url stringlengths 15 1.66k | text stringlengths 100 943k | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k | backtracking_raw stringlengths 343 1.47k | is_solution_raw stringlengths 386 1.47k | verification_raw stringlengths 322 1.48k | subgoal_setting_raw stringlengths 352 1.43k | backward_chaining_raw stringlengths 0 1.56k |
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https://ncatlab.org/nlab/show/Alan%20Weinstein | # nLab Alan Weinstein
## Selected writings
On groupoids:
• Alan Weinstein, Groupoids: Unifying Internal and External Symmetry – A Tour through some Examples, Notices of the AMS 43 7 (1996) (pdf, pdf)
category: people
Last revised on July 27, 2021 at 12:49:33. See the history of this page for a list of all contribut... | 2022-12-10 06:11:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It appears to be a straightforward informational page about Alan Weinstein's work on groupoids, with a list of references and m... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
math
## Text domain (specific)
Group Theory, Category Theory
## Rationale
The text appears to be a biographical entry for Alan Weinstein, listing one of his writings on groupoids. There is no expli... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work, such as comparing results to known values or checking calculations. T... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting or steps to achieve a specific goal. It appears to be a brief bibliography entry with a link to a paper b... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text appears to be a brief bibliography entry or a wiki page about Alan Weinstein, listing one of his publications. There is no evidence of ... |
http://openstudy.com/updates/55fa096ce4b08bf9c20dc618 | ## anonymous one year ago Suppose the density ρ of a fluid varies from point to point as well as with time, that is, ρ = ρ(x,y,z,t). If we follow the fluid along a streamline, then x, y, z are functions of t such that the fluid velocity is V = i dx/dt + j dy/dt + k dz/dt. Show that then dρ/dt = ∂ρ/∂t + v (dot) ∇ρ. Comb... | 2017-01-19 04:47:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>
## Rationale
The text provided is a mathematical discussion about fluid dynamics, and it does not exhibit any backtracking behavior. The writers present their thoughts and calculations in a linear and lo... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Fluid Dynamics
## Rationale
The text discusses fluid dynamics, specifically the variation of fluid density with time and space, and the relationship between the ... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>2</count>.
## Rationale
The writer explicitly checks their own work in two instances. Firstly, the derivation of the equation $dρ/dt = ∂ρ/∂t + v (dot) ∇ρ$ is verified by combining it with the equatio... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain explicit subgoal setting where the model breaks down the problem into smaller, intermediate goals. The text appears to be a discussion... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>2</count>
## Rationale
The text exhibits backward-chaining behavior in two instances. The first instance is when the writer is trying to derive the equation `dρ/dt = ∂ρ/∂t + v... |
https://genviz.org/module-06-review/0006/01/01/Review/ | Q & A, Discussion, Integrated Assignments, and Working with Your Own Data
In this section we provide some additional exercises covering a range of topics to reinforce concepts and topics throughout this course series. We encourage students to attempt to do these exercises on their own. We have provided hints and an an... | 2019-02-21 04:18:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. The writer presents a clear and linear narrative, first introducing the topic, then providing historical context, and finally p... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Epidemiology and Data Analysis
## Rationale
The text describes a historical event, the Golden Square outbreak of cholera in London, and presents a problem for th... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The text does not contain explicit subgoal setting where the problem is broken down into smaller, intermediate goals. Although the text provides hints and guidance on ho... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text does not exhibit backward-chaining behavior. It appears to be a instructional exercise where the goal is to recreate a map to support John Snow'... |
https://www.toppr.com/guides/maths/exponents-and-powers/application-of-laws-of-exponents/ | # Application of Laws of Exponents
Hello, friends! Today we will discuss an important concept in mathematics. This concept will form the base of future concepts and enable the students to easily understand them. We will look at the exponential formula or rather the sets of them, study their applications on the basis o... | 2022-12-09 20:11:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. The writer presents a clear and structured explanation of the concept of exponents, their rules, and applications, without aban... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Algebra, Exponents and Powers
## Rationale
The text does not present a specific problem to be solved, but rather provides an explanation and application of the laws ... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting, where the model breaks down the problem into smaller, intermediate goals. The text appears to be an educ... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text does not exhibit backward chaining behavior. It appears to be a straightforward explanation of the concept of exponents and their applications, ... |
