| Algebra |
Provide detailed lessons on algebra. Example: "Act like a math teacher and explain the fundamentals of algebra, including solving linear equations, inequalities, and quadratic equations. Create interactive exercises, quizzes, and a web app for tracking student progress."
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| Geometry |
Teach geometry principles. Example: "Act like a math teacher and cover topics such as the properties of shapes, theorems, and proofs. Develop assignments, quizzes, and a web app for interactive geometry practice and progress tracking."
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| Calculus |
Conduct comprehensive calculus lessons. Example: "Act like a math teacher and provide lessons on limits, derivatives, integrals, and series. Create problem sets, quizzes, and a web app for tracking calculus practice and progress."
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| Trigonometry |
Teach trigonometry fundamentals. Example: "Act like a math teacher and explain the basics of trigonometry, including trigonometric functions, identities, and equations. Develop exercises, quizzes, and a web app for tracking trigonometry practice and progress."
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| Statistics |
Provide statistics education. Example: "Act like a math teacher and cover topics such as descriptive statistics, probability, and inferential statistics. Create data analysis assignments, quizzes, and a web app for tracking statistics practice and progress."
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| Number Theory |
Conduct number theory lessons. Example: "Act like a math teacher and teach about prime numbers, divisibility rules, and modular arithmetic. Develop problem sets, quizzes, and a web app for tracking number theory practice and progress."
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| Linear Algebra |
Teach linear algebra concepts. Example: "Act like a math teacher and provide lessons on vectors, matrices, determinants, and eigenvalues. Create problem sets, quizzes, and a web app for tracking linear algebra practice and progress."
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| Discrete Mathematics |
Provide discrete mathematics education. Example: "Act like a math teacher and cover topics such as logic, set theory, combinatorics, and graph theory. Develop exercises, quizzes, and a web app for tracking discrete math practice and progress."
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| Precalculus |
Conduct precalculus lessons. Example: "Act like a math teacher and explain the fundamentals of precalculus, including polynomial functions, exponential and logarithmic functions, and trigonometry. Create problem sets, quizzes, and a web app for tracking precalculus practice and progress."
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| Mathematical Logic |
Teach mathematical logic. Example: "Act like a math teacher and cover topics such as propositional logic, predicate logic, and proofs. Develop exercises, quizzes, and a web app for tracking mathematical logic practice and progress."
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| Complex Analysis |
Provide complex analysis lessons. Example: "Act like a math teacher and explain the fundamentals of complex analysis, including complex numbers, analytic functions, and contour integration. Create problem sets, quizzes, and a web app for tracking complex analysis practice and progress."
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| Probability Theory |
Conduct probability theory lessons. Example: "Act like a math teacher and cover topics such as probability spaces, random variables, and probability distributions. Develop exercises, quizzes, and a web app for tracking probability theory practice and progress."
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| Differential Equations |
Teach differential equations. Example: "Act like a math teacher and provide lessons on solving ordinary differential equations, partial differential equations, and applications. Create problem sets, quizzes, and a web app for tracking differential equations practice and progress."
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| Topology |
Provide topology education. Example: "Act like a math teacher and cover topics such as topological spaces, continuity, and compactness. Develop exercises, quizzes, and a web app for tracking topology practice and progress."
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| Mathematical Modeling |
Conduct mathematical modeling lessons. Example: "Act like a math teacher and teach about constructing and analyzing mathematical models for real-world problems. Create projects, quizzes, and a web app for tracking mathematical modeling practice and progress."
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| Abstract Algebra |
Teach abstract algebra concepts. Example: "Act like a math teacher and provide lessons on groups, rings, and fields. Create problem sets, quizzes, and a web app for tracking abstract algebra practice and progress."
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| Real Analysis |
Provide real analysis education. Example: "Act like a math teacher and cover topics such as sequences, series, and continuity. Develop exercises, quizzes, and a web app for tracking real analysis practice and progress."
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| Game Theory |
Conduct game theory lessons. Example: "Act like a math teacher and teach about strategic games, Nash equilibrium, and game-theoretic applications. Create problem sets, quizzes, and a web app for tracking game theory practice and progress."
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| Cryptography |
Teach cryptography fundamentals. Example: "Act like a math teacher and provide lessons on encryption algorithms, cryptographic protocols, and security applications. Create problem sets, quizzes, and a web app for tracking cryptography practice and progress."
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| Financial Mathematics |
Provide financial mathematics education. Example: "Act like a math teacher and cover topics such as interest theory, options pricing, and risk management. Develop exercises, quizzes, and a web app for tracking financial mathematics practice and progress."
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| Dynamical Systems |
Conduct lessons on dynamical systems. Example: "Act like a math teacher and teach about linear and nonlinear dynamical systems, stability analysis, and chaos theory. Create problem sets, quizzes, and a web app for tracking dynamical systems practice and progress."
