url stringlengths 18 640 | text stringlengths 100 855k | date stringlengths 19 19 | metadata stringlengths 1.07k 1.1k | backtracking_raw stringlengths 84 1.45k | is_solution_raw stringlengths 84 1.43k | verification_raw stringlengths 84 1.47k | subgoal_setting_raw stringlengths 84 1.42k | backward_chaining_raw stringlengths 62 1.52k |
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http://shogun-toolbox.org/doc/en/latest/StreamingMMD_8h.html | SHOGUN 3.2.1
StreamingMMD.h File Reference
Go to the source code of this file.
## Classes
class CStreamingMMD
Abstract base class that provides an interface for performing kernel two-sample test on streaming data using Maximum Mean Discrepancy (MMD) as the test statistic. The MMD is the distance of two probability... | 2014-08-01 03:46:52 | {"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 appears to be a documentation or reference page for a software library, specifically the SHOGUN Machine Learning Toolbox. It describes a class and its purpose, but does no... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Machine Learning, Statistical Testing
## Rationale
The text appears to be a documentation for a machine learning library, specifically describing a class for perf... | <|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 documentation page for a software library, specifically describing a class and its purpose. There is no evidence of the writer explicitly chec... | <|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 documentation page for a specific class in a machine learning library, describing its purpose and functionality. There is no evidence o... | <|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 excerpt for a machine learning library, specifically describing a class for performing kernel two-sample ... |
https://questions.examside.com/past-years/jee/question/let-y--yx-be-the-solution-of-the-differential-equation-x-jee-main-mathematics-trigonometric-functions-and-equations-oudpuyrxxr8edkp0 | 1
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let y = y(x) be the solution of the differential
equation (x $$-$$ x3)dy = (y + yx2 $$-$$ 3x4)dx, x > 2. If y(3) = 3, then y(4) is equal to :
A
4
B
12
C
8
D
16
2
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)... | 2023-03-21 13:42:09 | {"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 contain any instances of backtracking behavior. The text appears to be a collection of mathematical problems and solutions, with no narrative or explanatory text ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
no
## Text domain (broad)
math
## Text domain (specific)
Calculus, Differential Equations
## Rationale
The text appears to be a collection of math problems from the JEE Main 2021 exam, specifically focusing on differential... | <|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 appears to be a collection of mathematics problems from the JEE Main 2021 exam, specifically focusing on differential equations. The text does not cont... | <|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 collection of mathematics problems, specifically differential equations, from the JEE Main 2021 exam. The problems are ... |
https://en.citizendium.org/wiki/Chain_(mathematics) | # Chain (mathematics)
Jump to navigation Jump to search
This disambiguation page lists articles associated with the same or a similar title.
In mathematics, chain may refer to: | 2022-08-08 00:41:02 | {"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 is a straightforward disambiguation page that lists articles associated with the title "Chain (mathematics)" without any ind... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
math
## Text domain (specific)
Disambiguation in Mathematics Terminology
## Rationale
The text appears to be a disambiguation page, listing various articles associated with the term "chain" in math... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text is a disambiguation page that lists articles associated with the title "Chain (mathematics)". It does not contain any mathematical calculations, results, or c... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The provided text is a disambiguation page that lists various articles associated with the term "chain" in mathematics. It does not contain any problem-solving or goal-o... | <|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 does not exhibit backward-chaining behavior. It appears to be a disambiguation page that lists various articles associated with the ter... |
http://math.stackexchange.com/questions/346797/what-goes-wrong-in-this-derivative | # What goes wrong in this derivative?
$$f(x) = \frac{2}{3} x (x^2-1)^{-2/3}$$
and f'(x) is searched.
So, by applying the product rule $(uv)' = u'v + uv'$ with $u=(x^2-1)^{-2/3}$ and $v=\frac{2}{3} x$, so $u'=-\frac{4}{3} x (x^2-1)^{-5/3}$ and $v' = \frac{2}{3}$, I obtain
$$f'(x) = - \frac{2}{9} (x^2-1)^{-5/3} x^2 +... | 2015-04-18 07:59:01 | {"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>1</count>.