https://sw.khanacademy.org/video?lang=sw&format=lite&v=dgyS7t0-2Uk | # Proof (Advanced): Field from infinite plate (part 1)
Electric field generated by a uniformly charged, infinite plate | 2019-05-23 21:49:04 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not contain any instances of backtracking behavior. It appears to be a title or introduction to a topic, and there is no evidence of the writer abandoning a thought o... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
science
## Text domain (specific)
Physics, specifically Electromagnetism
## Rationale
The text appears to be an introduction to a topic in physics, specifically electromagnetism, and does not pose ... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing results to known values or verifying calculations. The te... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting or steps to break down a problem into smaller, intermediate goals. It appears to be a title or heading fo... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text is a brief statement about the electric field generated by a uniformly charged, infinite plate, and it does not demonstrate any reasoni... |
https://questions.examside.com/past-years/jee/question/the-total-number-of-orbitals-associated-with-the-principal-q-jee-main-physics-units-and-measurements-ravbjdwqrosk40rw | 1
### JEE Main 2016 (Online) 9th April Morning Slot
The total number of orbitals associated with the principal quantum number 5 is :
A
5
B
10
C
20
D
25
2
### JEE Main 2017 (Offline)
The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg... | 2021-10-23 02:37:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It consists of a series of explanations and calculations for different problems, with each problem being addressed in a straigh... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Physics/Chemistry, specifically Quantum Mechanics and Atomic Structure
## Rationale
The text appears to be a collection of problems and solutions from the Joint ... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting, where the model breaks down the problem into smaller, intermediate goals. The text appears to be a colle... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>2</count>
## Rationale
The text exhibits backward chaining in two instances. The first instance is in the explanation of the radius of the second Bohr orbit for a hydrogen ato... |
http://infamousheelfilcher.blogspot.com/2014/ | ## Wednesday, December 31, 2014
### [E]valuation is nontrivial
You know how when you're in a debate with a smart person, and the debate wants to fragment -- you need some kind of tree structure to keep track of all the threads that the two of you have brought up, because some of them are irrelevant to the main point ... | 2017-05-22 19:17:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any instances of backtracking behavior, where the writer realizes a path won't work and explicitly goes back to try a different approach. The text appears... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math/science
## Text domain (specific)
Set Theory, Logic, and Metal Music
## Rationale
The text contains discussions on various mathematical topics such as set theory, logic, and combinatorics, i... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing results to known values or checking the outcome of a calc... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting, where the model breaks down the problem into smaller, intermediate goals. The text appears to be a colle... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>2</count>
## Rationale
The text exhibits backward chaining in two instances. The first instance is in the post "Fundamental theorem on chain conditions" where the author start... |
https://docs.typo3.org/m/typo3/reference-coreapi/main/en-us/ApiOverview/Hooks/Events/Extbase/Persistence/EntityAddedToPersistenceEvent.html | # EntityAddedToPersistenceEvent¶
Event which is fired after an object/entity was persisted on add.
The event is dispatched after persisting the object, before updating the reference index and adding the object to the persistence session.
## API¶
class TYPO3\CMS\Extbase\Event\Persistence\EntityAddedToPersistenceEven... | 2022-01-24 20:15:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It is a straightforward description of an event in a programming context, specifically the EntityAddedToPersistenceEvent, and i... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
computer science
## Text domain (specific)
Object-Oriented Programming, Event-Driven Architecture, specifically in the context of the TYPO3 content management system
## Rationale
The text appears t... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work, such as comparing results to known values or verifying calculations. ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting. It appears to be a documentation of an event in a software system, describing when the event is fired an... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text appears to be a documentation of an event in a software system, specifically the EntityAddedToPersistenceEvent. It describes the event'... |
http://www.chegg.com/homework-help/questions-and-answers/ground-state-wave-function-hydrogen-atom-given-r-radial-coordinate-electron-a0-bohr-radius-q2592149 | The ground-state wave function for a hydrogen atom is given below, where r is the radial coordinate of the electron and a0 is the Bohr radius.
