text:
#### General Information

NOTE: The information on the current version of this page should be generally correct, but we may make some additions and changes between now and the start of classes.

Course Goals
This course is a sequel to MATH 3 and is appropriate for students who have successfully completed an AB calculus curriculum in secondary school. The first third of the course is devoted to topics in one-variable calculus such as Taylor series, and techniques and applications of integration. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables. Topics include limits and continuity, partial derivatives, tangent planes and differentials, the Chain Rule, directional derivatives, and optimization problems including the use of Lagrange multipliers.
Overall course goal: Students will be able to solve problems on these topics and their applications, and to explain their solutions.

Teaching Methods
During a typical class period, we may use the projector, use the blackboard, ask questions of the class, and ask for individual or small group work on your own in class. We ask you to work on problems in class because this is a good way to learn, and we call on you to ask for your ideas on a topic because we want to get feedback and hear from everyone. This should not be regarded as a performance test.

General Expectations
Attendance in class is highly desirable but not mandatory. However, class participation may be considered in assigning letter grades in borderline cases.
Homework is assigned each class day. Information about due dates and grading policies is in the Homework section below. We encourage you to discuss your grading concerns early in the term.
Please make ample use of the office hours, which offer you one-on-one teaching and provide us with valuable feedback. Also, please make use of the tutorials.

Textbook
Calculus (eighth edition) by James Stewart (ISBN: 978-1-285-74062-1)

Scheduled Lectures
(Section 1) Jones MWF 10:10 - 11:15
(x-hour) Th 12:15 - 1:05
105 Kemeny
(Section 2) Groszek MWF 11:30 - 12:35
(x-hour) Tu 12:15 - 1:05
007 Kemeny
(Section 3) Lafreniere MWF 12:50 - 1:55
(x-hour) Tu 1:20 - 2:10
007 Kemeny
Math 8 will occasionally use x-hours, for example if classes need to be rescheduled, so please keep the x-hour open. We will use the first x-hour for an optional calculus review session.

Instructors Office Office Hours Email Office Hour Location
Professor M. Jones Office: 216 Kemeny Hall Office Hours: M 2-3, W 1-2, Th 12:15-1:15, F 11:30-12:30 Email 216 Kemeny
Professor M. Groszek Office: 330 Kemeny Hall Office Hours: M 1-2:30, Th 1:45-3:15, and by appt. Email 330 Kemeny
Professor N. Lafreniere Office: 318 Kemeny Hall Office Hours: M 10-11, W 9-11, F 9-10 Email 229 Kemeny

Exams
Midterm Exam 1 Wednesday, October 9, 2019 4:00-6:00pm Room Silsby 28
Midterm Exam 2 Wednesday, October 30, 2019 4:00-6:00pm Room Silsby 28
Final Exam Friday, November 22, 2019 11:30am - 2:30pm Room Silsby 28

Homework

There are three kinds of homework, described below. Written homework will be posted to the assignments page.

We do not accept late homework. Missing homework is counted as zero. Missing homework can be excused only in the event of serious and unexpected problems such as extended illness or family emergency.

WeBWorK is online homework; there is more about the WeBWorK system below. WeBWorK is assigned each class day, and due by 10am on the next class day, so homework assigned Monday is due on Wednesday, homework assigned Wednesday is due on Friday, and homework assigned on Friday is due on Monday.

Preliminary written homework is assigned each class day, and is due at the beginning of the next class. You should submit preliminary homework by bringing it to class with you. Preliminary homework is designed to get you started thinking about the topic we are about to discuss. It is graded credit or no credit, and you do not have to get the problems right in order to get credit. Your work must show that you have thought about the problems and tried to do them. The lowest 2 preliminary homework grades will be dropped when we compute your final grade.

Standard written homework, generally called simply written homework, is assigned each class day, and is due by 10am on the following Monday. Submit written homework by putting it in the homework boxes in the basement of Kemeny Hall (outside room 008). Written homework will be graded on both the correctness of your solutions and the completeness, correctness, and clarity of your work and explanations. Explaining your work both demonstrates your understanding and helps your learning. Try to write so that another student in the class, who does not understand the material as well as you do and has not yet thought about this homework problem, would be easily able to understand your reasoning.

Each day's written homework will be graded on a scale of 0-10. You can get 5 points for making a good attempt at all parts of the problem. To get 10 points, your solution must be correct and your work or explanations must also be correct and understandable. Remember that on exams we will grade your work and your explanations, so written homework is good practice. Your lowest written homework grade will be dropped when we compute your final grade.
0: Did not do.
5: Attempted the assignment.
6: Made some progress; either got some answers correct, or began with a correct procedure, or gave a reasonable explanation of something.
7: Got at least some things mostly right.
8: Got half or more of the assignment right, or got most of the assignment right but explanations were clearly lacking, or got only a few things right but explanations were complete and exemplary.
9: Mostly right and mostly clearly explained.
10: Completely right with work clearly shown and reasoning clearly explained.

Both kinds of written homework should be submitted on standard sized (8.5 by 11) paper, with no ragged edges, using one side only. (It is fine to use the blank side of scratch paper, as long as you obviously cross out anything on the reverse side.) Please state each problem before launching into your solution. You do not have to repeat the problem word for word, but we should be able to grade your homework without looking the problems up. Also, it is good practice to begin by saying what you are about to do. Please write neatly; if we cannot read your homework, we cannot grade it. If your handwriting is less than stellar, writing large and leaving enough white space can go a long way.

Due dates summary: WeBWorK assigned each class is due at 10am the following class day, and is submitted online. Preliminary homework assigned each class is due at the beginning of the next class, and is submitted in class. Written homework assigned each class day is due at 10am the following Monday, and is submitted in homework boxes outside Kemeny 008.

We encourage you to work together. On written homework, you must write up your answers yourself. You may work together on WeBWorK using the practice accounts. Consult the honor principle (below) as it applies to this course.

WeBWorK

WeBWorK is an online homework system we will use in Math 8. You should receive a message welcoming you to WeBWorK and telling you how to log on. Start with the Day0 assignment, which will help you navigate the system. (To get started, select Homework Sets from the main menu, click on Day0, click on Problem 1, type your answers in the boxes, and click on Submit Answers.)

When you have finished a problem, you can use the Preview button to make sure you have entered things correctly. You submit your answers by clicking the Submit button when you have finished each problem. The system will tell you whether your answer is correct. If you get something wrong, you can try again, repeatedly if necessary.

One of the features of WeBWorK is that each student is assigned a slightly different version of the problems. We have created accounts that you can use for practice, or to work together, that have their own versions of the problems, which should be slightly different from yours. You can use these accounts to work together, or with a tutor, to learn how to do the homework problems before you do your assignment. To log on to practice account number 1, use the login name practice1 and the password practice1. There are twenty practice accounts numbered 1 to 20, so if one is busy, you can use another.