## Rationale
The writer initially calculates $f'(x)$ using the product rule and obtains an incorrect result. They then re-examine their calculation, specifically the term $uv'$, and realize that it is ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Calculus, Derivatives
## Rationale
The text discusses a mathematical problem related to finding the derivative of a given function $f(x) = \frac{2}{3} x (x^2-1)^{-2... | <|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 by comparing their result to a known value from Wolfram Alpha and also by re-evaluating their calculation for $u'v$ to identify the... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>5</count>.
## Rationale
The text contains several steps where the model breaks down the problem into smaller, intermediate goals to verify the answer. These steps include:
1. Identifying the ... | <|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. Firstly, the writer starts with the goal of finding the derivative $f'(x)$ and works backward to i... |
https://www.zbmath.org/serials/?q=se%3A00001156 | ## IMA Journal of Mathematics Applied in Medicine and Biology
Short Title: IMA J. Math. Appl. Med. Biol. Publisher: Oxford University Press, Oxford ISSN: 0265-0746 Online: http://imammb.oxfordjournals.org/content/by/year Successor: Mathematical Medicine and Biology Comments: No longer indexed
Documents Indexed: 312 ... | 2022-05-29 02:41:21 | {"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": 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 appears to be a list of academic publications, authors, and fields of study, presented in a straightforward and organized ma... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
science
## Text domain (specific)
Mathematical Biology and Medicine
## Rationale
The text appears to be a collection of metadata and citations from a scientific journal, specifically the IMA Journa... | <|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 collection of mathematical models and research papers related to biology, medicine, and epidemiology. It does not contain any explicit verific... | <|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?
No
## Number of backward chaining instances
<count>0</count>
## Rationale
The provided text appears to be a collection of academic articles and authors related to the field of mathematics applied in medicine and biology. It doe... |
https://codereview.stackexchange.com/questions/229781/recursive-code-to-generate-a-parametric-sweep-of-input-values/229788 | # Recursive code to generate a parametric sweep of input values
I generate a set of data based off every combination of inputs. The source range that's inputs requires headers to identify the parameters. In its present state I'm not content as it's not as straightforward as I'd like it to be. Specifically the module v... | 2021-02-26 16:04:56 | {"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 recursive implementation of a parametric sweep and discusses potential improvements to the code, including... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
computer science
## Text domain (specific)
Programming, Software Development, Code Review, and Refactoring, specifically in the context of recursive algorithms and data structures in VBA (Visual B... | <|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 code re... | <|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. Firstly, the writer starts with the goal of generating a parametric sweep of input values... |
https://math.stackexchange.com/questions/1978450/criterium-involving-ergodicity-and-weak-mixing | # Criterium involving ergodicity and weak mixing
A transformation $T$ on $X$ is ergodic iff for any two measurable sets $U$ and $V$ holds: $\lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1} m(T^{-j}U\cap V)=m(U)m(V)$,
(or equivalently iff every invariant measurable function is constant almost everywhere or iff every T-inv... | 2021-05-15 14:49:22 | {"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 does not exhibit any backtracking behavior. The writer presents definitions and properties related to ergodicity and weak mixing, and then poses a question about proving t... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
partial
## Text domain (broad)
math
## Text domain (specific)
Ergodic Theory and Measure-Preserving Transformations
## Rationale
The text discusses specific concepts from ergodic theory, such as ergodicity, weak mixing, an... | <|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 results to known values or checking the outcome of a calculat... | <|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 problem is broken down into smaller, intermediate goals to verify an answer. Instead, it presents m... | <|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. Firstly, the writer starts with the goal of proving that three properties are equivalent ... |
https://www.esaral.com/q/a-solid-is-composed-of-a-cylinder-with-hemispherical-ends-54719/ | A solid is composed of a cylinder with hemispherical ends.