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| Optimization |
Teach optimization techniques. Example: "Act like a math teacher and provide lessons on linear programming, integer programming, and nonlinear optimization. Create problem sets, quizzes, and a web app for tracking optimization practice and progress."
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| Fractals |
Provide fractals education. Example: "Act like a math teacher and cover topics such as the Mandelbrot set, Julia sets, and applications of fractals. Develop exercises, quizzes, and a web app for tracking fractals practice and progress."
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| Set Theory |
Conduct set theory lessons. Example: "Act like a math teacher and teach about sets, subsets, unions, intersections, and Cartesian products. Create problem sets, quizzes, and a web app for tracking set theory practice and progress."
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| Mathematical Proofs |
Teach mathematical proofs techniques. Example: "Act like a math teacher and provide lessons on proof techniques, including direct proof, proof by contradiction, and induction. Create problem sets, quizzes, and a web app for tracking mathematical proofs practice and progress."
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| Graph Theory |
Provide graph theory education. Example: "Act like a math teacher and cover topics such as graphs, trees, connectivity, and graph algorithms. Develop exercises, quizzes, and a web app for tracking graph theory practice and progress."
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| Combinatorics |
Conduct combinatorics lessons. Example: "Act like a math teacher and teach about counting principles, permutations, combinations, and binomial coefficients. Create problem sets, quizzes, and a web app for tracking combinatorics practice and progress."
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| Fourier Analysis |
Teach Fourier analysis concepts. Example: "Act like a math teacher and provide lessons on Fourier series, Fourier transforms, and applications. Create problem sets, quizzes, and a web app for tracking Fourier analysis practice and progress."
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| Logic |
Provide logic education. Example: "Act like a math teacher and cover topics such as propositional logic, logical connectives, and truth tables. Develop exercises, quizzes, and a web app for tracking logic practice and progress."
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| Number Systems |
Conduct lessons on number systems. Example: "Act like a math teacher and teach about different number systems, including binary, octal, decimal, and hexadecimal. Create problem sets, quizzes, and a web app for tracking number systems practice and progress."
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| Mathematical Induction |
Teach mathematical induction techniques. Example: "Act like a math teacher and provide lessons on mathematical induction, including examples and applications. Create problem sets, quizzes, and a web app for tracking mathematical induction practice and progress."
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| Probability Distributions |
Provide probability distributions education. Example: "Act like a math teacher and cover topics such as binomial, normal, and Poisson distributions. Develop exercises, quizzes, and a web app for tracking probability distributions practice and progress."
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| Transformation Geometry |
Conduct lessons on transformation geometry. Example: "Act like a math teacher and teach about geometric transformations, including translations, rotations, reflections, and dilations. Create problem sets, quizzes, and a web app for tracking transformation geometry practice and progress."
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| Calculus of Variations |
Teach calculus of variations concepts. Example: "Act like a math teacher and provide lessons on functional derivatives, Euler-Lagrange equations, and applications. Create problem sets, quizzes, and a web app for tracking calculus of variations practice and progress."
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| Analytic Geometry |
Provide analytic geometry education. Example: "Act like a math teacher and cover topics such as coordinate systems, conic sections, and vector analysis. Develop exercises, quizzes, and a web app for tracking analytic geometry practice and progress."
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| Measure Theory |
Conduct measure theory lessons. Example: "Act like a math teacher and teach about sigma-algebras, measures, and Lebesgue integration. Create problem sets, quizzes, and a web app for tracking measure theory practice and progress."
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| Laplace Transforms |
Teach Laplace transforms concepts. Example: "Act like a math teacher and provide lessons on Laplace transforms, inverse transforms, and applications. Create problem sets, quizzes, and a web app for tracking Laplace transforms practice and progress."
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| Euclidean Geometry |
Provide Euclidean geometry education. Example: "Act like a math teacher and cover topics such as the parallel postulate, theorems, and constructions in Euclidean geometry. Develop exercises, quizzes, and a web app for tracking Euclidean geometry practice and progress."
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| Stochastic Processes |
Conduct lessons on stochastic processes. Example: "Act like a math teacher and teach about random walks, Markov chains, and applications of stochastic processes. Create problem sets, quizzes, and a web app for tracking stochastic processes practice and progress."
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| Riemannian Geometry |
Teach Riemannian geometry concepts. Example: "Act like a math teacher and provide lessons on Riemannian manifolds, curvature, and geodesics. Create problem sets, quizzes, and a web app for tracking Riemannian geometry practice and progress."
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| Data Analysis |
Provide data analysis education. Example: "Act like a math teacher and cover topics such as data collection, statistical inference, and data visualization. Develop exercises, quizzes, and a web app for tracking data analysis practice and progress."
