, and the whole thing is then flattened ∊.

format: plain


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Improving the Strength of Schedule Model, and Week 4 NFL Picks

I promised you all that before Sunday, I’d try to get you the offensive and defensive ratings of the 32 NFL teams, as computed by the strength-of-schedule model I introduced in my last post.

Well, it’s Saturday, I’m making good on that promise. Here they are, in order of strongest overall to weakest overall

Offense/Defense NFL Strength Ratings

 Team Offense Defense Total (=Off-Def) Pittsburgh 9.3454 -12.8488 22.1942 Atlanta 7.998 -9.2423 17.2403 Green Bay 9.3868 -6.5442 15.931 Tennessee 3.4918 -8.0904 11.5822 Chicago 3.6899 -6.6026 10.2925 NY Jets -1.0105 -9.9763 8.9658 Philadelphia 7.0592 -1.5056 8.5648 Miami 5.4238 1.781 3.6428 Baltimore -1.2518 -4.5747 3.3229 Kansas City -3.0222 -6.1722 3.15 Minnesota -9.2154 -12.2434 3.028 Indianapolis 1.3655 -1.3805 2.746 New Orleans 4.4175 1.8985 2.519 Dallas -3.4686 -5.4919 2.0233 New England 13.5998 11.6069 1.9929 Detroit 5.7315 4.7494 0.9821 San Diego 4.8438 5.4278 -0.584 Houston 5.8486 7.742 -1.8934 Cleveland -1.8498 0.4057 -2.2555 Cincinnati -4.6325 -1.8317 -2.8008 Seattle -3.6599 0.0247 -3.6846 Tampa Bay -2.1605 2.139 -4.2995 Buffalo -6.334 -1.2093 -5.1247 St. Louis -6.8654 -1.6255 -5.2399 Washington -2.2807 4.1093 -6.39 Arizona -2.2533 4.7989 -7.0522 Oakland -0.7469 6.4701 -7.217 Denver -1.4403 6.3187 -7.759 NY Giants -1.4845 11.6852 -13.1697 San Francisco -5.6359 9.0157 -14.6516 Jacksonville -10.8193 4.4598 -15.2791 Carolina -14.07 6.7069 -20.7769

A few things to note about these ratings. First the numbers are in points-scored/allowed-above-average-per-game. So for offenses, positive numbers are good. For defenses, negative numbers are good. And when you subtract the defensive points from the offensive points, you get total point differential, or what I’m calling the strength rating.

If you’re observant, you’ll notice something else. The total numbers don’t match the numbers I computed in my last post, when the model didn’t break things down into offense and defense. So what gives?

Well, I discovered a minor coding error in what I did last time. I fixed it, so now when we compute single strength ratings and compare them to the offense/defense totals, we get:

 Team Single Output O-D Total (from above) Pittsburgh 22.0813 22.1942 Atlanta 16.9875 17.2403 Green Bay 15.4567 15.931 Tennessee 11.8251 11.5822 Chicago 10.2158 10.2925 NY Jets 8.8681 8.9658 Philadelphia 8.1996 8.5648 Miami 3.2691 3.6428 Baltimore 2.9968 3.3229 Kansas City 3.2809 3.15 Minnesota 2.9843 3.028 Indianapolis 3.0042 2.746 New Orleans 2.5907 2.519 Dallas 2.0974 2.0233 New England 1.8985 1.9929 Detroit 0.6533 0.9821 San Diego -0.5271 -0.584 Houston -1.4855 -1.8934 Cleveland -2.4303 -2.2555 Cincinnati -3.0073 -2.8008 Seattle -3.3511 -3.6846 Tampa Bay -4.1288 -4.2995 Buffalo -5.6052 -5.1247 St. Louis -5.0459 -5.2399 Washington -5.998 -6.39 Arizona -7.2695 -7.0522 Oakland -7.3101 -7.217 Denver -7.3261 -7.759 NY Giants -12.736 -13.1697 San Francisco -14.6399 -14.6516 Jacksonville -15.0712 -15.2791 Carolina -20.4773 -20.7769

The numbers very nearly match, which they should. The difference can be attributed to randomness in the optimization routine used to the solve the system of equations, and its effect on bets will be negligible. (In other words, we’d never bet a game where the line was close enough to ours that this small difference affected the side we took.)

Using the Model to Pick Games

So I’ll show you how we’d use these strength ratings to pick a few games.  First, notice that when we combine offense and defense ratings into a single number, we’re throwing away some good information, since we could have gotten that single number without breaking it down.  For now, that’s ok, but in the future, we’ll want to use that extra information to possibly say something about matchups.

Maybe, for example, when a bad offense plays against a bad defense, they often score a lot of points, but when a great offense plays a great defense, they don’t score much, in general.  This type of information would certainly be useful for choosing bets, but which we can’t do that without significant backtesting.  So for now, we just ignore the offense/defense breakdown.  But even just using the single strength rating, there’s still one more thing we need to do before we can really interpret these as meaningful values.

A 19-Point Favorite?  We Need to Fix That…

Notice how large some of the values are. For example, Pittsburgh’s rating is a whopping 22 points per game, while their opponent Baltimore’s is a more reasonable 3.

Interpreting the ratings as points per game, as is natural, this tells us the Steelers should beat the Ravens by a 19 points, before we even consider that their home field advantage.  19 POINTS??  They’re only a 2 point favorite, at home!

So what’s the problem?  Well, remember how last time I mentioned that we haven’t yet accounted for reversion to the mean?  In general, teams that look really good right now aren’t going to be this good all year, and teams that look really bad aren’t going to be quite this bad all year.  As the data piles up, teams will all tend to look more average than they do now, as a rule.

Let’s see what we can do to quantify this and make an adjustment.  Check out this histogram of NFL teams’ strength ratings going into Week 4, as computed by our model, from 2002-2007:

You can see that most of the teams’ ratings fall between -10 and 10, but with some in the -30 to -40 range on the low end, and the 20- to 30 range on the high end.  Compare this to the same graph, but of teams’ ratings heading into Week 16:

Ahh, a much tighter distribution!  There’s just one amazing outlier, a team that managed to be 20 points better than most of the league for the entire season. Three guesses as to which model-dating, prettyboy quarterback engineered that one.  (Of course, we all know their coach was cheating.)

Jealousy aside, we need to account for this somehow.  We do it by looking at variance, a measure of how widely spread around the mean a set of datapoints is.  What we find is this: The variance of the Week 4 ratings is very large, about 148.3, while the variance of the Week 16 ratings is only about 41.9.

This means that in order to compare teams in Week 4, we need to shrink the variance of our Week 4 ratings by a factor of $$148.3/41.9\approx 3.5$$.

In this case, since the mean is zero (remember, we required that of values when we solved for the solution), the variance $$\sigma^2$$ can be expressed $$\sigma^2 = E(X^2).$$ Since we want to shrink the variance by 3.5, this means we need to divide the X’s (our Week 4 strength ratings) by a factor of $$\sqrt{3.5}$$ in order to make the spread of our team abilities match what we know it should look like after lots of games have revealed teams’ true abilities.  These “variance-adjusted strengths” appear below.

