MathSE ID int64 795 4.87M | Math Question stringlengths 23 305 | Tag stringclasses 2
values |
|---|---|---|
137,352 | What are the domain and range of the map f in Devaney's definition of chaos on a metric space? | Unambiguous |
2,561,078 | How does the triangle inequality apply to the proof for f-g using epsilon and delta? | Ambiguous |
735,461 | For a completely positive map $f: M_n \to M_m$ with $f(a) = I_m$ for some $a \in M_n$, prove or disprove that there exists a positive element $b \in M_n$ such that $f(b) = I_m$. | Unambiguous |
2,461,048 | What is the cyclic subgroup generated by -1? | Ambiguous |
578,647 | What is an intuitive explanation of the Fourier transform and how is it used to analyze signals in the frequency domain? | Unambiguous |
2,430,945 | Decide if the statement " $n^2-1$ is multiple of $4$ if and only if $n-1$ is multiple of $4$" is true or false. | Unambiguous |
1,403,539 | Prove that $\arctan (x) + \arctan(1/x) = \frac{\pi}{2}$ for $x >0$. | Unambiguous |
510,991 | Prove that every continuous function defined on a compact metric space is uniformly continuous. | Unambiguous |
2,904,744 | Prove that $\lim_{x\to 1} f(x) = 3$ where $f(x) = \frac{x^3-1}{x-1}$ for $x \neq 1$. | Unambiguous |
982,186 | Decompose the expression $\frac{1}{4n^2-1}$ into partial fractions. | Unambiguous |
4,087,621 | Between which two consecutive integers does the value of $\sqrt{12}$ lie? | Unambiguous |
697,675 | How do you multiply a matrix by a row vector from the left? | Unambiguous |
1,025,321 | Find the derivative $\frac{dy}{dx}$ using implicit differentiation for the equation $\ln(1+xy) = xy$. | Unambiguous |
3,313,255 | What is the definition and standard form of Sum of Products (SOP) in boolean algebra? | Unambiguous |
578,647 | In the Fourier transform, what does the cross term mean? | Ambiguous |
3,843,282 | finding quotient group relationship | Ambiguous |
3,372,191 | Asymptotic behavior of $a_{n+1}=a_n + f(a_n)$ | Ambiguous |
2,694,508 | Find the range of values of $k$ such that both roots of $x^2 - 2kx + k^2 - 1 = 0$ lie in the interval $(-2, 4)$. | Unambiguous |
3,735,022 | What is the formula for the curvature of a Frenet curve constrained to lie on a sphere? | Unambiguous |
4,870,757 | If I know the dimension, depth, and codimension of $R$ and $I$, can I determine the depth of $I$? | Ambiguous |
166,794 | Proof that the set of irrational numbers is uncountable | Unambiguous |
4,127,695 | Evaluate the sum $\sum_{r=0}^n 2^{n-r} \binom{n+r}{r}$ for non-negative integers $n$ and $r$. | Unambiguous |
2,949,838 | Can every basis of a finite dimensional vector space be orthogonal? | Ambiguous |
7,391 | How do I evaluate the definite integral $\int_0^{\pi} \sin(2x)\sin(x) dx$? | Unambiguous |
1,315,088 | Evaluate the limit $\lim_{x \to 0} \left( \frac{1}{\sin(x)\arctan(x)} - \frac{1}{\tan(x)\arcsin(x)} \right)$ | Unambiguous |
36,134 | Modern Equivalent of Carr's Synopsis? | Ambiguous |
2,526,693 | Evaluate the limit: $\lim_{x \to 0^+} x^{\sqrt{x}}$ | Unambiguous |
432,999 | Prove that the limit of the sequence $\frac{n}{2^n}$ as $n$ approaches infinity is 0. | Unambiguous |
1,572,032 | Why is the CDF of $Y_n$ equal to $(\frac{t- \theta}{\theta})$ and what are the restrictions on $t$? | Ambiguous |
2,186,358 | What is the correct term for $I^n f(x)$ where $I$ is the integral operator? | Ambiguous |
606,172 | If the sequence $(x_n)$ of real numbers converges and $\lim_{n \to \infty} (2x_{n+1} - x_n) = x$, is it true that $\lim_{n \to \infty} x_n = x$? | Unambiguous |
4,468,673 | If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the maximum value of the product $xy$? | Unambiguous |
166,794 | I found a proof arguing that the irrationals are countable based on the density of the rationals. I know this is wrong, but where is the mistake in the logic? | Ambiguous |
1,191,610 | Prove that the composition of two group homomorphisms is also a group homomorphism. | Unambiguous |
4,437,668 | What are some interesting examples of elementary proofs by mathematical induction for students? | Unambiguous |
1,354,331 | Does there exist a function that is discontinuous at a point but has a continuous derivative on its domain? | Unambiguous |