Clicking on WeBWorK at the top of this page will take you to the WeBWorK login page.

The course grade will be based upon the scores on the midterm exam, homework, and the final exam as follows.
Preliminary Homework 2 percent
Written Homework 5 percent
WeBWorK 8 percent
Midterm Exams 25 percent (each)
Final Exam 35 percent

For students whose grades fall just below a division between letter grades, we may consider factors such as a consistent record of improvement.

The following conversion gives guaranteed minimum letter grades based on your numerical grade. We reserve the right to grade more generously, depending on the difficulty of our exams and homework. This means a grade of 89% will definitely be at least a B+ but may be an A-. A grade of 90 will always be at least an A-. On the other hand, a grade below 50% definitely is not passing.
Grade guarantees: 95% A; 90% A-; 85% B+; 80% B ; 75% B-; 70% C+; 65% C; 60% C-; 50% pass.

The Honor Principle

Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.

Homework: Collaboration is permitted and encouraged, but no copying , and to be clear, this means no copying even from a board or scrap of paper on which a solution was hashed out collaboratively. What a student turns in as a homework solution is to be his or her own understanding of how to do the problems. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Academic Honor Code.

Moreover, if in working with someone they have provided you with an important idea or approach, they should be explicitly given credit in your writeup. Hints given in office hours need not be cited. Note: It is not sufficient to annotate your paper with a phrase like I worked with Joe on all the problems.'' Individual ideas are to be credited at each instance; they represent intellectual property.

We do encourage collaboration. You can work with anyone, and consult any person or source that will help you learn the material. Giving another person credit for an idea will never lower your grade. You get credit for your understanding no matter how you acquired it.

On WeBWorK, you may work together using the practice accounts (described above), but you should do your individual problems yourself. This applies if you have a tutor, as well. You can work with your tutor on the practice accounts to learn how to do the problems, but you should do your individual problems yourself. If you can do the practice account problems but something goes wrong with your individual problem, please ask for help in office hours or at tutorial.

Exams: On exams, you may not receive assistance of any kind from any source (living, published, electronic, etc), except the professor, you may not consult any written materials including your notes and textbook, and you may not give assistance to anyone. Once you begin working on the exam, you should not consult any electronic devices, including calculators and phones, until you are finished.

Matters of clarification are to be left to the professor.

In General: If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to us, and we will be glad to help clarify things. It is always easier to ask beforehand.

Tutorials
Tutorial assistance for this course, that is, help with your homework or other questions about the course material, will be available in 008 Kemeny, Sunday, Tuesday, and Thursday evenings 7 - 9pm. Tutorials will begin on Tuesday, September 17. Your tutors are Richard Haburcak, Albert Chang, and Benjamin Adenbaum.

Study Groups
There will be four different study groups for Math 8, each meeting once a week. The current meeting days and times are: Saturdays, 1:30pm-3:00pm; Mondays, 7:30pm-9:00pm; Mondays 9:00pm-10:30pm; Thursdays, 5:00pm-7:00pm. Study groups meet beginning Thursday, September 26, and ending Tuesday, November 19. They are led by students who have been successful at learning this material and have been trained as group leaders.

You can sign up for a study group on the Study Groups registration website beginning noon on Wednesday, September 25.

Accessibility, Religious Observances, etc.
The following statements cover a number of specific issues. However, we are here in general to help you. Please come to your instructor's office hours if you have any questions or problems, about the material, about the course, or about anything else we as faculty members may be able to help you with.

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see their instructor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (205 Collis Student Center, 646-9900, Student.Accessibility.Services@Dartmouth.edu). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their instructor. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.

Students who have some other conflict with exams, such as a job, lab period, or extracurricular activity, should consult their instructor as soon as possible. While your academic commitments take priority, we are often able to accommodate your other commitments, provided we have enough advance notice.

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean , Counseling and Human Development ), and the Student Wellness Center ). We encourage you to use these resources to take care of yourself throughout the term, and to come speak to us if you experience any difficulties.

The Sexual Respect Website at Dartmouth provides a wealth of information on your rights with regard to sexual respect and resources that are available to all in our community. Please note that, as a faculty member, I am obligated to share disclosures regarding conduct under Title IX with Dartmouth's Title IX Coordinator. Confidential resources are also available, and include licensed medical or counseling professionals (e.g., a licensed psychologist), staff members of organizations recognized as rape crisis centers under state law (such as WISE), and ordained clergy (see here. Should you have any questions, please feel free to contact Dartmouth's Title IX Coordinator or the Deputy Title IX Coordinator for the Guarini School. Their contact information can be found on the sexual respect website.

Marcia Groszek
Last updated October 31, 2019


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# Checking Word Grids

Given a list of words, check if they form a valid word grid. They form a valid grid if there are N words with N letters and they spell the same words vertically as they do horizontally. The words can be given in any order. [FILE, ICED, LEAD, EDDY] = True and [FILE, LEAD, EDDY, ICED] = True. Print True if it is valid or False if it is not

Here's some more examples

F I L E
I C E D
L E A D
E D D Y

O G R E
G A I A
R I G S
E A S Y

C A M P
A X E L
M E M O
P L O W

S P A S M
P A S T A
A S P E N
S T E E L
M A N L Y

This is code golf so lowest bytes wins

• So we have to check all permutations of the input right? – Maltysen Jul 22 '15 at 19:44
• @Maltysen Correct. Permutations of the words not the letters in the words – SirParselot Jul 22 '15 at 19:46
• Any truthy/falsy values are fine, or the exact strings "True" and "False" ? – Optimizer Jul 22 '15 at 19:51
• @SirParselot Probably because they find the challenge is fairly trivial / uninteresting. – Kade Jul 22 '15 at 20:24
• @SirParselot I might also guess someone is unhappy their language has to convert to True/False while others have them natively. – xnor Jul 23 '15 at 1:51

# Pyth - 10 9 bytes

The actual check is very easy, in just three bytes with CIQ. The permutation part takes the other 6.

.EmCId.pQ

It maps over the .permutations of the (Q) input, each time checking if the loop var(d) is Invarient under (C) rotation. Then it checks if .Eany are true.

## CJam (25 24 bytes)

q~e!{_z=},"True""False"?

Online demo. Pretty trivial apart from the specified output, because CJam doesn't have a Boolean type.

With thanks to Sp3000 for saving one stroke.