Reduced-Variance NFL Strength Ratings

 Team Reduced-Variance Strength Pittsburgh 11.7381 Atlanta 9.0303 Green Bay 8.2165 Tennessee 6.2860 Chicago 5.4306 NY Jets 4.7141 Philadelphia 4.3588 Miami 1.7378 Baltimore 1.5930 Kansas City 1.7441 Minnesota 1.5864 Indianapolis 1.5970 New Orleans 1.3772 Dallas 1.1149 New England 1.0092 Detroit 0.3473 San Diego -0.2802 Houston -0.7897 Cleveland -1.2919 Cincinnati -1.5986 Seattle -1.7814 Tampa Bay -2.1948 Buffalo -2.9796 St. Louis -2.6823 Washington -3.1884 Arizona -3.8643 Oakland -3.8859 Denver -3.8944 NY Giants -6.7702 San Francisco -7.7823 Jacksonville -8.0116 Carolina -10.8854

It’s these numbers that we should use to make our picks. I’ll emphasize again that this is a simplified version of the model, so I wouldn’t advise making any bets with it yet (unless strictly for fun).  We’re not even accounting for any injuries yet!

But for the fun of it, here’s what we’d do if we were betting.

The System’s Week 4 NFL Picks

Look at the Baltimore-Pittsburgh game.  The Steelers are laying 2 points.  We have the Ravens at 1.59; the Steelers are the best team in the league at 11.73, so the difference is $$11.73-1.59=10.14.$$ Add to that 2.5 for the Steelers homefield advantage, and they should be a 12.5-point favorite.  (Yeah, I know that’s huge.  That happens early in the year, because the model uses no preconceived notions about the team abilities, only what’s in the data.)

So in this case, much as I hate to say it, the model would take the Steelers.  I’ll do one more, then you’re on your own:

• Denver +7 at Tennessee. Denver = -3.89, Tennessee = 6.28.  So the difference is greater than 10, in favor of Tennessee, plus home field for them.  Way more than 7, so we take Tennessee, laying the points.

Get the idea?

Continuing in this way, the model would pick:

• Pittsburgh minus 2
• Denver plus 7 [This is a typo. According to the above, the pick should have been Tennessee minus 7 (which is a loser).]
• Cleveland plus 3
• Atlanta minus 7
• Chicago plus 3.5
• Miami plus 1

The bold are the most favorable bets, according to the model.  The other games listed are still good, and for games not listed, the model’s prediction was too close to the actual line to make a bet.  (For the record, JMS, it likes your Lions getting 14, but just barely.)

In the future, I’d like to find a better way—possibly using pattern-recognition or other machine-learning software—to recognize favorable bets, given the offense/defense ratings, week number, and spread.  That’s something I didn’t get anywhere with when I tried it before, but I’m hoping a few bright minds out there will have some suggestions.

So there you go.  Week 4 NFL picks, from our very (right now) basic model.  I’m planning to introducing a little more each week, along with an additional post every week about another topic, just to lighten things up.  Sound good?

If you’re on board for that, subscribe to Thinking Bettor to make sure you never miss a post.  Come on, it’s free!

2 Responses to Improving the Strength of Schedule Model, and Week 4 NFL Picks
October 4, 2010 | 11:02 am

And now the post that every bettor hates…

… any. given. sunday.

What a bazaar week!

• Matt
October 4, 2010 | 11:37 am

Yeah, not a great start for the model, was it? These picks weren’t from the full version of it and were more to illustrate how it works, but I think that even the full version would have been well under .500, because this basic model is still at the heart of it.

The injuries to 2 QB’s on teams the model picked got me thinking about injuries though. I have a decent method of accounting for them that’s a pain in the ass to actually implement, but what I’m wondering is if picks should be adjusted because of the possibility of injury.

For example, if bad conditions are likely, the spread becomes less because anything can happen. This isn’t quite that, but how about this argument: If each team has equal chance of sustaining a big injury during a game, does that favor the underdog for the same reason?

Or, another way of thinking about it: A big favorite likely has more stars on the team. If one gets hurt, they lose a lot by having to go to the bench. The big dogs will have smaller difference between starters and bench players, so an injury will probably not hurt them as much.

Definitely something to think about more…this is the type of thing that machine-learning tools are good at figuring out and accounting for. Which is why that version of the model is better.


text:
## Teaching with Moodle

### Best pracitces for teaching Math(s) in Moodle

This discussion has been locked because a year has elapsed since the last post. Please start a new discussion topic.
Best pracitces for teaching Math(s) in Moodle

I'll start by saying that I've not yet been able to get the math filters to display the functions, but I'm working on it. From what I see, however, it's just not something for the easily frustrated math teachers out there. The syntax will turn them off.

But, I'd LOVE to start a discussion (I didn't find one when I searched) about how teachers are getting over the hurdles associated with writing formulas and expressions. What are some of the best ways that you've found to TEACH math in a Moodle class, given the requirements for writing expressions, etc? How are students turning in their work if they, too, must write expressions?

Several moodle managers in our area are working on starting a user group and I'm SURE that this will be one of the first topics to come up for discussion, and I'd love to point them to this thread for your responses.

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Re: Best pracitces for teaching Math(s) in Moodle

Hi
I am a Science teacher not Maths but I have worked with some of our Maths staff.

To me a succesful way is to use OpenOffice or StarOffice (you can get a school license for free from Sun). The Math editor is reasonably easy to use and then the pdf export is excellent. Staff can post  links as a resource to pdf files.

Regards Alex

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free aplis

Hello

Microsoft leaves the office started excel, word, powerpoint free. in 2013 published pdf version.

Always consider the new alternative we really free Free Office, as Sun has left us hanging first, closing the open office.

My point is if you work for free, developers are also entitled to bring home a paycheck.

Would give free classes every day?

Un saludo

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Re: free aplis

I like gratis, but I am passionate about libre.

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Re: Best pracitces for teaching Math(s) in Moodle

I teach rather low level high school math courses, so the mathematical text that I produce is not very complicated. When I started using moodle, I generated the LaTeX using MathType, a WSYWYG math editor recommended by Microsoft as an upgrade to their own Equation Editor. MathType can be configured so that when you copy (control-C) equation text in a MathType window and paste it into a text area (such as into a moodle HTML editor), it pastes the LaTeX markup! Then you merely need to surround the LaTeX by the double dollar signs to make it palatable to moodle.

After a short time of watching the text being generated by MathType, I became familiar with LaTeX and began typing the LaTeX myself. I now rarely use MathType. Typing LaTeX is actually quite easy and fast.  In fact, it doesn't feel as if my typing slows up when I transition from text to math.

I can't imagine MY students ever learning LaTeX or having patience to use a tool like MathType. I have only used quizzes and lessons with them so far, and these do not require them to type math expressions.

One major problem that I have encountered with LaTeX is the following. If you include LaTeX markup in a GIFT file (GIFT is a format for bulk import of questions), you must escape the characters { } ~ and = because those characters have special meaning in GIFT. Perhaps someone has solved that problem already.

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Re: Best pracitces for teaching Math(s) in Moodle

You can scape the control symbols in GIFT using \, write \{1,2,3\} to obtain {1,2,3}. Same apply to other special characters.