Question:
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
Solution:
Height of the cylinde... | 2022-05-17 17:08:12 | {"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": 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 is a mathematical solution to a problem and does not exhibit any backtracking behavior. The writer follows a straightforward approach to calculate the surface area of the ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Geometry, specifically surface area calculations of 3D shapes
## Rationale
The text presents a problem involving the calculation of the surface area of a solid comp... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The 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 a calcula... | <|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 for the purpose of answer verifi... | <|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 in the solution to the problem. The goal is to find the cost of polishing the surface of the solid. However, instead... |
https://www.physicsforums.com/threads/opinion-about-y-f-y.334349/ | 1. Sep 2, 2009
### Zaphys
Hello science companions ;)
I was wondering for a while how to solve this ODE (y''=f(y)) and I finally found one way to integrate it. I don't know actually if it is correct but as I see them, all steps are mathematically consistent. Here I show how I came to the general solution (for all st... | 2017-09-21 13:06:28 | {"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 writer does not exhibit any backtracking behavior in the provided text. They present a solution to an ordinary differential equation (ODE) and engage in a discussion with others about t... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Differential Equations, specifically Ordinary Differential Equations (ODEs) of the form y'' = f(y)
## Rationale
The text discusses a specific type of Ordinary Diffe... | <|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 by applying the derived method to a known differential equation and verifying that it produces the correct solution. This occurs in... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>5</count>.
## Rationale
The original poster, Zaphys, breaks down the problem of solving the differential equation y'' = f(y) into smaller, intermediate steps. These steps include:
1. multiply... | <|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 in Zaphys' approach to solving the differential equation y'' = f(y). Zaphys starts with the goal of finding the gene... |
https://dsp.stackexchange.com/questions/27661/how-does-delta-modulation-work-practically | # How does delta modulation work practically?
How does delta modulation work in practice? And where is it used? I find it confusing that, in 1-bit quantization we use only 2 level; if we apply this quantization, there will be loss in information. So, why do we use this technique?
One key point to note about delta mod... | 2019-07-16 15:14:43 | {"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 text provided is a discussion about delta modulation and its practical applications. The conversation flows with questions, explanations, and clarifications, but there is no instance wh... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Digital Signal Processing, specifically Delta Modulation and Quantization
## Rationale
The text discusses the concept of delta modulation, its practical applicat... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
no
## Number of answer verification steps
<count>0</count>.
## Rationale
The text provided does not contain explicit verification steps where the writer checks their own work by comparing results to known values or checking the result of a calculati... | <|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 conversation appears to be 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 text does not exhibit backward chaining behavior. The writer is asking a question about how delta modulation works in practice and where it is used, ... |
http://blog.stata.com/2012/08/29/using-statas-random-number-generators-part-3-drawing-with-replacement/ | Home > Numerical Analysis > Using Stata’s random-number generators, part 3, drawing with replacement
## Using Stata’s random-number generators, part 3, drawing with replacement
The topic for today is drawing random samples with replacement. If you haven’t read part 1 and part 2 of this series on random numbers, do so... | 2016-05-01 07:56:00 | {"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 text provided does not exhibit any backtracking behavior. The author presents a step-by-step solution to drawing random samples with replacement using Stata's random-number generators a... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Numerical Analysis, Statistics, and Data Sampling
## Rationale
The text discusses the use of Stata's random-number generators to draw random samples with replacem... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>3</count>.