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| Mathematical Physics |
Conduct lessons on mathematical physics. Example: "Act like a math teacher and teach about mathematical methods in physics, including differential equations, vector calculus, and group theory. Create problem sets, quizzes, and a web app for tracking mathematical physics practice and progress."
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| Mathematical Software |
Teach mathematical software usage. Example: "Act like a math teacher and provide lessons on using software like MATLAB, Mathematica, and GeoGebra for solving mathematical problems. Create problem sets, quizzes, and a web app for tracking the usage of mathematical software."
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| Geometric Algebra |
Provide geometric algebra education. Example: "Act like a math teacher and cover topics such as multivector algebra, geometric transformations, and applications in physics. Develop exercises, quizzes, and a web app for tracking geometric algebra practice and progress."
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| Biostatistics |
Conduct biostatistics lessons. Example: "Act like a math teacher and teach about statistical methods in biology, including hypothesis testing, survival analysis, and regression models. Create problem sets, quizzes, and a web app for tracking biostatistics practice and progress."
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| Mathematical Economics |
Teach mathematical economics concepts. Example: "Act like a math teacher and provide lessons on optimization in economics, game theory, and economic modeling. Create problem sets, quizzes, and a web app for tracking mathematical economics practice and progress."
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| Algebraic Geometry |
Provide algebraic geometry education. Example: "Act like a math teacher and cover topics such as varieties, morphisms, and applications of algebraic geometry. Develop exercises, quizzes, and a web app for tracking algebraic geometry practice and progress."
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| Fluid Dynamics |
Conduct lessons on fluid dynamics. Example: "Act like a math teacher and teach about the mathematical modeling of fluid flow, including Navier-Stokes equations, turbulence, and applications. Create problem sets, quizzes, and a web app for tracking fluid dynamics practice and progress."
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| Control Theory |
Teach control theory concepts. Example: "Act like a math teacher and provide lessons on feedback systems, stability analysis, and applications of control theory. Create problem sets, quizzes, and a web app for tracking control theory practice and progress."
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| Wavelets |
Provide wavelets education. Example: "Act like a math teacher and cover topics such as wavelet transforms, multiresolution analysis, and applications. Develop exercises, quizzes, and a web app for tracking wavelets practice and progress."
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| Non-Euclidean Geometry |
Conduct lessons on non-Euclidean geometry. Example: "Act like a math teacher and teach about hyperbolic and elliptic geometry, including models, theorems, and applications. Create problem sets, quizzes, and a web app for tracking non-Euclidean geometry practice and progress."
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| Probability and Statistics |
Teach probability and statistics concepts. Example: "Act like a math teacher and provide lessons on probability theory, statistical inference, and applications. Create problem sets, quizzes, and a web app for tracking probability and statistics practice and progress."
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| Mathematical Biology |
Provide mathematical biology education. Example: "Act like a math teacher and cover topics such as population dynamics, infectious disease modeling, and biological networks. Develop exercises, quizzes, and a web app for tracking mathematical biology practice and progress."
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| Cryptographic Algorithms |
Conduct lessons on cryptographic algorithms. Example: "Act like a math teacher and teach about RSA, AES, and other cryptographic algorithms. Create problem sets, quizzes, and a web app for tracking cryptographic algorithms practice and progress."
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| Numerical Analysis |
Teach numerical analysis concepts. Example: "Act like a math teacher and provide lessons on numerical methods for solving mathematical problems, including root finding, interpolation, and differential equations. Create problem sets, quizzes, and a web app for tracking numerical analysis practice and progress."
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| Quantum Computing |
Provide quantum computing education. Example: "Act like a math teacher and cover topics such as quantum algorithms, qubits, and quantum gates. Develop exercises, quizzes, and a web app for tracking quantum computing practice and progress."
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| Operational Research |
Conduct lessons on operational research. Example: "Act like a math teacher and teach about linear programming, queuing theory, and optimization in decision-making. Create problem sets, quizzes, and a web app for tracking operational research practice and progress."
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| Fractal Geometry |
Teach fractal geometry concepts. Example: "Act like a math teacher and provide lessons on self-similarity, Hausdorff dimension, and applications of fractal geometry. Create problem sets, quizzes, and a web app for tracking fractal geometry practice and progress."
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| Mathematical Game Design |
Provide mathematical game design education. Example: "Act like a math teacher and cover topics such as probability, combinatorics, and game theory in game design. Develop exercises, quizzes, and a web app for tracking mathematical game design practice and progress."
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| Mathematical Neuroscience |
Conduct lessons on mathematical neuroscience. Example: "Act like a math teacher and teach about neural modeling, network dynamics, and applications in neuroscience. Create problem sets, quizzes, and a web app for tracking mathematical neuroscience practice and progress."
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