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Re: Best pracitces for teaching Math(s) in Moodle
James,

I will be teaching a contemporary mathematics course online for the first time this summer. The topics in this course are broad, but they are not very in depth. Here are my initial thoughts on some of the hurdles:

Use "ascii math"

~(p ^ q) <=> ~p v ~q

P( A | B ) = P ( A ^ B ) / P( B )

Use Math filters

@@y = mx + b@@

Obviously there will be other hurdles. Having students graph a function is one problem.

A whiteboard type of assignment might be nice for students to draw graphs or diagrams.

I have a TabletPC that I use to write the notes. I can create PDF files of my notes easily.

I like the idea of sharing thoughts though, let's keep it going!

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Re: Best pracitces for teaching Math(s) in Moodle

Hello math(s) teachers,

Even tough I'm not a math(s) teacher I'm very interested in this discussion. During my moodle staff development courses I am often asked by math(s) teachers whether it's possible for students to draw graphs and share them with the class.

Do you think this will be possible with the COVCELL project whiteboard? http://moodle.org/mod/forum/discuss.php?d=41187. Are there any other ways to do this?

Ulrike

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Re: Best pracitces for teaching Math(s) in Moodle

I, too, would like to know of whiteboard solutions to this problem. I still cannot get my math formulas to work at all, but I agree with the above comment that trying to have kids use that syntax would add a heavy burden to their efforts to try to learn the math concepts in general.

The whiteboard, although requiring a synchronous event, may be the best bet. Still.... finding a way for kids to submit quiz answers is difficult at best.

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Re: Best pracitces for teaching Math(s) in Moodle

That whiteboard probably would be extremely useful. There have been many whiteboard threads on moodle.org over the last two years. For my institution, such a module would be helpful for math and science and also basic grammar instruction.

My school has been using the Elluminate web conference to deliver synchronous math and science courses. We've found the whiteboard/one-way voice to be an extremely successful combination. The instructor can prompt student users. Students and instructor can work together on images or problems on the whiteboard. If moodle had a whiteboard module you could do the same thing for much less money.

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Re: Best pracitces for teaching Math(s) in Moodle

I've been linking to a free resource from General Electric corporation. It seems to serve our purposes quite well. It's called Imagination Cube. Here's a link: http://www.imagination3.com/

Here's another link that describes the service: http://cwcdn.geimaginationatwork.com/@v=092520050111@/imaginationatwork/flash.html

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Re: Best pracitces for teaching Math(s) in Moodle
Hi David

I'm not a math teacher bu thanks so much for supplying the Imagination Cube link, http://www.imagination3.com/

My work mates and I spent about half an hour mucking around on it!!  It's fun to use and I will be sharing this link with others who may find a more educational reason to use it

Teresa

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Re: Best pracitces for teaching Math(s) in Moodle

Hello all,

I don't know if this will help (I cross-posted this at the discussion above).  I found a whiteboard that we
modified.  I think it was the same one that was planned for moodle at one point (I see references in the
source code).  Although it is excellent, the problem was it could not manage distinct images for different groups/classes/projects.

I went ahead and hacked it, and your welcome to try it out.

Here is my post from the other discussion:

Hello

If anyone would like, they can use this whiteboard.  It is based
on an excellent whiteboard at http://sourceforge.net/projects/drawboard/
written by Tomek Zielinski.  I think the Coccinella3 has great promise, but
we were going to have to install to much extra software to make it work.

The piece I added to the original made it "group enabled" meaning that
the server manages the images for different instances (the original
could have many clients sharing one instance, where moodle needs distinct
image management per class or group, etc...)

I had to disable some of the image mailing and saving features, (see
http://drawboard.sourceforge.net/ for more complete documentation)
but I will put them back after I get done cleaning up the code.
But each group's image is saved and is persisted between invocations
of the whiteboard.

Anyway, this is a moodle module (activity), so unzip it to the
mod directory and access the admin page to install the it.

Then you will have to go to that same directory and launch the Server
process.  Here is how it looks on our server.

% cd /home/httpd/html/moodle/mod/whiteboard
% java -cp drawboard.jar drawboard.server.Server

There is probably a better way to run this as a deamon or a windows
service.

The client machines will need to access port 7904 on the server where
you are hosting the whiteboard application (That is where the
drawboard.server.Server is listening).  Sometimes tech directors will
close off access to remote ports but the usual 80, 8080, 22, 2401, etc.

I will be adding some features to this, including an equation editor and
function plotter for math teaching.  There will also be a way to "export"
a snapshot of the current image, and "import" an image from the hard
drive.  That way, Math teachers can set up the equations and diagrams ahead
of time and import them during class.

Best Regards,

Bob Piercy

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Re: Best practices for teaching Math(s) in Moodle

Thanks, Bob. Can't wait to try this out.

"We" decided to keep BB for another year just for the Math classes as we felt that there was no way our math teachers would learn either Latex or the Algebra filters, and REALLY no way that the 9th grade students could learn it well enough to reply with expression answers. Math is very difficult to teach online anyway, but when the expressions are as awkward to write as this it was felt that we'd watch for improvements down the road.

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Re: Best practices for teaching Math(s) in Moodle

Hi James and Bob

You can try TalkAndWrite a Skype's plug-in with a whiteboard and it is freeware

Marcelo

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Re: Best pracitces for teaching Math(s) in Moodle

I'm very interested in getting a whiteboard working here. I've installed the whiteboard.zip file from your post above, and the server seems to start properly. I created a language file with modulename and modulenameplural strings, but when I go to add a Whiteboard activity I get an error "Course module is incorrect", although the activity is actually inserted in the course. Again, when I click on the Whiteboard activity, I get the same error message.

My Moodle version is 1.6.1.

Do you have any suggestions, or idea of what I'm doing wrong?

Barry Bookout

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Has anyone tried digital pens?

Our math faculty use images for formulas -- not very pretty and kind of time consuming, but it's working. The problem that we're struggling with now is how students can complete calculations and submit their working documents so that the instructor can see their process.

We're thinking of trying digital pens (like Leapfrog's Fly Fusion Pentop computer or Logitech's Digital Pen) -- students could write out their calculations on special paper and upload the completed work for submission. I think this would solve our needs, but I thought I'd see if any other Moodlers have tried this?

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Re: Has anyone tried digital pens?

Unless this is something that must be done daily, why not just scan the pages of student work, save as a jpeg and upload ?

Scanning only takes a minute.

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Re: Has anyone tried digital pens?

I see that you are at a community college. For students at such a level, I would consider using the DragMath equation editor, rather than buying special hardware. DragMath allows students to build mathematical expressions in a traditional two-dimensional way using a graphical drag-and-drop interface, and outputs the finished expression in LaTeX. It works as a popup window off of the HTML editor, so it is available most everywhere that students enter text, including Quiz Essay questions and Online Assignments, neither of which permits attachments.

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Re: Has anyone tried digital pens?

Thanks for your suggestion, John.  We did try DragMath on our Test site a few months back, and while we (technical support) liked it, our faculty didn't really take to it.  We might try again when they're fresh after the holiday break.

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Re: Has anyone tried digital pens?

I bought a "tablet" pc almost a year ago, with a pen that I can use to "type" without the keyboard or write in freehand.  However after a year I've not mastered (nor, frankly, have I tried very hard) to figure out a way to use the stylus to post free-form material for my students.