• @Sp3000, true. I'm so used to expecting the interleaved string approach to be shorter that I didn't even try the naïve approach. – Peter Taylor Jul 22 '15 at 20:09
• Has Peter abandoned GolfScript in favor of CJam?? – Alex A. Jul 22 '15 at 20:17
• @AlexA., not entirely. But for this question, GS can't possibly get anywhere near CJam. e! would require writing a recursive function in GS: that's 6 characters before it even does anything. – Peter Taylor Jul 22 '15 at 20:22

# Julia, 114 bytes

Did somebody say "super long solution"?? It just so happens that I have one for you.

a->(L=length(a);P(x)=reshape(split(join(x),""),L,L);print(any([P(p)==P(p)'for p=permutations(a)])?"True":"False"))

This creates an unnamed function that accepts an array and prints to stdout. It works by generating all permutations, turning the arrays into matrices of letters and checking whether each matrix is equal to its transpose. Unfortunately booleans are lowercase in Julia, otherwise I wouldn't have had to do the ternary.

import Data.List
any((==)=<<transpose).permutations

Usage example: any((==)=<<transpose).permutations $["LEAD","FILE","ICED","EDDY"] -> True. How it works: check if any of the permutations equals it's transposition. Luckily Haskell's native boolean values are True and False. # Python 2, 87 85 Bytes Straightforward solution using zip() to transpose. Saved two bytes on both thanks to xnor. from itertools import* print any(zip(*c)==map(tuple,c)for c in permutations(input()))  Solution without relying on imports, 139 138 136 Bytes p=lambda l:[[j]+k for i,j in enumerate(l)for k in p(l[:i]+l[-~i:])]if~-len(l)else[l] print any(zip(*c)==map(tuple,c)for c in p(input()))  If there's a way to get around using enumerate, let me know! :) Input for both should be formatted like so: ["FILE","ICED","EDDY","LEAD"]  Psst. Hey! Here's a solution in Symbolic, something I'm working on. Ƥ(Ʌ(ʐ(*c)==ϻ(ϰ,c)ϝcϊƥ(Ί))) • You can do any() for sum()>0. – xnor Jul 22 '15 at 22:07 • are you submitting this for the bounty? – Maltysen Jul 23 '15 at 1:49 • @Maltysen No, I just did it because I was experimenting :) – Kade Jul 23 '15 at 1:55 • Symbolic looks really cool! But fyi, the 31 characters in that solution make for a score of 41 bytes in UTF-8. It may not be the most competitive golfing language. ;) – Alex A. Jul 23 '15 at 15:20 • @AlexA. I don't think I could make anything on the level of Pyth/CJam/GolfScript, I'm just doing it for fun ;P – Kade Jul 23 '15 at 15:22 # Python 2, 74 s=input().split() print all(''.join(s)[s.index(w)::len(w)]in s for w in s)  # Brachylog, 6 bytes p⟨\=≡⟩  Try it online! Assuming output can be "true." and "false." instead of "True" and "False". If not, it's a trivial change to: ### 22 bytes p⟨\=≡⟩∧"True"|∧"False"  Try it online! # Mathematica (48 42 bytes) Or@@(#==#&/@Characters@Permutations@#)&  Luckily Transpose can be represented by a single unicode character. •  is this the character for transpose? I found a different one on wolfram's website – SirParselot Jul 22 '15 at 20:42 • Yes, U+F3C7. But it actually doesn't render correctly on my system. Copy&Pasting the code however works fine. – murphy Jul 22 '15 at 20:52 # JavaScript ES6, 90 58 bytes s=>s.every((l,i)=>s.map(p=>p[i]).join==l)?'True':'False'  Old answer: s=>~(n=s.split ).map((l,i)=>n.map(p=>p[i*2]).join ==l).indexOf(!1)?'False':'True'  The newline is significant and counts as a byte. ES5 Demo: function t(s) { return ~(n=s.split('\n')).map(function(l,i){return n.map(function(p){return o=p[i*2]}).join(' ')==l}).indexOf(!1)?'False':'True' } // Demo document.getElementById('go').onclick=function(){ document.getElementById('output').innerHTML = t(document.getElementById('input').value) };

Word Grids Snippet

<textarea placeholder="Text here..." style="resize:none;width:70px;height:70px;border:1px solid #DDD;" id="input"></textarea><button id='go'>Run!</button>

Output:

 • Note: The code snippet will only return true if there is a single space between each letter in the code grid, as in the OP examples. – Ayelis Jul 22 '15 at 23:02 # Ruby, 97 bytes 91 bytes if we remove .chomp inside map a=gets.chomp.split','.map{|_|_.chomp.chars};p a.permutation.map{|p|p[0].zip(*p[1..-1])===p}.any?  # MATLAB - 75 98 bytes Note: I didn't see that you had to output True or False, so I had to create an additional cell array that stores these two choices then we choose from this array when we're done. This is a rather brute-force solution. This assumes that you have loaded A in as a character matrix and that A is symmetric in size (i.e. # of rows is equal to # of columns): c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1}  The overall process is to first create a 2D array of all possible permutations that goes from 1 up to as many words as we have N. Each row of this matrix gives you a permutation enumerated from 1 up to N, and we can check either the number of rows or columns for the value N. Next, we go through every possible permutation and rearrange the matrix A's rows based on the permutation vector produced by that permutation. For example, if N=4, and if we had [1,4,2,3] as the permutation vector, it would rearrange the matrix A so that row 1 of the original matrix A appears first, followed by row 4 of the original matrix A appearing second, row 2 of the original matrix A appearing third and finally row 3 of the original matrix A appearing last. The above problem is essentially checking to see that if we all of these matrix rearrangements for A over all possible permutations, we check to see if this rearranged matrix is equal to its transpose. In order to facilitate this, I do an element-by-element equality check of the characters, and sum over this result. If the sum is equal to the total size of the matrix, then we have a true result. This code will check all possible permutations, even if we have found a match before we exhaust all possibilities. The statement o=0 is an indicator variable o that tells us whether we have found the condition being true or false. Inside the loop, we keep updating o and checking for the above summation condition by logical ORing with the current result and with the current rearranged matrix condition. It will be set to true if we have found such a condition or it gets to 1, and will stay false if we don't, or stays at 0. ## Minor Note The for loop behaviour is rather undocumented, but if you specify a matrix to be what is iterating over the for loop, each value k would be a column of the said matrix. For example, if we did: B = [0 0 0 0; 1 1 1 1; 2 2 2 2; 3 3 3 3]; for k = B disp(k); end  We would select out the first column of B, display it, then the next column of B, display it, etc... so you would get a series of [0,1,2,3]'s. # Example Runs >> A = ['FILE'; 'ICED'; 'LEAD'; 'EDDY']; >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = True >> A = ['FILE'; 'LEAD'; 'EDDY'; 'ICED']; >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = True >> A = ['OGRE'; 'GAIA'; 'RIGS'; 'EASY']; >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = True >> A = ['CAMP', 'AXEL', 'MEMO', 'PLOW']; >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = True >> A = ['SPASM', 'PASTA', 'ASPEN', 'STEEL', 'MANLY']; >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = True  Just to be sure, here's an example of where it shouldn't work: >> A = ['CBMP'; 'APEL'; 'MCTO'; 'DLOX']; >> A A = CBMP APEL MCTO DLOX >> c={'False','True'};o=0;for k=perms(1:size(A,1))'o=o|sum(sum(A(k,:)==A(k,:)'))==numel(A);end,c{o+1} ans = False  # 05AB1E, 11 bytes øQi”‰¦”ë”žä  Try it online. Explanation: ø # Zip the (implicit) input, swapping columns and rows Q # Check if it is equal to the (implicit) input # That's it, we're done.. If it weren't for the requirement of explicitly # outputting the strings "True"/"False" instead of a truthy/falsey result.. i # If the result is 1 (truthy): ”‰¦” # Output "True" ë # Else: ”žä # Output "False"  See here to understand why ”‰¦” is True and ”žä is False. 11 bytes alternative: øQ”žä‰¦”#sè  Try it online. # Java (OpenJDK 8), 134 bytes a->{int b=a.length,i=0,j=0;for(;i++<b;){for(;j<b;j++){if(a[j].length()!=b||a[i].charAt(j)!=a[j].charAt(i))return false;}}return true;}  Try it online! ### Explanation: int b=a.length,i=0,j=0; //Create Variables for(;i++<b;){for(;j<b;j++){ //Nested Loop if(a[j].length()!=b||a[i].charAt(j)!=a[j].charAt(i)) //Is the grid valid? return false; //if not, return false }} return true; //if it gets this far, return true  • Is this work with "The words can be given in any order." rule? – mazzy Aug 13 '18 at 11:15 # PowerShell, 93 bytes param($a)"$($a|%{$n++;''+($_|% t*y|sort)}|sort)"-eq"$(0..--$n|%{''+($a|% ch*$_|sort)}|sort)"

