Update app.py

app.py

@@ -13,12 +13,52 @@ model = SentenceTransformer('all-MiniLM-L6-v2')
 # Math domain definitions (trimmed for brevity)
 DOMAINS = {
     "Real Analysis": "Studies properties of real-valued functions, sequences, limits, continuity, differentiation, Riemann/ Lebesgue integration, and convergence in the real number system.",
+    "Complex Analysis": "Explores analytic functions of complex variables, contour integration, conformal mappings, and singularity theory.",
     "Functional Analysis": "Deals with infinite-dimensional vector spaces, Banach and Hilbert spaces, linear operators, duality, and spectral theory in the context of functional spaces.",
-    "Graph Theory": "Deals with the study of graphs, networks, trees, connectivity, and coloring problems.",
+    "Measure Theory": "Studies sigma-algebras, measures, measurable functions, and integrals, forming the foundation for modern probability and real analysis.",
+    "Fourier and Harmonic Analysis": "Analyzes functions via decompositions into sines, cosines, or general orthogonal bases, often involving Fourier series, Fourier transforms, and convolution techniques.",
+    "Calculus of Variations": "Optimizes functionals over infinite-dimensional spaces, leading to Euler-Lagrange equations and applications in physics and control theory.",
+    "Metric Geometry": "Explores geometric properties of metric spaces and the behavior of functions and sequences under various notions of distance.",
+    "Ordinary Differential Equations (ODEs)": "Involves differential equations with functions of a single variable, their qualitative behavior, existence, uniqueness, and methods of solving them.",
     "Partial Differential Equations (PDEs)": "Deals with multivariable functions involving partial derivatives, including wave, heat, and Laplace equations.",
-    "Optimization": "Studies finding best outcomes under constraints, including convex optimization, linear programming, and integer programming.",
+    "Dynamical Systems": "Studies evolution of systems over time using discrete or continuous-time equations, stability theory, phase portraits, and attractors.",
+    "Linear Algebra": "Focuses on vector spaces, linear transformations, eigenvalues, diagonalization, and matrices.",
+    "Abstract Algebra": "General study of algebraic structures such as groups, rings, fields, and modules.",
+    "Group Theory": "Investigates algebraic structures with a single binary operation satisfying group axioms, including symmetry groups and applications.",
+    "Ring and Module Theory": "Extends group theory to rings (two operations) and modules (generalized vector spaces).",
+    "Field Theory": "Studies field extensions, algebraic and transcendental elements, and classical constructions.",
+    "Galois Theory": "Connects field theory and group theory to solve polynomial equations and understand solvability.",
+    "Algebraic Number Theory": "Applies tools from abstract algebra to study integers, Diophantine equations, and number fields.",
+    "Representation Theory": "Studies abstract algebraic structures by representing their elements as linear transformations of vector spaces.",
     "Algebraic Geometry": "Examines solutions to polynomial equations using geometric and algebraic techniques like varieties, schemes, and morphisms.",
-    "Others": "Covers problems that span multiple mathematical areas or do not fall neatly into a traditional domain."
+    "Differential Geometry": "Studies geometric structures on smooth manifolds, curvature, geodesics, and applications in general relativity.",
+    "Topology": "Analyzes qualitative spatial properties preserved under continuous deformations, including homeomorphism, compactness, and connectedness.",
+    "Geometric Topology": "Explores topological manifolds and their classification, knot theory, and low-dimensional topology.",
+    "Symplectic Geometry": "Studies geometry arising from Hamiltonian systems and phase space, central to classical mechanics.",
+    "Combinatorics": "Covers enumeration, existence, construction, and optimization of discrete structures.",
+    "Graph Theory": "Deals with the study of graphs, networks, trees, connectivity, and coloring problems.",
+    "Discrete Geometry": "Focuses on geometric objects and combinatorial properties in finite settings, such as polytopes and tilings.",
+    "Set Theory": "Studies sets, cardinality, ordinals, ZFC axioms, and independence results.",
+    "Mathematical Logic": "Includes propositional logic, predicate logic, proof theory, model theory, and recursion theory.",
+    "Category Theory": "Provides a high-level, structural framework to relate different mathematical systems through morphisms and objects.",
+    "Probability Theory": "Mathematical foundation for randomness, including random variables, distributions, expectation, and stochastic processes.",
+    "Mathematical Statistics": "Theory behind estimation, hypothesis testing, confidence intervals, and likelihood inference.",
+    "Stochastic Processes": "Studies processes that evolve with randomness over time, like Markov chains and Brownian motion.",
+    "Information Theory": "Analyzes data transmission, entropy, coding theory, and information content in probabilistic settings.",
+    "Numerical Analysis": "Designs and analyzes algorithms to approximate solutions of mathematical problems including root-finding, integration, and differential equations.",
+    "Optimization": "Studies finding best outcomes under constraints, including convex optimization, linear programming, and integer programming.",
+    "Operations Research": "Applies optimization, simulation, and probabilistic modeling to decision-making problems in logistics, finance, and industry.",
+    "Control Theory": "Mathematically models and regulates dynamic systems through feedback and optimal control strategies.",
+    "Computational Mathematics": "Applies algorithmic and numerical techniques to solve mathematical problems on computers.",
+    "Game Theory": "Analyzes strategic interaction among rational agents using payoff matrices and equilibrium concepts.",
+    "Machine Learning Theory": "Explores the mathematical foundation of algorithms that learn from data, covering generalization, VC dimension, and convergence.",
+    "Spectral Theory": "Studies the spectrum (eigenvalues) of linear operators, primarily in Hilbert/Banach spaces, relevant to quantum mechanics and PDEs.",
+    "Operator Theory": "Focuses on properties of linear operators on function spaces and their classification.",
+    "Mathematical Physics": "Uses advanced mathematical tools to solve and model problems in physics, often involving differential geometry and functional analysis.",
+    "Financial Mathematics": "Applies stochastic calculus and optimization to problems in pricing, risk, and investment.",
+    "Mathematics Education": "Focuses on teaching methods, learning theories, and curriculum design in mathematics.",
+    "History of Mathematics": "Studies the historical development of mathematical concepts, theorems, and personalities.",
+    "Others / Multidisciplinary": "Covers problems that span multiple mathematical areas or do not fall neatly into a traditional domain."
 }
 
 domain_names = list(DOMAINS.keys())