I teach Greek, not math, but the problem is similar:  I'd like my students to be able to write in Greek and upload their work so I and others can see their actual handwriting.  They do learn to type in a Greek font, but I want them also to be able to write with their own hand and a pen or pencil.

Given my own limited success using the stylus for writing things, I abandoned any thought of having my students do so. At this point, I just tell them early on that they will need to make arrangements at least occasionally fax or scan their handwritten work. I have an efax number so their faxes come to me via email.  My students and I are geographically and technologically quite diverse -- certainly not all have access to scanners, and getting to a fax machine is problematic for some --

It's a problem....

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Re: Has anyone tried digital pens?

Susan,

 Re: Has anyone tried digital pens? by Susan Jeffers - Wednesday, December 19, 2007, 10:47 PM Susan, you wrote, "I bought a "tablet" pc almost a year ago, with a pen that I can use to "type" without the keyboard or write in freehand. However after a year I've not mastered (nor, frankly, have I tried very hard) to figure out a way to use the stylus to post free-form material for my students. I teach Greek, not math, but the problem is similar: I'd like my students to be able to write in Greek and upload their work so I and others can see their actual handwriting. They do learn to type in a Greek font, but I want them also to be able to write with their own hand and a pen or pencil. Given my own limited success using the stylus for writing things, I abandoned any thought of having my students do so. At this point, I just tell them early on that they will need to make arrangements at least occasionally fax or scan their handwritten work. I have an efax number so their faxes come to me via email. My students and I are geographically and technologically quite diverse -- certainly not all have access to scanners, and getting to a fax machine is problematic for some -- It's a problem...."

Have you, or anyone perhaps had any luck with a digital pen (USB graphic pen) application since? I want my students to be able to draw pictures, write math free hand, that sort of thing. I'd also like to write some lectures with it. Do you have any suggestions? Thank you!

Concerning teacher lecture lessons with hand drawn pictures, maybe this work of Marcelo might wok below. Has anyone tied it since August 2006? Thanks--Erich

 by Marcelo Rezende - Saturday, August 12, 2006, 01:05 AM Marcello wrote, "Hi All I'm a mathematician and I developed a whiteboard (freeware) that is a Skype plug-in. to teacher Math Please try it TalkAndWrite www.talkandwrite.com Marcelo"

Erich

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Re: Best pracitces for teaching Math(s) in Moodle

I'm working on putting a college level precalculus class online and while I do have the advantage of already knowing Latex I find that I commonly use the algebra syntax and it is very simple.  This is especially true if the teachers are already using graphing calculators or Excel in their classes as the syntax is just a combination of the two.  It is somewhat limited, but so far I haven't found much I can't get around, to the point that I will be expecting my students to use it as well in the fall.

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Re: Best pracitces for teaching Math(s) in Moodle

Hi All

I'm a mathematician and I developed a whiteboard (freeware) that is a Skype plug-in.

to teacher Math

Marcelo

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Re: Best pracitces for teaching Math(s) in Moodle

I'm interested in helping my colleagues learn more about what can be done in Moodle for testing and teaching maths (and Physics too actually).

Can anyone explain how they use Moodle for UK 'A'-level to first year university level maths (and Physics)?

It would be great to be able to show them an example quiz or course where the focus is on the maths rather than the features.

(I do love the features... but it's just the difference of looking at something from a maths' lecturer's point of view, rather than someone who's already wowed about Moodle).

Thanks!

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Re: Best pracitces for teaching Math(s) in Moodle

Hi Steve

I can comment  on A Level physics, where I use moodle mainly to support classroom learning:
• Loads of obvious stuff like links to handouts, useful websites; as of two weeks ago, pdf's of lessons done on my shiny new interactive whiteboard
• Wiki's for research projects - e.g. working in pairs to summarise features of energy resources
• Forums - to explain ideas to each other, like photoelectric effect; or to load and share results of experiments
• Lessons to  deliver content, mixed in with quizzes
In the coming soon department, moving revision podcasts from a loudblog installation into moodle.

The big thing this year is to build activities in moodle around a car racing simulation (Racing Academy - try not to get addicted to the download) - I'm planning sequences of activities, that may include forums and wikis for planning how to use the game and recording progress; reflective diaries etc. The materials will eventually be freely available.

All the best

Andy D

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Re: Best pracitces for teaching Math(s) in Moodle

By all means have a look at my Moodle course, which is aimed at year 13 Further Maths A Level students. It's early days so far, so it's nowhere near finished, but I thought I'd start using it straightaway and getting feedback from the students before I put in a million hours of effort into something that doesn't fit their needs:

I have edited the maths using Tex (the $$mathstuff$$ notation) and have found it very simple and easy to use, although I wouldn't dream of asking the students to try and get their heads round it...

http://webserver.churston.torbay.sch.uk/moodle/course/view.php?id=333

Feedback welcome!

At the moment I'm just using Moodle at A level to support delivery: notes, worked examples and links, and for posting the odd assignment. Haven't tried Wikis or Forums yet. Still looking for best practice out there.

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Re: Best pracitces for teaching Math(s) in Moodle

I´m a math teacher in an online secondary education institution, and we use moodle as CMS. Last year I had to build the contents of a math course, and actually I have to teach online with them. It´s very difficult. I´ve realized that the activities and resources uses are quite conditioned by the use of the math symbolic language. The students are technologically crippled to communicate with us in this language using the standard tools of moodle (we can´t expect a pupil to learn Tex). If we want they to solve exercises for us, they will have to make them in paper and therefore send them (except for students with scanner) by ordinary mail.
I use pdf and html formatted contents and use also a great tool to build interactive activities for math: the Descartes applet. This is a free java applet (spanish education ministery) that can achive lots of math goals, and can be easily integrated in moodle activities and resources. You can use it in almost situations.
To improve my work, now I´m testing the use of a tablet pc to record video-lectures (video handwriting whith voice), ink annotation on scanned works, the use of electronic ink as a way to overpass the writing problems in math, ..etc.

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Re: Best pracitces for teaching Math(s) in Moodle

Hi Jose,
After downloading Descartes, I'm wondering exactly how to integrate it into Moodle. Do I need to create a SCORM package? Please give us more details.

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Re: Best pracitces for teaching Math(s) in Moodle

John,

Did you ever receive any additional information from Jose regarding Descartes? The Ministry has a compete English Language version of their website up http://descartes.cnice.mecd.es/ingles/ and I was excited that they were offering a separate package of the applet and glue in one download and the lessons they had developed in another, but both links turned out not to work.....

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Re: Best pracitces for teaching Math(s) in Moodle

Hi Marc,
No, I didn't follow up. Just tried it again, and did notice broken links (and got a frozen browser window -- grr).

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Re: Best pracitces for teaching Math(s) in Moodle

Hi,

We have help support Maths teaching and learning by providing multimedia flash-based Maths Contents to provide the needed contents for teaching and to provide learning aids like assessments and lessons to help students in self-paced learning.

I'm wondering whether any of you guys here are interested to try out this approach with your students?

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Re: Best pracitces for teaching Math(s) in Moodlemultimedia flash-based Maths Contents

Can you explain how to provide multimedia flash-based Maths Contents, please?