## Rationale
The writer explicitly checks their own work in three instances. Firstly, they verify that the solution works for the case where n<N by trying an example with n=10 and N=52. Se... | <|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 for answer verification. The tex... | <|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 author is explaining how to draw a random sample of size n... |
https://ora.ox.ac.uk/objects/uuid:54a7200b-eebc-49b4-ac68-2c41ca1a5270 | Journal article
### The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem
Abstract:
In this paper, we prove that the partial sum process of general orthogonal series is a geometric 2-rough process under the same cond... | 2020-10-28 18:27:26 | {"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 appears to be a journal article abstract and publication information, and does not contain any instances of backtracking behavior. The text is formal and presents informat... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Functional Analysis, Orthogonal Series, Fourier Series
## Rationale
The text appears to be a journal article discussing a mathematical concept, specifically the par... | <|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 journal article abstract and publication information, and does not contain any explicit verification steps, such as comparing results to known... | <|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 journal article abstract and publication information, and does not contain any explicit subgoal setting or step-by-step breakdown 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 provided text appears to be a journal article abstract and publication information, which does not exhibit backward-chaining behavior. Backward chain... |
https://www.hackmath.net/en/math-problem/14543 | # College 2
College student is moving into a dormitory. The student rent a truck for $19.95 plus$0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost$144.67. Using a linear equation, explain the process to find how many miles the student drove the truck
Cor... | 2020-10-25 08:13:13 | {"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 contain any instances of backtracking behavior. The writer presents a problem, provides a solution, and then lists several other math problems without revisiting ... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Algebra, Linear Equations
## Rationale
The text describes a scenario where a college student rents a truck and incurs costs, including a fixed fee and a per-mile ch... | <|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 collec... | <|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 in the problem "College student is moving into a dormitory. The student rent a truck for $19.95 plus $0.99 per mile.... |
https://socratic.org/questions/5670e42d11ef6b7df9d86f6d#287470 | # Question #86f6d
Jul 12, 2016
Draw a couple of triangles and make use of the sum formula for sine to get $\sin \left({\cos}^{- 1} \left(- \frac{33}{65}\right) + {\tan}^{- 1} \left(\frac{13}{35}\right)\right) = \frac{1531}{65 \sqrt{1394}}$.
#### Explanation:
These questions require us to remember what sine and cosi... | 2021-10-25 05:05:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 46, "mathjax_inline_tex": 1, "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 text provided is a step-by-step solution to a trigonometry problem. The author presents a clear and logical approach to solving the problem, using diagrams and formulas to derive the so... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Trigonometry, specifically the use of inverse trigonometric functions and the sum formula for sine.
## Rationale
The text does not present a problem to be solved, bu... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>1</count>.
## Rationale
The writer explicitly checks their work by comparing the calculated result to a known value at the end of the explanation, where they derive the result $\sin \left({\cos}^{- 1... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>7</count>.
## Rationale
The text contains explicit subgoal setting, where the problem is broken down into smaller, intermediate goals. The steps include:
1. Letting $x = {\cos}^{- 1} \left(- ... | <|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. Firstly, the writer starts with the goal of finding $\sin \left({\cos}^{- 1} \left(- \fra... |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-2-section-2-1-linear-equations-in-one-variable-exercise-set-page-56/90 | ## Intermediate Algebra (6th Edition)
Published by Pearson
# Chapter 2 - Section 2.1 - Linear Equations in One Variable - Exercise Set: 90
#### Answer
$x+4=x+5$
#### Work Step by Step
In order to write an equation in x that has no solution, we can write an equation where both sides have the same variable terms bu... | 2017-06-25 19:39:24 | {"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 text does not exhibit any backtracking behavior. The writer presents a clear and direct approach to demonstrating that the equation $x+4=x+5$ has no solution, and does not abandon or re... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Algebra, Linear Equations
## Rationale
The text discusses a specific mathematical concept, linear equations in one variable, and provides an example of an equation ... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>1</count>.
## Rationale
The writer explicitly checks their work by simplifying the equation $x+4=x+5$ and verifying that it results in a false statement ($4=5$), which confirms that the original equa... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>3</count>.
## Rationale
The text describes a step-by-step process to verify if an equation has a solution. The steps include: (1) writing an equation with the same variable terms but different... | <|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 in the explanation of how to write an equation with no solution. The writer starts with the goal of creating an equa... |
https://electronics.stackexchange.com/questions/342859/bjt-common-base-output-resistance-derivation | # BJT common-base output resistance derivation
In Sedra/Smith the following image may be founded that is used for output resistance equation derivation of common-base BJT amplifier. The question is why the gm*v and v/re currents are directed up? Why they are not displayed in down direction?
The equation of output res... | 2022-07-03 17:27:08 | {"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?
yes
## Number of backtrack steps
<count>2</count>.