http://www.webassign.net/pse/p42-09.gif
(b) Find the probability of locating the electron between r1 = 2a0/2 and r2 = 4a0/2. | 2016-08-30 10:23:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It presents a problem related to the ground-state wave function of a hydrogen atom and asks for the probability of locating an ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
no
## Text domain (broad)
science
## Text domain (specific)
Quantum Mechanics/Atomic Physics
## Rationale
The text provides a mathematical expression for the ground-state wave function of a hydrogen atom and asks for the p... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting or steps to break down the problem into smaller, intermediate goals. It presents a problem to find the pr... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text appears to be a physics problem related to quantum mechanics, specifically asking to find the probability of locating an electron withi... |
http://math.stackexchange.com/questions/128877/finding-concavity-and-factoring | # Finding concavity and factoring
I am trying to graph $$y=\frac{x^2}{x^2+3}$$but it is incredibly difficult for me because I am so bad with graphing rules and factoring.
I have come down to concavity and I just can't figure out what to do. I know the second derivative is something close to
$$\frac{6x^4 + 36x^2 +54-... | 2015-11-30 01:30:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
yes
## Number of backtrack steps
<count>2</count>.
## Rationale
The writer backtracks when they realize their expression for the second derivative is not factorable and decide to try a different approach by not expanding it, as suggested by André Nicol... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Calculus, specifically finding concavity and factoring in the context of graphing functions
## Rationale
The text describes a problem with graphing a function, $y=\... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of a ca... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>5</count>.
## Rationale
The text contains several instances of subgoal setting, where the problem is broken down into smaller, intermediate goals. For example, the user is trying to graph a fu... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>2</count>
## Rationale
The text exhibits backward-chaining behavior in two instances. The first instance is when the writer is trying to find the second derivative of the give... |
http://en.wikibooks.org/wiki/GLSL_Programming/Unity/Nonlinear_Deformations | # GLSL Programming/Unity/Nonlinear Deformations
Jump to: navigation, search
## Contents
Illustration of deformations by corsets. These are examples of nonlinear deformations that cannot be modeled by a linear transformation.
This tutorial introduces vertex blending as an example of a nonlinear deformation. The main... | 2014-08-30 02:28:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. The writer presents a clear and linear explanation of the concept of vertex blending and nonlinear deformations, without any in... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
computer science
## Text domain (specific)
Computer Graphics, GLSL Programming, Unity, 3D Modeling
## Rationale
The text does not describe a specific problem to be solved, but rather presents a so... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting where the model breaks down the problem into smaller, intermediate goals. The text is a tutorial on GLSL ... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text does not exhibit backward-chaining behavior. It presents a tutorial on vertex blending for nonlinear deformations in Unity, starting with the in... |
https://mathzsolution.com/has-there-ever-been-an-application-of-dividing-by-00/ | # Has there ever been an application of dividing by 00?
Regarding the expression $a/0$, according to Wikipedia:
In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by $0$, gives $a$ (assuming $a\not= 0$), and so division by zero is undefined.
Is there some other kind of mat... | 2022-10-01 06:10:24 | {"extraction_info": {"found_math": true, "script_math_tex": 8, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The writer does not exhibit any backtracking behavior in the provided text. They present a clear and linear line of reasoning, exploring the concept of division by zero and its potential ap... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Division by Zero, Abstract Algebra
## Rationale
The text discusses the concept of dividing by zero, which is a problem in ordinary arithmetic. However, it also prov... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>1</count>.
## Rationale
The writer verifies their work by checking the result of a calculation in the context of the parallel resistance formula. Specifically, when $R_1=0$, the formula yields a resu... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification occur?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain explicit subgoal setting where the problem is broken down into smaller, intermediate goals. The text discusses the concept of di... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>1</count>
## Rationale
The text exhibits backward chaining when the writer starts with the goal of finding an application of dividing by 0 and works backward to find a suitabl... |
https://www.nature.com/articles/s41598-021-97836-w?error=cookies_not_supported&code=41ebab53-eaa4-43da-9df1-3470027df5dc | Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles an... | 2021-10-28 15:38:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It is a well-structured scientific article that presents a clear and linear narrative, without any instances of the author aban... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Medical Research, specifically Oncology and Pharmacology, focusing on MALT lymphoma treatment with Azithromycin.