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Re: Best pracitces for teaching Math(s) in Moodle

Greetings All,

My name is Robert and I teach HS math in SouthWest Kansas.  Here's my "Moodle Story."

I have held off doing anything with Moodle because of this very problem, (math symbols).  I once had LaTeX running (server-side script) through the LaTeXRender plugin.  A few months ago, my server went down, my ISP had to move all my stuff to another server and  .  .  .  Latex hasn't worked since.  That's the bad news!

The good news.  There is a client-side plugin called jsMath that is very easy to install, easy for high school kids to learn, and looks really good.  The only "technical" requirement (if you call it that) is possibly having to download and install the fonts on your local machine.  You can get instructions for this procedure from my wiki (mentioned below).

Problems that remain, as I see it;  Even with jsMath, (Tex or Latex), running properly, students cannot submit math sybols as quiz (test) answers.  Thus, we seem to be limited to asking multiple choice, true-false, or some select calculated (numerical) answers.  However, students can quite easily write/submit math expressions in all the other activities such as forums, etc.

The following is the link to the CVS site where you can download all the required files to install it as a Moodle filter:  http://moodle.cvs.sourceforge.net/moodle/contrib/plugins/filter/jsmath/

Not only am I now (as of just a couple of days ago) using it Moodle, but I'm also using it PMWiki.  This is a wonderful tool as well.  PMWiki is extremely easy to set-up (no ISP assistance required), easy to use, and with jsMath plugin installed, makes math notation easy for students.  I also use it extensively in many of my HTML pages.  It is a very versitile tool!

You may visit my wiki at the following address:  http://robertfant.com/PMWiki/pmwiki.php

If you would like to play around in the sandbox, just let me know and I can set you up with a password.

++++++++++

All that said, I am looking for ideas on setting up an online math course.  I now have almost all of the "tools" that I need, but now need ideas on "what an online (math) course looks like."  This probably sounds ridiculous  .  .  .  just being honest.

Another tool that I would like to bring to everyone's attention is GoeGebra.  If you are not familiar, do yourself a favor and check it out.  This is an open-source, Algebra, Geometry, and Calculus program.  { I could talk on this for a long time   }    Take a look at it and then consider, there is a plug-in to incorporate GeoGebra applets into Moodle.

OK, this is turning into a book;  I'm almost done.   I'll end with this, I am looking for folks (just like some of you) to collaborate with.   I am a one-man-band here at my location and must do everything myself.  Makes for some very long days.  I'm willing to share my tools and web-server if you'd be willing to share time, effort, and expertise.  Interested?    Visit my website and contact me.

Robert

P.S.  This is a test to see if the jsMath plugin is insalled on this site:

$$x = \frac{-b \pm sqrt{b^2-4ac}}{2s}$$

It kinda looks like they've got LaTeX installed.  jsMath typically looks much nicer than this.

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Re: Best pracitces for teaching Math(s) in Moodle

Students cannot submit math sybols as quiz (test) answers. Thus, we seem to be limited to asking multiple choice, true-false, or some select calculated (numerical) answers. However, students can quite easily write/submit math expressions in all the other activities such as forums, etc.

You can use an Essay question. Students can write LaTeX markup in the essay text area. Of course you must grade essay questions manually.

But this raises a philosophical question: Should we expect students of elementary mathematics to "write math" in LaTeX? I think not. They should be writing math directly in the language of mathematics. For extremely simple math, they can use typewriter math, e.g., 3x^2 + 2x + 5 = 0, but for anything more complicated, they should have a WYSIWYG editor. But without an integrated WYSIWYG equation editor in Moodle, the best we can do currently is have them use a tool like MathType or TeXaide to construct mathematical expressions in a WYSIWYG fashion, then paste the LaTeX into Moodle. That way, students can focus on the math, not the LaTeX. In any case, for quizzes you will need to use an Essay question and grade the answers manually.

If you are more adventurous, there are several projects underway to integrate computer algebra systems with Moodle (Webwork, AiM, Serving Mathematics -- see the Math tools forum).

Another concern is the lack of attachments in Essay questions. For example, students could then attach a GoeGebra worksheet that they created during an exam. I am also very enthusiastic about GeoGebra.

You'll find lots of discussions about LaTeX, jsMath, GeoGebra, computer algebra systems, and more in the Mathematics tools forum.

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Re: Best pracitces for teaching Math(s) in Moodle DEBIAN servers

I am running my moodle on a debian server and my post is specific to this. If you are having trouble with the built in algebra and TeX filters in moodle and are running on Debian, you should look into this solution for rendering.
Specifically if you run the TeX filter debugger (yourmoodlelocal/filter/tex/texdebug.php) and under the "show command execution" option you get the following message:
\$ /usr/bin/latex --interaction=nonstopmode /hermes/bosweb/web042/b425/ipw.peakperf/moodledata/temp/latex/d1e56126337cd6e29b16fe759232ce90.tex
OUTPUT: This is e-TeX, Version 3.14159-2.1 (Web2C 7.4.5)
I can't find the format file latex.efmt'!
RETURN CODE: 1
`
Then try jsMath.

After MUCH debugging attempts, I found that this is a (fixable) bug in debian. It is not a moodle issue, but a Debian issue, there is a fix but requires recoding Debian. Details on the issue and bug fix here: http://osdir.com/ml/debian.devel.documentation/2004-08/msg00043.html
Since I couldn't do that on my shared server, I went with jsMath and it works "out of the box".
jsMath can be found at http://www.math.union.edu/~dpvc/jsmath/
Make sure to install the font family included in case learners don't have the TeX fonts on their local machine (jsMath will substitute these if the TeX fonts are absent.)
I will also be providing a link to the TeX fonts for my learners in case they want to/have the skills(!?) to install them on their local machines. The link for the TeX fonts are at: http://www.math.union.edu/~dpvc/jsmath/download/jsMath-fonts.html

This was a seamless installation with minimal configuration and the install includes a test and debug file. I am very happy with it on my Debian server for which nothing included in moodle worked (again LaTeX issues)

Hope someone finds this helpful. This looks like a small forum and this is a pretty specific issue, but it might save someone else some time.

Also, you might consider it a plug for jsMath. It was an easy install and since it uses LaTeX syntax requires no learning if you know the language.