## Rationale
The writer backtracks when they initially derive the output resistance equation with the current directed downwards, obtaining $R_out = r_o + (1 - g_m * r_o) * Re'$, but then realizes this... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Electronics, specifically BJT (Bipolar Junction Transistor) amplifiers and output resistance derivation
## Rationale
The text discusses a specific problem relate... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count> 5 </count>.
## Rationale
The writer explicitly checks their own work in several instances. For example, they derive the equation for output resistance using their own schematic and then compare it t... | <|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 of deriving the output resistance of a common-base BJT amplifier is broken down into smaller, ... | <|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. Firstly, the writer is trying to derive the output resistance equation for a common-base ... |
https://teachercenter.cciu.org/mod/page/view.php?id=239 | General Information
COSTS AND SCHEDULING
Usage Fee
There is no charge to Chester County public school teachers for visiting the Teacher Center; however there are daily limits for certain materials. Please see the linked sheet for information in regard to daily limits.
There is a $25.00 materials fee per day per teac... | 2018-03-21 12:55:06 | {"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 presents information in a straightforward and organized manner, without the writer abandoning a thought or approach and tryi... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
no
## Contains Solution?
no
## Text domain (broad)
education
## Text domain (specific)
Teacher Resources and Professional Development
## Rationale
The text appears to be providing general information about the costs and scheduling of a Teacher Cent... | <|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, where the model breaks down the problem into smaller, intermediate goals. The text appears to be informa... | <|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 presentation of information about costs, scheduling, and service... |
http://bootmath.com/conditional-probability-containing-two-random-variables.html | Conditional probability containing two random variables
-Define $X$ and $X_1$ to be two dependent non-negative random variables.
Specifically, $X_1$ depends on two (continuous) random variables, termed $X_1^{(1)}$ and $X_1^{(2)}$, and $X$ depends on these two random variables in addition to a third one, termed $X^{(3)... | 2018-07-16 01:12:02 | {"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?
yes
## Number of backtrack steps
<count>2</count>.
## Rationale
The writer exhibits backtracking behavior in two instances. Firstly, after attempting to use Bayes' theorem, the writer becomes stuck and explicitly states "But how to proceed from here? H... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
math
## Text domain (specific)
Probability Theory, specifically Conditional Probability with Multiple Random Variables
## Rationale
The text discusses conditional probability involving multiple d... | <|start_header_id|>assistant<|end_header_id|>
## Does verification?
yes
## Number of answer verification steps
<count>1</count>.
## Rationale
The writer of the solution attempts to verify the given relation by trying to prove it analytically and then looks for a counterexample to disprove it. The verification step o... | <|start_header_id|>assistant<|end_header_id|>
## Does answer verification?
yes
## Number of answer verification steps
<count>2</count>.
## Rationale
The text contains two explicit subgoal steps to verify the given relation. The first step involves using Bayes' theorem to decompose the conditional probability, and th... | <|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 when the writer attempts to prove the relation $P(X_1=a,Y_1=b \mid X=c,Y=d)=... |
https://stats.stackexchange.com/questions/213318/generalized-linear-mixed-model-glmmadmb-date-as-random-effect | # Generalized linear mixed model - glmmADMB - date as random effect
I have a couple related questions about using a generalize linear mixed effects model to analyze data from an agricultural field experiment. I have found several posts that are similar to this question, but nothing that quite gets at my points of conf... | 2022-01-21 12:39:58 | {"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 text provided does not exhibit any backtracking behavior. The writer presents their problem, explains their thought process, and receives feedback and guidance from others. The conversa... | <|start_header_id|>assistant<|end_header_id|>
## Contains Problem?
yes
## Contains Solution?
yes
## Text domain (broad)
science
## Text domain (specific)
Statistics, specifically Generalized Linear Mixed Models
## Rationale
The text describes a problem with analyzing data from an agricultural field experiment usin... | <|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 explicit subgoal setting, where the model breaks down the problem into smaller, intermediate goals. The text appears to be a discussio... | <|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. Firstly, the writer starts with their goal of analyzing data from an agricultural field e... |
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