970,133 | Prove that the infinite series $\sum_{n=1}^\infty \frac{n^2(n-1)}{2^n}$ converges to 20. | Unambiguous |
419,859 | Prove that the graph $y=x^{p/q}$ has a vertical tangent. | Ambiguous |
105,575 | What is the difference between the soundness and completeness theorems in first-order logic? | Unambiguous |
456,595 | Prove: $\frac{1}{1^2} +\frac{1}{2^2} + \cdots + \frac{1}{n^2} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2} < 2$ | Ambiguous |
3,075,859 | What is the next step after showing $(c^k)^t = (id)$ for cycle orders? | Ambiguous |
2,538,727 | How to use Cantor's diagonal to prove my space is not sequentially compact? | Ambiguous |
217,966 | What is the relationship between monomorphisms and pullbacks in category theory? | Unambiguous |
3,117,992 | Could different physical systems follow different underlying mathematics? | Ambiguous |
181,367 | Provide a counterexample to show that a pseudocompact topological space is not necessarily a compact space. | Unambiguous |
854,380 | How to distinguish between walking on a sphere and walking on a torus? | Ambiguous |
3,087,356 | Why is the number 2 included in the definition of prime numbers instead of being excluded as the only even prime? | Unambiguous |
4,468,673 | If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$? | Ambiguous |
4,060,048 | How do I solve integrals of the form integral of (polynomial * exponential) dx using integration by parts? | Unambiguous |
1,024,830 | What is the intuitive meaning of a compact set in the context of a metric space or topology? | Unambiguous |
3,172,708 | How to efficiently update the inverse of a lower triangular matrix after changing 4 individual elements? | Unambiguous |
1,133,113 | How do we define arc length? | Ambiguous |
2,490,690 | In how many ways can a payment of $107$ shekels be made using coins/bills of denominations $1$, $10$, and $50$ shekels, assuming an unlimited supply of each? | Unambiguous |
1,711,154 | Prove that f is differentiable at x=0 | Ambiguous |
551,148 | Why is $2x^3 + x$, where $x \in \mathbb{N}$, always divisible by 3? | Ambiguous |
2,304,892 | Probability of rolling any set of size k on n dice with m sides | Ambiguous |
1,576,678 | Can my sine formula with $\pi/6$ be put into Excel somehow to plot the graph? | Ambiguous |
2,982,578 | Prove that every finitely generated module over a ring $R$ is a homomorphic image of a free module. | Unambiguous |
1,619,762 | What are the equivalent statements of the Generalized Riemann Hypothesis (GRH) expressed in terms of the summatory functions of the Möbius and Liouville functions? | Unambiguous |
1,882,798 | Is there a mathematical rule to check if positive numbers $a$ and $b$ satisfy my modulo $P$ equation? | Ambiguous |
289,779 | I'm looking at the sequence $a_n = 3^n - 2^{n+100}$. How do I handle this? | Ambiguous |
1,320,951 | Prove that the intersection of any two cyclic subgroups of a group is also a cyclic subgroup. | Unambiguous |
2,449,459 | What's wrong with this fake proof that $2+2=5$? | Ambiguous |
1,017,503 | Prove by induction that $\sum_{k=0}^n k\cdot k! = (n+1)! - 1$ for all $n \in \mathbb{N}$. | Unambiguous |
3,490,887 | Question on existence of square root function! | Ambiguous |
3,791,238 | Why is a curve homeomorphic to a knot? | Ambiguous |
2,284,995 | Expected count of "double records" | Ambiguous |
3,468,876 | Suppose $Y_1$ and $Y_2$ are independent and $X=Y_1+Y_2$. What is the distribution of $X$? | Ambiguous |
243,106 | How to apply $\epsilon-\delta$ definition to a 2-valued function? | Ambiguous |
2,396,246 | One tank holds more than another by some amount. When the smaller one is about 2/3 full, it holds roughly as much as half the larger one. What is the capacity? | Ambiguous |
303,933 | Evaluate the limit $\lim_{n \to \infty} \frac{(\log(n))^a}{n^b}$ for positive real constants $a$ and $b$. | Unambiguous |
975,836 | How to solve linear recurrence relations using the method of repeated substitution? | Unambiguous |
164,244 | Prove that if a subgroup of index p is the smallest prime dividing the order of a finite group, then it is a normal subgroup. | Unambiguous |
2,344,993 | What are some unexpected real-world applications or occurrences of the natural logarithm in mathematics and science? | Unambiguous |