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Re: Best pracitces for teaching Math(s) in Moodle

Hi all,
I've been teaching Algebra, Geometry, Algebra 2 (and last year AP Statistics) for 8 years now in the "smallest" county in Maryland. (I was in business in Washington DC for 22 years before changing careers). Being a former business woman, I used technology pretty extensively (mind you I used it, I didn't create or correct it), so using such for teaching is "no big deal". ("Chalk and talk" was not the way I was "taught to teach".) What has become a big deal is the amount of time and energy that is consumed (and not easily regenerated) by the "format over content" battle (aka "style versus substance"). If something isn't "pretty" and/or interestingly and effectively formatted students don't stay engaged AND they focus on the way the material is presented instead of what the material is. This is exacerbated when we need to deal with special characters, symbols, and notations. Furthermore, "the answer" isn't what I want when students are demonstrating mastery of the material. I want to see their thinking, more often referred to as "show your work!" This becomes almost impossible without paper and pencil/pen. Most students don't know how to use MathType, nor is it "fast enough" when answering multiple questions as in quiz, test, or even class work formats. Furthermore, access to this software and to keeping it current is more costly than my county can afford. Lastly, many of my students do not have dependable access to computers and/or the Internet (being rural, dial-up is still the norm for most who can afford and need/want Internet access.)
I am surprised that there haven't been more recent posts to this discussion, am I missing something?
FYI, I use ActivInspire (on an interactive whiteboard in my classroom), I have a Wiki, I work with Quia.com to maintain some "games" for students to use to better learn the material, our grades are all maintained on-line (accessible 24/7 by parents and students) and now I'm trying to use Moodle as well. Frankly, these are too many things to maintain, when I was in business, we had many more resources to keep everything updated and current. As a teacher I find I'm pretty much a "one-woman-band" who feels more often like a "one-armed paper hanger".
Would love to know what recent revelations others have discovered to make using interactive technology work well for enhancing math learning without making teachers work 3 times as many hours. (I already put in 70+ hours a week which is as much if not more than I did in business for about 35% of the compensation. No, I did NOT get into teaching for the "money").
Cheers.
Lonnise

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Re: Best pracitces for teaching Math(s) in Moodle
Hi Lonnise, I can relate to all of that. I am coming to the conclusion that such things as computer-rooms, Internet and word processors are doing more harm than good.

I do not say this lightly, as I have noticed that this generation of students seem to think in terms of instant gratification - "I need an answer, and I need it now." They seem to get quite annoyed when it does not happen. As well, traditional skills, reading, writing, remembering are going down the gurgler faster and faster. "Why remember anything, we have the computer to remember for us," seems to be the attitude.

And here am I teaching computing studies, digital photography, multi-media, applications, web apps, dbi and a host of other technology courses. Heresy...

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Re: Best pracitces for teaching Math(s) in Moodle
Which is why young people will not read more than a few paragraphs and why J K Rowling has to work at Mc Donalds flipping burgers because young people will not read her overly long story books.

Every generation believes that the next generation is going to hell in a handbasket/handcart and that next generation says the same about the next to come along....

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Re: Best pracitces for teaching Math(s) in Moodle

Marcus,
you note: "I do not say this lightly, as I have noticed that this generation of students seem to think in terms of instant gratification - 'I need an answer, and I need it now.'"
I agree and encourage you to read

-mark w. matthews

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Re: Best pracitces for teaching Math(s) in Moodle

Hi Lonnise,

I have found your comment really interesting. It is true that there is a great amount of work behind using digital tools. Having coordinated teams of people reusing content seems the only way to solve it to me.

Regarding interactive technology for maths I would say that automatic or self evaluation of students is one of the interesting topics.

I suggest a couple of alternatives

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Re: Best pracitces for teaching Math(s) in Moodle

Hi Ramon:
Took a break to clear my "cerebral cache" and "adjust my attitude" and now I'm back. Thanks so much for the alternatives, I'm particularly intrigued by the WIRIS solution. Not sure I can convince my cash-starved County to purchase this, but it's worth a try.
Hope the last few months ("summer") have been great. Cheers.
Lonnise

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Re: Best pracitces for teaching Math(s) in Moodle
If they won't spring for WIRIS you can try the DragMath plugin (linked earlier). It sets up a decent online equation editor button in the Moodle editor toolbar.

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Re: Best pracitces for teaching Math(s) in Moodle
I want to see their thinking, more often referred to as "show your work!"

I don't think their thinking can be seen. All you have is some end product, whether the end result or a snapshot of some arbitrary moment in the process. But why do you need to see their thinking anyway? See this (indirectly) related fable for an a possible approach.

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text:
for Journals by Title or ISSN for Articles by Keywords help
 Subjects -> MATHEMATICS (Total: 947 journals)     - APPLIED MATHEMATICS (82 journals)    - GEOMETRY AND TOPOLOGY (20 journals)    - MATHEMATICS (701 journals)    - MATHEMATICS (GENERAL) (43 journals)    - NUMERICAL ANALYSIS (22 journals)    - PROBABILITIES AND MATH STATISTICS (79 journals) MATHEMATICS (701 journals)                  1 2 3 4 | Last

1 2 3 4 | Last

 Computational and Applied Mathematics   [SJR: 0.515]   [H-I: 15]   [2 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 0101-8205 - ISSN (Online) 1807-0302    Published by Springer-Verlag  [2351 journals]
• A descent algorithm for generalized complementarity problems based on
generalized Fischer-Burmeister functions
• Authors: Mohamed A. Tawhid; Wei-Zhe Gu; Benjamin Tran
Pages: 1 - 26
Abstract: We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are $$C^1$$ . Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0328-6
Issue No: Vol. 37, No. 1 (2018)

• Time-parallel solutions to differential equations via functional
optimization
• Authors: C. Lederman; R. Martin; J.-L. Cambier
Pages: 27 - 51
Abstract: We describe an approach to solving a generic time-dependent differential equation (DE) that recasts the problem as a functional optimization one. The techniques employed to solve for the functional minimum, which we relate to the Sobolev Gradient method, allow for large-scale parallelization in time, and therefore potential faster “wall-clock” time computing on machines with significant parallel computing capacity. We are able to come up with numerous different discretizations and approximations for our optimization-derived equations, each of which either puts an existing approach, the Parareal method, in an optimization context, or provides a new time-parallel (TP) scheme with potentially faster convergence to the DE solution. We describe how the approach is particularly effective for solving multiscale DEs and present TP schemes that incorporate two different solution scales. Sample results are provided for three differential equations, solved with TP schemes, and we discuss how the choice of TP scheme can have an orders of magnitude effect on the accuracy or convergence rate.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0319-7
Issue No: Vol. 37, No. 1 (2018)

• Boundary node Petrov–Galerkin method in solid structures
• Authors: M. Li; F. F. Dou; T. Korakianitis; C. Shi; P. H. Wen
Pages: 135 - 159
Abstract: Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0335-7
Issue No: Vol. 37, No. 1 (2018)

• Fast Fourier Transform for multivariate aggregate claims
• Authors: Elena-Gratiela Robe-Voinea; Raluca Vernic
Pages: 205 - 219
Abstract: The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this paper, we extend it to a multivariate setting by considering its application to a particular model that includes losses of different types and dependency between them. Since the Fourier transform method works with truncated claims distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To eliminate this problem, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0336-6
Issue No: Vol. 37, No. 1 (2018)

• A relaxed two-step splitting iteration method for computing PageRank
• Authors: Ya-Jun Xie; Chang-Feng Ma
Pages: 221 - 233
Abstract: In this paper, we extend the two-step matrix splitting iteration approach by introducing a new relaxation parameter. The main idea is based on the inner–outer iteration for solving the PageRank problems proposed by Gleich et al. (J Sci Comput 32(1): 349–371, 2010) and Bai (Numer Algebra Cont Optim 2(4): 855–862, 2012) and the two-step splitting iteration presented by Gu et al. (Appl Math Comput 271: 337–343, 2015). The theoretical analysis results show that the proposed method is efficient. Numerical experiments demonstrate that the convergence performances of the method are better than the existing methods.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0338-4
Issue No: Vol. 37, No. 1 (2018)