Try it online!

Unrolled:

param($a)$x=$a|%{$n++                                # number of words
$letters =$_|% toCharArray|sort    # sorted letters of the current word $_ ''+$letters                         # convert the letters to a string
}|sort

$y=0..--$n|%{
$letters =$a|% chars $_|sort # sorted letters of all words in the$_ position
''+$letters # convert the letters to a string }|sort Write-Output ("$x"-eq"\$y")              # convert both arrays to strings, compare them and return a result

# Burlesque, 35 bytes

ln)wdr@{Jtp==}ay{"True"}{"False"}IE

Try it online!

Core calculation is 11 bytes. Most of the cost is in parsing the word square (5 bytes) and outputting true or false rather than 1/0 (19 bytes)

ln                   #Split by newlines
)wd                  #Map split by spaces
r@                   #Permutation by words
{
Jtp==               #If the transpose is the same
}ay                  #Any
{"True"}{"False"}IE  #Print "True" or "False" accordingly

format: plain


text:
# A question about understanding the proofs for $x^3+y^3=z^3$

The problem is prove $$x^3 + y^3 = z^3$$ has no positive integer solutions. I understand this was proven in the 1700s by Euler, but I cannot find any books or in-depth references on the proof.

Here are some proofs I have tried to follow:

https://www.mathpages.com/home/kmath009/kmath009.htm

http://www2.washjeff.edu/users/mwoltermann/Dorrie/21.pdf

Reference request: Clean proof of Fermat's last theorem for $n=3$.

The equation $x^3 + y^3 = z^3$ has no integer solutions - A short proof

In your professional opinion, what would be the first step to understanding the proofs linked above? Do you know of any books or other references that go into more detail on this problem?

Also this is one attempt I made:

Starting with assuming $$x^3+y^3=z^3$$ has a solution such that $$xyz\neq0$$ and x,y,z are co-prime.

$$\therefore z^3-x^3-y^3 + (x+y-z)^3 = (x+y-z)^3$$

I believe this simplifies to:

$$3(x+y)(z-x)(z-y)=(x+y-z)^3$$

But aren't these factors also co-prime and therefore not cubic?

• What is wrong about the proofs given at your links? The first one, for example, is really very detailed. I would try to follow it. For shorter proofs you will definitely need more algebraic number theory, or at least some commutative algebra. – Dietrich Burde Oct 27 '20 at 15:20
• another reference would be 13 Lectures on Fermat's Last Theorem by Paulo Ribenboim, Lecture III Section 3 "The Cubic Equation" – J. W. Tanner Oct 27 '20 at 15:24
• I get stuck when they rush over some explanations in the lemmas. I was just wondering if there are any other references. – Joseph Oct 27 '20 at 15:24
• Thank you for that reference. – Joseph Oct 27 '20 at 15:31
• For example, many of these proofs make statements like the following: (1) Let x be a positive, odd factor of a2 + 3b2 (2) Then, there exists a value f such that: a2 + 3b2 = xf (3) We can assume that x is greater than 1 (since if x = 1 it's only factor is itself and 1 = 12 + 3(0)2.) (4) There exists integers m,n such that: a = mx ± c b = nx ± d where c,d can be positive or negative. That is all fine until step 4. I do not understand why a = mx+c, b=nx+d. To me it is not obvious. – Joseph Oct 28 '20 at 10:01


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### Stata FAQ How do I use version 7 graph commands in later versions of Stata?

Say that we use the hsb2 data file for the examples shown here.
use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear
and say that you wanted to see the scatterplot and regression line between write and read. In Stata version 7 you might have done something like this.
regress write read
predict yhat
graph write yhat read, twoway symbol(oi) connect(.l) jitter(2) sort
And you would get a graph that looks something like this.
But if you execute the graph command in Stata version 8 or later you get this error message.
writegraph_g.new yhat read, twoway symbol(oi) connect(.l) jitter(2)
write is not a valid graph subcommand
r(198);
You get this error message because the syntax of the graph command has been completely revised (and substantially enhanced) since version 8 and the syntax that you would have used in version 7 is not compatible with the current syntax.

There are two ways that you can deal with this.  You can instruct Stata to run the command as though you were using Stata version 7 (instead of a later version) or you can convert the command to use the newer syntax.  We discuss both below.

#### Using Stata 7 graphic commands in Stata 8

With a little bit of extra effort you can get Stata to run commands in the same way that they ran in Stata 7.  With respect to graph commands, there are 3 strategies you could choose.  The first is that you could use the graph7 command (abbreviation gr7 ) as shown below.
graph7 write yhat read, twoway symbol(oi) connect(.l) jitter(2) sort
and this produces a graph that looks just like you were using Stata version 7. Another trick is to use the version command to instruct Stata to run the graph command as though you were using version 7, as shown below.
version 7: graph write yhat read, twoway symbol(oi) connect(.l) jitter(2) sort
and again this produces a graph that looks just like you were using Stata version 7. If you are going to run a series of graph commands, you can issue a version 7 command on its own line and then all subsequent commands (graph commands and other types of commands) run as though they were from Stata version 7. This continues until you quit Stata or issue another version command on its own line. This is illustrated below.
version 7
graph write yhat read, twoway symbol(oi) connect(.l) jitter(2) sort
graph write
version 8 /* or 9 or 10 */
The strategy you choose will depend on the situation.  These strategies work the same way in the Stata command window or in a Stata .do file.