781,320 | Why does this curve cross the y-axis if $\cos(\sin x)$ is never zero? | Ambiguous |
2,834,788 | Is the EulerâMascheroni constant $\gamma$ known to be irrational? | Unambiguous |
3,247,615 | How do I evaluate the polynomial P(x) at x = -2? | Unambiguous |
1,329,195 | How to calculate a percentage increase when the result is above 100%? | Unambiguous |
2,449,459 | Where is the logical fallacy in the common fake proof that $2+2=5$? | Unambiguous |
3,017,476 | Interpreting an agreement function | Ambiguous |
1,169,872 | Is there a positional numeral system base $b$ such that every rational number has a terminating representation? | Unambiguous |
2,923,438 | How does the RSA cryptosystem work, and what are the steps for key generation, encryption, and decryption? | Unambiguous |
3,114,691 | How to find $\lim\limits_{n\to\infty} A^n$? | Ambiguous |
1,559,640 | How to find all natural numbers $n$ for quadratic permutations with a perfect square sum? | Ambiguous |
3,699,937 | The cyclic subgroups of $p^2$ order non-cyclic group are normal | Ambiguous |
551,148 | Prove that for every natural number $x$, the expression $2x^3 + x$ is always divisible by 3. | Unambiguous |
3,537,073 | Help with proof by induction, please! I may not be understanding how to work with factorials. | Ambiguous |
3,537,073 | Can you provide a step-by-step example of how to use proof by induction to prove a summation formula involving factorials? | Unambiguous |
1,647,675 | A Quadrilateral and A Triangle in a Trapizium | Ambiguous |
2,999,909 | In an arbitrary category, is the hom-set $Hom(X,Y)$ always equipped with an Abelian group structure? | Unambiguous |
1,466,540 | Find the $\lim_{x\to \infty} (\ln(x)-x)$ | Unambiguous |
4,247,524 | Finding the probability that at least 8 houses in a row are of same colour. | Ambiguous |
486,600 | Given that ai (where i is the imaginary unit) is a root of the polynomial $x^3-bx^2+a^2x-a^2b=0$, prove this fact and find the other two roots in terms of $a$ and $b$. | Unambiguous |
308,644 | Do I need to include the definition of union in this proof? | Ambiguous |
2,396,246 | How do I calculate the volume of water a cylindrical tank can hold given its radius and height? | Unambiguous |
3,560,940 | If the weights of three different items are 10g, 25g, and 5g, how do I divide 1kg among them? | Ambiguous |
2,561,078 | Prove that if functions $f$ and $g$ are continuous at a point $x$, then their difference $f-g$ is also continuous at $x$. | Unambiguous |
1,568,161 | Evaluating $\lim\limits_{x \to \pi} \frac{(\pi -x)\sin x}{1 + \cos x}$ | Ambiguous |
1,074,072 | Is there a notion dual to that of a path in a topological space? | Ambiguous |
2,664,926 | Evaluate the complex power $(-\sqrt{3} + i)^9$ using De Moivre's theorem. | Unambiguous |
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MathDisAm: Towards Math Query Disambiguation
Welcome to the official repository for the paper MathDisAm: Towards Math Query Disambiguation. This repository contains the dataset, query generation pipelines, and baseline classifier models designed to distinguish between ambiguous and unambiguous mathematical queries.
Dataset
The data directory contains the core datasets used for training and evaluating the disambiguation models:
MathDisAM_train.tsv: The training file containing MathSE IDs, mathematical questions, and their corresponding tags ("Ambiguous" or "Unambiguous").MathDisAM_test.tsv: The untouched, held-out test file used for final model evaluation.
Query Generation
The query generation process leverages a two-agent Large Language Model pipeline (using Gemma) to process natural mathematical questions:
- Ambiguous Query Generation:
- Uses an "Injector" agent to rewrite a math question to introduce deliberate ambiguity.
- Uses a "Verifier" agent to independently judge if the rewrite is genuinely ambiguous.
- The script processes questions until a target of 1,000 verified ambiguous questions is produced.
- Unambiguous Query Generation:
- Uses a "Clarifier" agent to rewrite queries to remove ambiguity.
- Uses a "Verifier" agent to evaluate if the query is fully well-posed and unambiguous.
- This pipeline also targets 1,000 verified unambiguous questions.
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