• Spatially dependent regularization parameter selection for total
generalized variation-based image denoising
• Authors: Tian-Hui Ma; Ting-Zhu Huang; Xi-Le Zhao
Pages: 277 - 296
Abstract: We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization parameter is utilized to adaptively fit the local image features, resulting in further exploitation of the denoising potential of the TGV regularization. The proposed model is formulated under a joint optimization framework, by which the estimations of the restored image and the regularization parameter are achieved simultaneously. Furthermore, the model is general purpose that can handle various types of noise occurring in image processing. An alternating minimization-based numerical scheme is especially developed, which leads to an efficient algorithmic solution to the nonconvex optimization problem. Numerical experiments are reported to illustrate the effectiveness of our model in terms of both peak signal-to-noise ratio and visual perception.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0342-8
Issue No: Vol. 37, No. 1 (2018)

• Asymptotic analysis of the fluid flow with a pressure-dependent viscosity
in a system of thin pipes
• Authors: Eduard Marušić-Paloka; Igor Pažanin
Pages: 297 - 305
Abstract: We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity–pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff’s law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity–pressure relation satisfied by other empiric laws.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0345-5
Issue No: Vol. 37, No. 1 (2018)

• A fast eigenvalue approach for solving the trust region subproblem with an
• Authors: M. Salahi; A. Taati
Pages: 329 - 347
Abstract: In this paper, we study the extended trust region subproblem (eTRS) in which the trust region intersects the Euclidean ball with a single linear inequality constraint. By reformulating the Lagrangian dual of eTRS as a two-parameter linear eigenvalue problem, we state a necessary and sufficient condition for its strong duality in terms of an optimal solution of a linearly constrained bivariate concave maximization problem. This results in an efficient algorithm for solving eTRS of large size whenever the strong duality is detected. Finally, some numerical experiments are given to show the effectiveness of the proposed method.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0347-3
Issue No: Vol. 37, No. 1 (2018)

• Valuing catastrophe bonds involving correlation and CIR interest rate
model
• Authors: Piotr Nowak; Maciej Romaniuk
Pages: 365 - 394
Abstract: Natural catastrophes lead to problems of insurance and reinsurance industry. Classic insurance mechanisms are often inadequate for dealing with consequences of catastrophic events. Therefore, new financial instruments, including catastrophe bonds (cat bonds), were developed. In this paper we price the catastrophe bonds with a generalized payoff structure, assuming that the bondholder’s payoff depends on an underlying asset driven by a stochastic jump-diffusion process. Simultaneously, the risk-free spot interest rate has also a stochastic form and is described by the multi-factor Cox–Ingersoll–Ross model. We assume the possibility of correlation between the Brownian part of the underlying asset and the components of the interest rate model. Using stochastic methods, we prove the valuation formula, which can be applied to the cat bonds with various payoff functions. We use adaptive Monte Carlo simulations to analyze the numerical properties of the obtained pricing formula for various settings, including some similar to the practical cases.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0348-2
Issue No: Vol. 37, No. 1 (2018)

• Jacobian consistency of a one-parametric class of smoothing
Fischer–Burmeister functions for SOCCP
• Authors: Xiaoni Chi; Yang Wang; Zhibin Zhu; Zhongping Wan
Pages: 439 - 455
Abstract: The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for second-order cone complementarity problems proposed by Tang et al. (Comput Appl Math 33:655–669, 2014). Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by Chen et al. (Math Comput 67:519–540, 1998), and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0352-6
Issue No: Vol. 37, No. 1 (2018)

• Relaxation oscillations in predator–prey model with distributed
delay
• Authors: Na Wang; Maoan Han
Pages: 475 - 484
Abstract: The predator–prey model with distributed delay is stated in present paper. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illuminated, and the existence of the relaxation oscillation is proved. It is indicated the characteristic of the relaxation oscillation is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. One case study is given to demonstrate the validity of theoretical results.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0353-5
Issue No: Vol. 37, No. 1 (2018)

• Ordered indices of the production structure of manufacturing systems based
on an information-theoretic approach
• Authors: Zhifeng Zhang; Dahai Rao; Hanyu Zuo; Xinyu Zhang
Pages: 501 - 514
Abstract: The production structure of a manufacturing system not only influences its transportation and operation cost, but also affects logistics and parts/machine assignment decisions. Based on the sending and feedback mechanisms of information, the principles of conditional entropy and classical probability are utilized to establish structure entropy models and ordered indices of the system with dynamic characteristics and generality, which provide effective solutions for the absence of quantitative method in evaluating the structural optimization of production system. In an empirical study, this paper analyzes different production structures when workpieces are processed by different working routes before and after the implementation of cellular manufacturing. Afterwards, the developed structure entropy models and ordered indices are utilized to calculate the orderliness of production structure under the two different states. The final result verifies well the validity of this quantitative method for evaluating the orderliness of production structures.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0354-4
Issue No: Vol. 37, No. 1 (2018)

• A new relaxed splitting preconditioner for the generalized saddle point
problems from the incompressible Navier–Stokes equations
• Authors: Yi-Fen Ke; Chang-Feng Ma
Pages: 515 - 524
Abstract: Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0357-1
Issue No: Vol. 37, No. 1 (2018)

• Balanced truncation-rational Krylov methods for model reduction in large
scale dynamical systems
• Authors: O. Abidi; K. Jbilou
Pages: 525 - 540
Abstract: In this paper, we consider the balanced truncation method for model reductions in large-scale linear and time-independent dynamical systems with multi-inputs and multi-outputs. The method is based on the solutions of two large coupled Lyapunov matrix equations when the system is stable or on the computation of stabilizing positive and semi-definite solutions of some continuous-time algebraic Riccati equations when the dynamical system is not stable. Using the rational block Arnoldi, we show how to compute approximate solutions to these large Lyapunov or algebraic Riccati equations. The obtained approximate solutions are given in a factored form and used to build the reduced order model. We give some theoretical results and present numerical examples with some benchmark models.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0359-z
Issue No: Vol. 37, No. 1 (2018)

• A modified homotopy method for solving the principal-agent bilevel
programming problem
• Authors: Zhichuan Zhu; Bo Yu
Pages: 541 - 566
Abstract: In this paper, the principal-agent bilevel programming problem with integral operator is considered, in which the upper-level object is the agent that maximizes its expected utility with respect to an agreed compensation contract. The constraints are the principal’s participation and the agent’s incentive compatibility. The latter is a lower-level optimization problem with respect to its private action. To solve an equivalent single-level nonconvex programming problem with integral operator, a modified homotopy method for solving the Karush–Kuhn–Tucker system is proposed. This method requires only an interior point and, not necessarily, a feasible initial approximation for the constraint shifting set. Global convergence is proven under some mild conditions. Numerical experiments were performed by our homotopy method as well as by fmincon in Matlab, LOQO and MINOS. The experiments showed that: designing a piecewise linear contract is much better than designing a piecewise constant contract and only needs to solve a much lower-dimensional optimization problem and hence needs much less computation time; the optimal value of the principal-agent model with designing piecewise linear contract tends to a limitation, while the discrete segments gradually increase; and finally, the proposed modified homotopy method is feasible and effective.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0361-5
Issue No: Vol. 37, No. 1 (2018)