#### Coverting Stata 7 graphics commands to the newer Stata syntax

You may want to just go ahead and convert your Stata 7 graphics commands to get the presentation quality graphs of the newer versions of Stata.

It is not possible to cover all of the different ways in which the current Stata graphics commands differ from the Stata 7 commands. However, it is possible to give suggestions that cover many commonly encountered situations. To completely cover the topic we would refer you to the resources at the Stata Topics: Graphics (including Stata Online Graphics Manual, via the Stata web site).

The current Stata graph command includes six different graph types:
graph twoway              scatterplots, line plots, etc.
graph matrix              scatterplot matrices
graph bar                 bar charts
graph dot                 dot charts
graph box                 box and whisker plots
graph pie                 pie charts
The graph twoway type includes the following graphs among others:
scatter         scatterplot
line            line plot
connected       connected-line plot
spike           spike plot
dot             dot plot
lowess          LOWESS line plot
lfit            linear prediction plot
lfitci          linear prediction plot with CIs
qfitci          quadratic prediction plot with CIs
function        line plot of function
histogram       histogram plot
kdensity        kernel density plot
Thus, a scatterplot can be done three different ways:
graph twoway scatter write read

scatter write read
However, if you want to combine several twoway graphs in one plot, you will need to include the twoway type declaration. The following are examples of ways that you can produce the scatterplot and regression line that we tried in Stata 7 above.
graph twoway (scatter write read, jitter(2)) (lfit write read, sort )

twoway scatter write read, jitter(2) || lfit write read, sort
All of these constructions produce a graph that looks like this.
Note this will not work:
(scatter write read) (lfit write read)
Note: The separate plots indicated by enclosing the specific command in parentheses "()" or by separating the commands with two vertical bars "||".

#### Problems converting symbol and connect options

Many Stata 7 twoway plots fail in the current version of Stata because Stata changed the way the symbol and connect options are implemented. In Stata 7 a scatter plot that includes two connected lines would be written like this:
graph write yhat read, twoway symbol(oi) connect(.l) jitter(2) sort
Note that, in both, symbol and connect the list of indicators is given without spaces. In newer versions of Stata you need to include a space between each of the items in the list. Further, you should change the option symbol to msymbol (for marker symbol). The equivalent Stata 8 or later command will look like this:
scatter write yhat read, msymbol(o i) connect(. l) jitter(2) sort
The above comments cover only a few of the many ways in which the current version of Stata graphics differ from the Stata 7 version. It is well worth you time to sit down and read the Stata Online Graphics Manual and see the Stata Topics: Graphics.

The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California.


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## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE

 Options: Use Classic View Use Monospaced Font Show Text Part by Default Condense Mail Headers Topic: [<< First] [< Prev] [Next >] [Last >>]

 Sender: Mailing list for the LaTeX3 project <[log in to unmask]> Date: Fri, 18 Jul 2003 14:01:31 -0400 Reply-To: Mailing list for the LaTeX3 project <[log in to unmask]> Subject: Re: XML, UTF-8 and TeX engines MIME-Version: 1.0 Content-Transfer-Encoding: 8bit In-Reply-To: <[log in to unmask]> Content-Type: text/plain; charset=iso-8859-7 From: William F Hammond <[log in to unmask]> Parts/Attachments: text/plain (50 lines) Torsten Bronger <[log in to unmask]> writes: > >> XML doesn't do it and I find this very convenient. In (La)TeX, for > > > > This statement about XML is not helpful without reference to a > > particular document type. So I guess you accept that point, but perhaps I did not need to say it for your benefit. > > For example, gellmu article does provide elements called "math" and > > "displaymath", which when formatted to LaTeX switch on the > > corresponding math mode. > > Well, you cut off the citation too soon. I am talking about > character treatment only, and in > I write "the program > -- or XML file format -- must provide a way to mark math areas, and > it must apply rules or whatever to typeset accordingly." Yes, sorry, I was reading too fast. > > As LaTeX is evolving it will be possible for gellmu's "alpha" (an > > empty element marked up in Gellmu source as \alpha) to be formatted in > > LaTeX as (math) \alpha when recursively inside a math element and not > > inside either of gellmu's "mbox" or "text", while outside of math > > "alpha" could easily be morphed to a suitable unicode point. > > So you distuguish between both cases within your Gellmu tools? > Okay, we have to, I do so, too; but actually I think that this is > something that the typesetter should provide. So, an \alpha in math > mode should be cmmi, and in text mode is must be part of a Greek > word. One way or another there should be a distinction. But I want gellmu article to be able to reach xhtml+mathml and for this I want to have a source markup way of identifying math symbols. For that purpose it is convenient for me to hold on to (the xml form of \alpha) until the end of any pipeline. Beyond that I think it inefficient use of xml structure to look individually at items of cdata. So my formatter is willing to think about how to handle but not about how to handle á (which will be understood only as the unicode object that it is and which, therefore, should not be found loose inside math). (The last sentence is supposed to have a single U+03B1 that is UTF-8 encoded; I don't know what will happen in the mail.)                                     -- Bill


text:
Free Version
Easy

# True for $f(x) = \tan {2x}$

APCALC-ULEDBI

Which of the following statements is true for $f(x) = \tan {2x}$?

I. $\mathop {\lim }\limits_{x \to \frac{\pi }{4}} f(x)$ does not exist.
II. $\mathop {\lim }\limits_{x \to {{\frac{\pi }{4}}^ + }} f(x) = \infty$
III. $\mathop {\lim }\limits_{x \to {{\frac{\pi }{4}}^ - }} f(x)\, = \infty$

A

I only

B

I and II only

C

I and III only

D

I, II, and III


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What are the coefficients of x...

# What are the coefficients of x in the following expressions ? 4x-3y, 8-x+y,y^2x-y,2z-5xz (b) what are the coefficients of y in the following expressions ? 4x-3y, 8-yz, yz^2+5, my+m

Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!

Solution :  Solution:
 a) Coefficient of x in 4x-y is 4
 Coefficient of x in 8-x+y is -1
 Step-by-step solution:
 Coefficient of x in 4x-3y is 4 as 4 is the constant multiplying the variable.
 Coefficient of x in 8-x is -1 as -1 is the constant multiplying the variable.
 We can't say Coefficient of x in as y is itself a variable.
 Similarly in 2z-5xz  as z is itself a variable.
 Thus, Coefficient of x in the following expression are 4 and -1
 b) 4x-3y
 So, Coefficient is -3
 8+yz
 So, Coefficient is z
 2yz+ 5
 So, Coefficient is 2z
 my+m
 So, Coefficient is m


text:
# Entropy Formula

Entropy is not a very familiar topic to most of the people. Also, in this topic, we will learn about entropy, entropy formula, its derivation and solved example. Moreover, you will explore the second law of the thermodynamics where entropy is introduced. Furthermore, you will inspect the formula for entropy and find out how to use it in a variety of cases.