## Rationale
The text describes a pilot study as... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count> 5 </count>.
## Rationale
The text contains several instances where the writer explicitly checks their own work or verifies the results of calculations. These instances include:
1. The comparison of ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting, where the model breaks down the problem into smaller, intermediate goals. The text appears to be a scien... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text provided is a scientific study on the use of azithromycin in treating MALT lymphoma patients. The study outlines its objectives, methods, and re... |
https://www.zbmath.org/?q=an%3A1415.14010 | # zbMATH — the first resource for mathematics
Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory. (English) Zbl 1415.14010
Howe, Everett W. (ed.) et al., Algebraic geometry for coding theory and cryptography, IPAM, Los Angeles, CA, USA, February 2016. Cham: Springer. Asso... | 2021-01-23 09:05:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It is a formal mathematical summary that presents a problem, provides context, and outlines the content of a publication withou... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
partial
## Text domain (broad)
math
## Text domain (specific)
Algebraic Geometry, Coding Theory
## Rationale
The text describes a specific question in algebraic geometry, namely determining the maximum number of rational p... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing results to known values or verifying calculations. The te... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting where the problem is broken down into smaller, intermediate goals. The text appears to be a summary of a ... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text does not exhibit backward-chaining behavior. It appears to be a summary of a mathematical research paper, where the author starts by introducing... |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/fundamenta-mathematicae/all/198/3/88680/minimal-actions-of-homeomorphism-groups | JEDNOSTKA NAUKOWA KATEGORII A+
# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty
## Minimal actions of homeomorphism groups
### Tom 198 / 2008
Fundamenta Mathematicae 198 (2008), 191-215 MSC: Primary 37B05; Secondary 54H15, 22F50. DOI: 10.4064/fm198-3-1
#### Streszczenie
Let $X$ be a ... | 2023-02-03 07:52:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>.
## Rationale
The provided text does not exhibit any backtracking behavior. It appears to be a formal mathematical article with a structured presentation of ideas, without any instances of the author aba... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Topology and Dynamical Systems
## Rationale
The text appears to be a mathematical research paper discussing the action of homeomorphism groups on certain topological... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text appears to be a mathematical research paper abstract and does not contain any explicit verification steps where the writer checks their own work by comparing ... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text appears to be a mathematical research paper abstract and does not contain any explicit subgoal setting or answer verification steps. The text is writte... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text appears to be a mathematical research article, and its structure follows a typical format of stating a problem, providing background in... |
http://mathhelpforum.com/advanced-algebra/27318-ordered-bases-matrix-representation-linear-transformations-print.html | # Ordered bases with matrix representation of Linear Transformations
• February 2nd 2008, 07:24 PM
Let V and W be vector spaces such that dim(V) = dim(W), and let T: V -> W be linear. Show that there exist ordered bases a and b for V and W, respectively, such that $[T]^{a}_{b}$ is a diagonal matrix.
My problem is I do... | 2014-08-23 09:29:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... | <|start_header_id|>assistant<|end_header_id|>
## Does backtrack?
no
## Number of backtrack steps
<count>0</count>
## Rationale
The writer of the text does not exhibit backtracking behavior. They express confusion and a lack of understanding about certain concepts, such as ordered bases and the matrix representation ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
no
## Text domain (broad)
math
## Text domain (specific)
Linear Algebra
## Rationale
The text discusses linear transformations, vector spaces, and matrix representation, which are key concepts in linear algebra. The author... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit verification steps where the writer checks their own work by comparing results to known values or verifying calculations. The te... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text does not contain any explicit subgoal setting where the problem is broken down into smaller, intermediate goals. The text appears to be a question or a... | <|start_header_id|>assistant<|end_header_id|>
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count>
## Rationale
The text does not exhibit backward-chaining behavior. The writer is seeking to understand the concept of ordered bases and the matrix representation of l... |
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