• Optimal control of anthropogenic carbon dioxide emissions through
technological options: a modeling study
• Authors: Maitri Verma; A. K. Misra
Pages: 605 - 626
Abstract: The anthropogenic emission of carbon dioxide ( $$\mathrm{CO}_{2}$$ ) is the prime culprit for the menace of global warming. To achieve the goal of mitigation of global warming, it is crucial to curb the anthropogenic carbon dioxide emissions. The prime anthropogenic source of $$\mathrm{CO}_{2}$$ is fossil fuel burning. In this paper, we propose a nonlinear mathematical model to study the impact of technological options, used for the reduction of $$\mathrm{CO}_{2}$$ emissions from fossil fuel burning and industrial processes, on the control of atmospheric $$\mathrm{CO}_2$$ . In the modeling process, it is assumed that the technological options are implemented to curb the $$\mathrm{CO}_{2}$$ emissions from the source at a rate proportional to the anthropogenic $$\mathrm{CO}_{2}$$ emissions. Model analysis reveals that the atmospheric level of $$\mathrm{CO}_{2}$$ can be effectively reduced by increasing the implementation rate of technological options and their efficiency. The strategies which optimally reduce atmospheric $$\mathrm{CO}_{2}$$ levels while minimizing the cost associated with the implementation of technological options are identified using optimal control theory. Numerical simulation has been carried out to illustrate theoretical results.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0364-2
Issue No: Vol. 37, No. 1 (2018)

• Using a meshless kernel-based method to solve the Black–Scholes
variational inequality of American options
• Authors: M. Moradipour; S. A. Yousefi
Pages: 627 - 639
Abstract: Under the Black–Scholes model, the value of an American option solves a free boundary problem which is equivalent to a variational inequality problem. Using positive definite kernels, we discretize the variational inequality problem in spatial direction and derive a sequence of linear complementarity problems (LCPs) in a finite-dimensional euclidean space. We use special kind of kernels to impose homogeneous boundary conditions and to obtain LCPs with positive definite coefficient matrices to guarantee the existence and uniqueness of the solution. The LCPs are then successfully solved iteratively by the projected SOR algorithm.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0351-7
Issue No: Vol. 37, No. 1 (2018)

• Optimal control of mathematical models for the radiotherapy of gliomas:
the scalar case
• Authors: Enrique Fernández-Cara; Laurent Prouvée
Pages: 745 - 762
Abstract: This paper deals with the optimal control of a mathematical model of glioma progression incorporating the basic facts of the evolution of primary brain tumors. We will consider a model of the simplest possible kind, based on the Fischer-Kolmogorov equations, using ideas from Pérez-García (Mathematical models for the radiotherapy of gliomas (preprint), 2016). The control is the 2n-tuple $$(t_1, \ldots , t_n; d_1, \ldots , d_n)$$ , where $$d_i$$ is the i-th applied radiotherapy dose and $$t_i$$ is the i-th administration for $$1 \le i \le n$$ . We search for controls that maximize the survival time, that is, the time at which the tumor mass reaches a critical value $$M_{*}$$ , over the class of admissible radiation times and doses. We present theoretical and numerical results that justify the relevance of the model and the existence of potential medical applications.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0366-0
Issue No: Vol. 37, No. 1 (2018)

• A predator–prey model with additional food supply to predators:
dynamics and applications
• Authors: Dinesh Kumar; Siddhartha P. Chakrabarty
Pages: 763 - 784
Abstract: In this paper, we present a modified ratio-dependent model by incorporating the supply of additional food to the predators. We analyze the dynamics of this modified model and as well as the ecological consequences of the additional food supply. The model exhibits a way of control over the predator–prey system by the appropriate handling of the quantity and quality of the additional food. An appropriate choice of these could lead to conservation of the species as well as biological control of a pest population.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0369-x
Issue No: Vol. 37, No. 1 (2018)

• Bicubic partially blended rational fractal surface for a constrained
interpolation problem
• Authors: A. K. B. Chand; P. Viswanathan; N. Vijender
Pages: 785 - 804
Abstract: This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.
PubDate: 2018-03-01
DOI: 10.1007/s40314-016-0373-1
Issue No: Vol. 37, No. 1 (2018)

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text:
Lessons:16Length:2.7 hours
• Overview
• Transcript

# 3.1 Closing

We’re done, and you’ve learned the basics! Now I get to point you towards the way of learning languages and the environments you’ll use them in.


text:
# Perpendicular orbitals in aryl and vinyl carbocations? [duplicate]

This point (iv) has been given under reasons for extremely low reactivity of aryl and vinyl halides. I cannot understand it. First of all, isn't the positive carbon atom in phenyl as well as vinyl carbocation sp-hybridized. But in the point, the positively charged carbon atom of the phenyl carbocation is referred to as sp2-hybridized. I cannot understand why. Also I cannot understand the "perpendicular part". That the orbitals are perpendicular and so the carbocation is not formed. But how are they perpendicular and how does this hinder the formation of carbocation. I cannot understand the last diagram (for vinyl carbocation). Please help.

## marked as duplicate by Mithoron, andselisk♦, Todd Minehardt, Mathew Mahindaratne, Nuclear ChemistFeb 10 at 15:24

• No, I do not think my question is a duplicate. My concerns are a bit different. If you read my question properly, you can understand. My question is mainly about why the perpendicularity of the orbitals destabilizes the carbocation, the hybridization of the carbon atoms and the meaning of the last diagram. – MrAP Feb 9 at 19:46

While the dissociation drawn in your reference for halogen is unlikely, I would however object the idea that aryl cations can not exist. The intermediate generation of the aryl diazonium ion at low temperatures, typically followed by release of nitrogen gas (triple bond $$\ce{N#N}$$) is one of rare cases where this high energy situation may be compensated, offering a wide array of subsequent chemistry.


text:
# scipy.signal.tukey¶

scipy.signal.tukey(M, alpha=0.5, sym=True)[source]

Return a Tukey window, also known as a tapered cosine window.

Parameters: M : int Number of points in the output window. If zero or less, an empty array is returned. alpha : float, optional Shape parameter of the Tukey window, representing the fraction of the window inside the cosine tapered region. If zero, the Tukey window is equivalent to a rectangular window. If one, the Tukey window is equivalent to a Hann window. sym : bool, optional When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis. w : ndarray The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).

References

 [R303] Harris, Fredric J. (Jan 1978). “On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform”. Proceedings of the IEEE 66 (1): 51-83. DOI:10.1109/PROC.1978.10837
 [R304] Wikipedia, “Window function”, http://en.wikipedia.org/wiki/Window_function#Tukey_window

Examples

Plot the window and its frequency response:

>>> from scipy import signal
>>> from scipy.fftpack import fft, fftshift
>>> import matplotlib.pyplot as plt

>>> window = signal.tukey(51)
>>> plt.plot(window)
>>> plt.title("Tukey window")
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")
>>> plt.ylim([0, 1.1])

>>> plt.figure()
>>> A = fft(window, 2048) / (len(window)/2.0)
>>> freq = np.linspace(-0.5, 0.5, len(A))
>>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
>>> plt.plot(freq, response)
>>> plt.axis([-0.5, 0.5, -120, 0])
>>> plt.title("Frequency response of the Tukey window")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")

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