## Entropy

Entropy refers to the number of ways in which a system can be arranged. Moreover, the higher the entropy the more disordered the system will become. Furthermore, we can understand it more easily with the help of an example. Suppose you sprayed perfume in one corner of the room. So, what will happen next? We all know that the smell will spread in the entire room and the perfume molecule will eventually fill the room.

In another example, you grab a ball and put it on a table. Moreover, the question here is in how many ways you can arrange this ball? The answer is one. After some time you put another ball on the table. So, now you can arrange the balls in two ways. Furthermore, the more you increase the ball the more ways it can be arranged.

Get the huge list of Physics Formulas here

### The Second Law of Thermodynamics

The second law of thermodynamics says that every process involves a cycle and the entropy of the system will either stay the same or increase. Also, even when the cyclic process is changeable then the entropy will not change. Moreover, when the process is unalterable then the entropy will increase.

For example, watching a movie is a changeable process because you can watch the movie from backward. On the other hand, blowing a building, frying an egg is an unalterable change. Besides, some other example of changeable phase is the melting of metals. In addition, some microscope process is reversible.

### Entropy Formula

Entropy is a thermodynamic function that we use to measure uncertainty or disorder of a system. Moreover, the entropy of solid (particle are closely packed) is more in comparison to the gas (particles are free to move). Also, scientists have concluded that in a spontaneous process the entropy of process must increase. Furthermore, it includes the entropy of the system and the entropy of the surroundings.

Besides, there are many equations to calculate entropy:

1. If the happening process is at a constant temperature then entropy will be

$$\Delta S_{system}$$ = $$\frac{q _{rev}}{T}$$

### Derivation of Entropy Formula

$$\Delta S$$ = is the change in entropy

$$q_{rev}$$ = refers to the reverse of heat

T = refers to the temperature in Kelvin

2. Moreover, if the reaction of the process is known then we can find $$\Delta S_{rxn}$$ by using a table of standard entropy values.

$$\Delta S_{rxn}$$ = $$\Sigma \Delta S_{products} – \Sigma \Delta S_{reactants}$$

### Derivation

$$\Delta S_{rxn}$$ – refers to the standard entropy values

$$\Sigma \Delta S_{products}$$ = refers to the sum of the $$\Delta S_{products}$$

$$\Sigma \Delta _{reactants}$$ – refers to the sum of the $$\Delta S_{reactants}$$

3. Is the Gibbs free energy ($$\Delta G$$) and the enthalpy ($$\Delta H$$) can also be used to find $$\Delta _S$$.

$$\Delta G$$ = $$\Delta H$$ – T$$\Delta _S$$

## Solved Example on Entropy Formula

#### Example 1

 Substance $$S^{\circ}\frac{j}{k\cdot mol}$$ $$H_{2(g)}$$ 130.6 $$F_{2(g)}$$ 202.7 $$HF_{2(g)}$$ 173.5

Find the entropy change for the following reaction using the table of entropy values.

$$H_{2 (g)} + F_{2 (g)}$$ $$\rightarrow$$ $$2HF_{g}$$

Solution:

$$\Delta S_{rxn}$$ = $$\Sigma \Delta S_{products} – \Sigma \Delta S_{reactants}$$

$$\Delta S_{rxn}$$ = $$2 \times 173.5) – (130.6 + 202. 7) \(\Delta S_{rxn}$$ = $$13.7\frac{j}{k\cdot mol}$$

So, the answer is $$13.7\frac{j}{k\cdot mol}$$.

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Typo Error>
Speed of Light, C = 299,792,458 m/s in vacuum
So U s/b C = 3 x 10^8 m/s
Not that C = 3 x 108 m/s
to imply C = 324 m/s
A bullet is faster than 324m/s

Guest

I have realy intrested to to this topic

Guest
umer

m=f/a correct this

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B. Akshaya

M=f/g

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Interesting studies

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Yashdeep tiwari

It is already correct f= ma by second newton formula…

Watch lectures, practise questions and take tests on the go.

No thanks.


