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from sentence_transformers import SentenceTransformer |
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from sklearn.metrics.pairwise import cosine_similarity |
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import gradio as gr |
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model = SentenceTransformer('all-MiniLM-L6-v2') |
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DOMAINS = { |
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"Real Analysis": "Studies properties of real-valued functions, sequences, limits, continuity, differentiation, Riemann/ Lebesgue integration, and convergence in the real number system.", |
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"Complex Analysis": "Explores analytic functions of complex variables, contour integration, conformal mappings, and singularity theory.", |
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"Functional Analysis": "Deals with infinite-dimensional vector spaces, Banach and Hilbert spaces, linear operators, duality, and spectral theory in the context of functional spaces.", |
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"Measure Theory": "Studies sigma-algebras, measures, measurable functions, and integrals, forming the foundation for modern probability and real analysis.", |
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"Fourier and Harmonic Analysis": "Analyzes functions via decompositions into sines, cosines, or general orthogonal bases, often involving Fourier series, Fourier transforms, and convolution techniques.", |
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"Calculus of Variations": "Optimizes functionals over infinite-dimensional spaces, leading to Euler-Lagrange equations and applications in physics and control theory.", |
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"Metric Geometry": "Explores geometric properties of metric spaces and the behavior of functions and sequences under various notions of distance.", |
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"Ordinary Differential Equations (ODEs)": "Involves differential equations with functions of a single variable, their qualitative behavior, existence, uniqueness, and methods of solving them.", |
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"Partial Differential Equations (PDEs)": "Deals with multivariable functions involving partial derivatives, including wave, heat, and Laplace equations.", |
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"Dynamical Systems": "Studies evolution of systems over time using discrete or continuous-time equations, stability theory, phase portraits, and attractors.", |
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"Linear Algebra": "Focuses on vector spaces, linear transformations, eigenvalues, diagonalization, and matrices.", |
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"Abstract Algebra": "General study of algebraic structures such as groups, rings, fields, and modules.", |
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"Group Theory": "Investigates algebraic structures with a single binary operation satisfying group axioms, including symmetry groups and applications.", |
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"Ring and Module Theory": "Extends group theory to rings (two operations) and modules (generalized vector spaces).", |
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"Field Theory": "Studies field extensions, algebraic and transcendental elements, and classical constructions.", |
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"Galois Theory": "Connects field theory and group theory to solve polynomial equations and understand solvability.", |
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"Algebraic Number Theory": "Applies tools from abstract algebra to study integers, Diophantine equations, and number fields.", |
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"Representation Theory": "Studies abstract algebraic structures by representing their elements as linear transformations of vector spaces.", |
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"Algebraic Geometry": "Examines solutions to polynomial equations using geometric and algebraic techniques like varieties, schemes, and morphisms.", |
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"Differential Geometry": "Studies geometric structures on smooth manifolds, curvature, geodesics, and applications in general relativity.", |
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"Topology": "Analyzes qualitative spatial properties preserved under continuous deformations, including homeomorphism, compactness, and connectedness.", |
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"Geometric Topology": "Explores topological manifolds and their classification, knot theory, and low-dimensional topology.", |
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"Symplectic Geometry": "Studies geometry arising from Hamiltonian systems and phase space, central to classical mechanics.", |
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"Combinatorics": "Covers enumeration, existence, construction, and optimization of discrete structures.", |
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"Graph Theory": "Deals with the study of graphs, networks, trees, connectivity, and coloring problems.", |
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"Discrete Geometry": "Focuses on geometric objects and combinatorial properties in finite settings, such as polytopes and tilings.", |
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"Set Theory": "Studies sets, cardinality, ordinals, ZFC axioms, and independence results.", |
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"Mathematical Logic": "Includes propositional logic, predicate logic, proof theory, model theory, and recursion theory.", |
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"Category Theory": "Provides a high-level, structural framework to relate different mathematical systems through morphisms and objects.", |
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"Probability Theory": "Mathematical foundation for randomness, including random variables, distributions, expectation, and stochastic processes.", |
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"Mathematical Statistics": "Theory behind estimation, hypothesis testing, confidence intervals, and likelihood inference.", |
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"Stochastic Processes": "Studies processes that evolve with randomness over time, like Markov chains and Brownian motion.", |
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"Information Theory": "Analyzes data transmission, entropy, coding theory, and information content in probabilistic settings.", |
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"Numerical Analysis": "Designs and analyzes algorithms to approximate solutions of mathematical problems including root-finding, integration, and differential equations.", |
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"Optimization": "Studies finding best outcomes under constraints, including convex optimization, linear programming, and integer programming.", |
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"Operations Research": "Applies optimization, simulation, and probabilistic modeling to decision-making problems in logistics, finance, and industry.", |
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"Control Theory": "Mathematically models and regulates dynamic systems through feedback and optimal control strategies.", |
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"Computational Mathematics": "Applies algorithmic and numerical techniques to solve mathematical problems on computers.", |
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"Game Theory": "Analyzes strategic interaction among rational agents using payoff matrices and equilibrium concepts.", |
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"Machine Learning Theory": "Explores the mathematical foundation of algorithms that learn from data, covering generalization, VC dimension, and convergence.", |
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"Spectral Theory": "Studies the spectrum (eigenvalues) of linear operators, primarily in Hilbert/Banach spaces, relevant to quantum mechanics and PDEs.", |
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"Operator Theory": "Focuses on properties of linear operators on function spaces and their classification.", |
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"Mathematical Physics": "Uses advanced mathematical tools to solve and model problems in physics, often involving differential geometry and functional analysis.", |
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"Financial Mathematics": "Applies stochastic calculus and optimization to problems in pricing, risk, and investment.", |
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"Mathematics Education": "Focuses on teaching methods, learning theories, and curriculum design in mathematics.", |
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"History of Mathematics": "Studies the historical development of mathematical concepts, theorems, and personalities.", |
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"Others / Multidisciplinary": "Covers problems that span multiple mathematical areas or do not fall neatly into a traditional domain." |
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} |
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domain_names = list(DOMAINS.keys()) |
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domain_texts = list(DOMAINS.values()) |
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domain_embeddings = model.encode(domain_texts) |
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def classify_math_question(question): |
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q_embed = model.encode([question]) |
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scores = cosine_similarity(q_embed, domain_embeddings)[0] |
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sorted_indices = scores.argsort()[::-1] |
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major = domain_names[sorted_indices[0]] |
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minor = domain_names[sorted_indices[1]] |
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major_reason = DOMAINS[major] |
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minor_reason = DOMAINS[minor] |
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explanation = f"**Major Domain:** {major}\\n\\n*Reason:* {major_reason}\\n\\n" + \\ |
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f"**Minor Domain:** {minor}\\n\\n*Reason:* {minor_reason}" |
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return explanation |
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iface = gr.Interface( |
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fn=classify_math_question, |
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inputs=gr.Textbox(lines=4, placeholder="Enter a math question..."), |
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outputs="textbox", |
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title="🔍 Math Domain Classifier (Major + Minor)", |
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description="Enter a math problem or statement, and get its major and minor domain with reasoning." |
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) |
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iface.launch() |