text:
## CryptoDB

### Igor Semaev

#### Publications

Year
Venue
Title
2018
TOSC
Multidimensional linear cryptanalysis of block ciphers is improved in this work by introducing a number of new ideas. Firstly, formulae is given to compute approximate multidimensional distributions of the encryption algorithm internal bits. Conventional statistics like LLR (Logarithmic Likelihood Ratio) do not fit to work in Matsui’s Algorithm 2 for large dimension data, as the observation may depend on too many cipher key bits. So, secondly, a new statistic which reflects the structure of the cipher round is constructed instead. Thirdly, computing the statistic values that will fall into a critical region is presented as an optimisation problem for which an efficient algorithm is suggested. The algorithm works much faster than brute forcing all relevant key bits to compute the statistic. An attack for 16-round DES was implemented. We got an improvement over Matsui’s attack on DES in data and time complexity keeping success probability the same. With 241.81 plaintext blocks and success rate 0.83 (computed theoretically) we found 241.46 (which is close to the theoretically predicted number 241.81) key-candidates to 56-bit DES key. Search tree to compute the statistic values which fall into the critical region incorporated 245.45 nodes in the experiment and that is at least theoretically inferior in comparison with the final brute force. To get success probability 0.85, which is a fairer comparison to Matsui’s results, we would need 241.85 data and to brute force 241.85 key-candidates. That compares favourably with 243 achieved by Matsui.
2015
EPRINT
2015
EPRINT
2015
EPRINT
2014
EPRINT
2014
EPRINT
2010
EPRINT
A system of algebraic equations over a finite field is called sparse if each equation depends on a low number of variables. Finding efficiently solutions to the system is an underlying hard problem in the cryptanalysis of modern ciphers. In this paper a deterministic Improved Agreeing-Gluing Algorithm is introduced. The expected running time of the new Algorithm on uniformly random instances of the problem is rigorously estimated. The estimate is at present the best theoretical bound on the complexity of solving average instances of the problem. In particular, this is a significant improvement over those in our earlier papers [10, 11]. In sparse Boolean equations a gap between the worst case and the average time complexity of the problem has significantly increased.
2007
EPRINT
A system of algebraic equations over a finite field is called sparse if each equation depends on a small number of variables. Finding efficiently solutions to the system is an underlying hard problem in the cryptanalysis of modern ciphers. In this paper deterministic Agreeing-Gluing algorithm introduced earlier by Raddum and Semaev for solving such equations is studied. Its expected running time on uniformly random instances of the problem is rigorously estimated. This estimate is at present the best theoretical bound on the complexity of solving average instances of the above problem. In particular, it significantly overcomes our previous results. In characteristic 2 we observe an exciting difference with the worst case complexity provided by SAT solving algorithms.
2007
EPRINT
A new method for solving algebraic equation systems common in cryptanalysis is proposed. Our method differs from the others in that the equations are not represented as multivariate polynomials, but as a system of Multiple Right Hand Sides linear equations. The method was tested on scaled versions of the AES. The results overcome significantly what was previously achieved with Gr\"{o}bner Basis related algorithms.
2006
PKC
2006
EPRINT
Most of the recent cryptanalysis on symmetric key ciphers have focused on algebraic attacks. The cipher being attacked is represented as a non-linear equation system, and various techniques (Buchberger, F4/F5, XL, XSL) can be tried in order to solve the system, thus breaking the cipher. The success of these attacks has been limited so far. In this paper we take a different approach to the problem of solving non-linear equation systems, and propose a new method for solving them. Our method differs from the others in that the equations are not represented as multivariate polynomials, and that the core of the algorithm for finding the solution can be seen as message-passing on a graph. Bounds on the complexities for the main algorithms are presented and they compare favorably with the known bounds. The methods have also been tested on reduced-round versions of DES with good results. This paper was posted on ECRYPT's STVL website on January 16th 2006.
2005
FSE
2004
EPRINT
The aim of the paper is the construction of the index calculus algorithm for the discrete logarithm problem on elliptic curves. The construction presented here is based on the problem of finding bounded solutions to some explicit modular multivariate polynomial equations. These equations arise from the elliptic curve summation polynomials introduced here and may be computed easily. Roughly speaking, we show that given the algorithm for solving such equations, which works in polynomial or low exponential time in the size of the input, one finds discrete logarithms faster than by means of Pollard's methods.
2003
EPRINT
Let $E$ be an elliptic curve defined over a prime finite field $F_p$ by a Weierstrass equation. In this paper we introduce a new partition of $E(F_p)$ into classes which are generally larger than $\{\pm R\}$. We give an effective procedure to compute representatives of such classes. So one can iterate the pseudorandom function, related to a discrete logarithm problem in $E(F_p)$, on the set of representatives of classes and get probably some speed up in computing discrete logarithms. The underlying idea how to enlarge known classes on anomalous binary elliptic curves is given.

#### Coauthors

An Braeken (1)
An Commeine (1)
Stian Fauskanger (2)


text:
Public Group

# Embedded object causes segfault with SDL

This topic is 4810 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I had some nasty segfaults (whatever they are) with SDL. After debugging and playing around I sort of find out the reason. It was because the constructor of an embedded object was calling an SDL_image function, it seems before SDL_Init was called. I'd like to initialize SDL either in a member routine of the class that owns that object, or in its constructor. (see code below). So my question is, which constructors get called in what order when you embed an object? (How) is it possible to initialize SDL in say class A, which has an object of class B where the constructor of B calls SDL_image functions?
class Game
{
public:
Game() {SDL_Init(SDL_INIT_VIDEO);}  //Not real code of course, just an example
private:
Block CurrentBlock;                 //Embedded evil object, yes it's tetris.
};

class Block
{
public:
Block() {Square = IMG_Load("images\\SomeImage.png");} //Causes a segfault, I think.
private:
SDL_Surface* Square;
};

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That's very strange, since in C++ constructors of parent objectes (that contain other objects) are called before constructors of those embedded ones. So, the example you provided should run with no problems. Could you put fprintf(stderr, "Called from function: (insert function name)"); in constructors of Game and Block and see what stderr.txt will contain? IMHO the problem lies somewhere else...

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That's weird. I'm quite sure that when I remove the IMG_Load() call the whole thing just works. Also when I didn't embed the object, but just created an instance in a member function it worked too.
I'm trying and figuring out that fprintf stuff now. Looks useful.

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your block is a member of Game. When an object is constructed, the constructors of the member objects are called first.So Block constructor is called before SDL is initialized.you should call SDL_Init at the begining of your main() function, or replace CurrentBlock by a pointer to block.

If you load your image in the constructor of Block, you will load it each time you create a block. it would be better to load it once, and put it where you can find it.

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fprintf(stderr, "call from constructor x") gives in stderr.txt only the call from the embedded class. So that seems to be constructed first. Maybe it's because I have #include "Block.h" in Game.h? It doesn't make sense.

Maybe I just screwed up somehow. The debugger (using the one with DEV-CPP) gives output like: "Error: dll starting at 0xa31000 not found", "Segmentation-fault" and "No symbol 'include' in current context". There's a whole bunch of other output, but I just can't make any sense out of it, sadly.

EDIT: Thanx DrakeSlayer, that helped. It seems I've got to make some adjustments to where I load my surfaces now...

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Ooops, sorry man, that was stupid mistake from my side. I wasn't sure what was the order of constructors call, so I opened book and read about order of destructors call [embarrass] of course that was unintentional, I thought that I was reading definition for constructors :-/ shit, I should be more careful next time I want to help someone.

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Don't worry, my mind is all clear now. You still got me finally using this fprintf stuff which I have not been doing. That is very handy indeed. I just fixed a bug that involved doing something in the wrong scope thanx to fprintf(). Big timesaver for a newbie like me who is constantly chasing bugs.

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# Tag Archives: theorycrafting

## Tankadin Patch 5.4 Survival Guide

Protection paladins are receiving a number of peripheral changes in 5.4, but nothing that changes our core mechanics.  We’re still going to be stacking haste thanks to Sanctity of Battle – in fact it’s even on two of our tier … Continue reading

Posted in Tanking, Theck's Pounding Headaches | | 60 Comments

## EF & You?

If you’ve been paying attention to the PTR patch notes, you’ve probably noticed that there’s a big change coming in 5.4.  I’m not talking about the change to Grand Crusader, which is mostly irrelevant to how we gear and spec.  … Continue reading

| | 75 Comments

## Stamina Breakpoints?

Last week I investigated two different situations where Simcraft was giving a user stat weights that seemed wrong.  These turned out to be pretty interesting, and are situations that other players could encounter at some point, so I decided it … Continue reading

| | 12 Comments

## Updated Diminishing Returns Coefficients – All Tanks

A few weeks ago, Taser contacted me about calculating the avoidance diminishing returns coefficients for monks to greater accuracy.  As you might remember, we managed to do this for paladins a little less than a year ago by using an … Continue reading

| | 11 Comments

## Simulationcraft 101: Getting Started

As I mentioned on twitter last week, version 530-5 of Simulationcraft has been released.  This is the first version to include the Theck-Meloree Index, a damage smoothing metric we developed in a series of previous blog posts. However, Simcraft is … Continue reading

| | 124 Comments

## Blood, Toil, Tears, and Threat

A few days ago, my friend Llarold asked me if I had done any calculation about the new threat bonus on taunts in 5.4.  In the past, I had worked out a rough formula for how long it took to … Continue reading

| | 17 Comments

## The Making of a Metric: Part 3

In our last installment, we nailed down the weight factors we’ll use for our smoothness metric.  Today we’re going to wrap it up by specifying normalization conditions for the histogram and formally defining the metric. To refresh your memory a … Continue reading

| | 55 Comments

## The Making of a Metric: Part 2

In our last post, we decided on a functional form for our metric.  And while I didn’t write it out in full mathematical formalism, the pieces were all there.  In short, we start with a damage histogram $H(x)$ computed by … Continue reading

| | 19 Comments

## The Making of a Metric: Part 1

Simulationcraft now has full support for protection paladin mechanics, and hopefully in a week or two I’ll get around to writing a how-to blog post on using it and interpreting the data.  Once I write a few batch files, it … Continue reading

| | 39 Comments

## SotRdämmerung

As was pointed out in the comments on a previous blog post, the protection 2-piece-turned-4-piece that returns holy power when Bastion of Glory (BoG) stacks are consumed will allow us to keep SotR up 100% of the time.  That comes … Continue reading

| | 59 Comments


text:
caralockhartsmith

Reflections in the Shed Window

There it is, in the background, my studio, aka The Tardis, and the poles for the runner beans; but what is not reflected is that washing line, high up above the garden, where the clothes are pulled up by ropes, and whip out in the wind. This is, apparently, a form of line constructed from those who have been in the navy. Tony was working in the merchant navy when he was 15, the boat had to be fettled and they were in Venice for a fortnight……

Portsmouth is apparently full of these washing lines..

February 19, 2023


text: Name Minkyoung Song POSTECH Session Jan 10 16:20~16:40 E11-101 Milnor's invariants and Hirzebruch-type invariants of homology cylinders Homology cobordism groups of homology cylinders are studied as generalizations of string-link concordance groups and mapping class groups in the last decade, and many invariants have been defined. We consider a filtration of subgroups using Garoufalidis-Levine invariants and Milnor's $\bar\mu$-invarints on homology cylinders, and extend Hirzebruch-type invariants on the subgroups. Also we consider additivity of the invariants. 101-1-10/2012_MKSong.pdf


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Tree Diagrams ( Real World ) | Probability | CK-12 Foundation

# Tree Diagrams

%
Best Score
Practice Tree Diagrams
Best Score
%

## Tree Diagram

### Topic

Representing Sports Outcomes with Discrete Random Variables and Tree Diagrams

### Vocabulary

• Random variables
• Discrete random variables
• Tree Diagram
• Probability
• Experimental Probability

### Student Exploration

#### Which sports outcomes can be represented with discrete random variables? How can you use a tree diagram to represent the possible outcomes?

Sports!

In most sports there are many different elements of the games that can be represented with discrete random variables. For each of the following sports situations create a tree diagram. A tree diagram is a way to show the outcomes of simple probability events, where each outcome is represented as a branch on the tree. If you need help creating the tree diagrams, revisit the lesson on tree diagrams.

Below are examples of the tree diagrams for #1 and 2.

1. Free throws in basketball. Make a tree diagram representing all the possible outcomes of shooting three free throws.

2. Penalty shoot-out kicks in soccer. Make a tree diagram representing all of the possible outcomes of shooting five shoot-out penalty kicks.

3. Sets won in a tennis match. Make a tree diagram representing all of the possible outcomes for two players in a tennis match that is in a best of five sets system.
4. Shots in a Hockey shoot-out. Make a tree diagram representing all of the possible outcomes of shooting three penalty shoots.
5. Why is it that we can use tree diagrams to represent situations with discrete random variables? And we cannot create tree diagrams for situations that cannot be represented with discrete random variables? Explain each!
(As a reminder, discrete random variables represent the number of distinct values that can be counted of an event, for more information revisit the lesson on discrete random variables).
Situations with discrete random variables can be represented with tree diagrams because there are a specific number of outcomes in the event and each of those outcomes can be represented with a branch in the tree diagram. Where as with situations that cannot be represented with discrete random variables, there are not a specific number of outcomes, and therefore it cannot bedetermined how many branches to make in the tree diagram.

Resources for Sports Rules:

6. Choose one of the situations from above and conduct your own experiment to determine your experimental probability of completely that situation successfully. Use proper probability notation to express the probability of you completing that task successfully.

Answers will vary but here is an example. $P(\text{scoring penalty kick}) = \frac{3}{5}$.

Tennis player.

### Extension Investigation

Many situations cannot be represented by a discrete random variable. Explain why each of these situations cannot.

1. The hitting options for one baseball or cricket player inone round at bat. (Need a hint? search for longest “at bat”). Technically a baseball player could be at bat for an unknown number of times. Even though a batter is given three strikes (where they attempt to hit the ball) and four balls (where the pitcher makes errors) because when they hit a foul ball it counts as a strike but they can’t get out on a foul ball. So the number of hits is unknown. Although there is not official record for the longest session at bat, there are many sports fans that have their commentary online see: http://www.sptimes.com/2006/04/13/Rays/The_longest_AB_We_hav.shtml or http://answers.yahoo.com/question/index?qid=20070420141850AAJlrox or http://en.allexperts.com/q/Baseball-Trivia-General-2552/longest-time-bat.htm.
2. The in and out serving options in a volleyball game.
3. The number of completed passes in an American football game.
4. The number of strokes made in a hole of golf.
5. Choose one of the situations from #7 – 10 and explain why it also cannot be represented with a tree diagram. You could not represent it with a tree diagram because the number of possible outcomes is unknown. There could be any number of strokes in on hole of golf.
6. Sometimes there might be too many outcomes to feasibly make a tree diagram. Give an example of this type of situation. What other methods might someone use to organize his or her work when a tree diagram is not useful?

Resources for Sports Rules:

### Connections to other CK-12 Subject Areas

• Tree Diagrams
• Discrete Random Distributions
• Probability and Permutations
• Theoretical and Experimental Probability


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# How do I create this bold style math?

What package or command should I use to achieve this (bolded?) style of LaTeX math?

Instead of this (regular) style. I know the color is gray in this second picture, but the style is completely different.

• Somewhat close... \documentclass{article} \usepackage{txfonts,bm} \begin{document} $\bm{\sum_{n=1}^\infty}$ \end{document} – Steven B. Segletes Aug 13 at 17:28
• @Steven B. Segletes Please post as an answer. – hesham Aug 13 at 17:53

$\displaystyle \sum_{n=1}^\infty$