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PlatformYouTube459Bilibili11X3

DisciplineMathematical modeling277Calculus73Algebra51Probability & statistics44Discrete mathematics17Applied mathematics8Geometry2General mathematics1

DifficultyIntroductory318Intermediate104Foundational46Advanced5

StyleWhiteboard209Visual explanation138Lecture124Problem solving2

Length5–15 min270Under 5 min17515–45 min28

TopicMatrices25Derivatives18Vectors14Probability13Integrals12Greatest common divisor10Distributions9Eigenvalues8Linear transformations8Expectation8Time series forecasting8Chain rule7Function limit7Normal distribution7Graph theory7Exponential smoothing forecasting7Basis6Random variables6Independence6Euclidean algorithm6Determinants5Bayes’ theorem5Means5Permutations5Function graph5Definite integral5Conditional probability5Binomial distribution5Game theory modeling5Calculus4Power series4Taylor series4Grey prediction model4Regression modeling4ARIMA modeling4Normalization and standardization in modeling4Entropy weight method4Dimensional analysis4Linear programming4Transportation problem4Cluster analysis modeling4Modular arithmetic4Fourier transform3Fractions3Hypothesis testing3Function approximation3Arc length3Mean value theorem3Partial derivative3Infinite series3Multivariable function3Fuzzy comprehensive evaluation3Interpolation methods for modeling3Agent-based modeling3System dynamics modeling3Error propagation in models3Principal component analysis3Network flow modeling3Monte Carlo simulation3Markov chain modeling3Cellular automaton model3Minimum spanning tree model3Model validation techniques3Least squares fitting3Inventory model3Assignment problem3Fourier series3Exponential growth3Markov chains3Partial differential equations3Linear equations3Ordinary differential equations3Linear span2Riemann sums2Gradient2Lagrange multipliers2Series convergence2Partial sums2Total differential2Jacobian determinant2Variance2Outlier handling in modeling2SIR epidemic model2Logistic growth model2Similarity and scaling in modeling2Model assumptions and simplification2Traveling salesman modeling2Shortest path models2Branch and bound2Structure of a modeling report2Population growth model2Uniform distribution2Topological spaces2Experimental design2Group representations2Sequence convergence2Connectedness2Uniform convergence2Pointwise convergence2Singular values2Bisection method2Unit circle2Huffman coding2Pythagorean theorem2Conditional entropy2Polyhedra2Graphs2Inverse functions2Three-dimensional space1Tangent line1Area under curve1Incidence matrix1Network conservation1Line integral of a vector field1Sequence limit definition (ε–N)1Divergence1Function limit definition (ε–δ)1Comparison test1Error estimate1Alternating series1Zeno’s paradox1Limit nonexistence1Secant line1Local linearization1Tangent plane1Normal vector1Directional derivative1Multivariable limit1Iterated integral1Volume under surface1Moment of inertia1Rectangle partition1Curve fitting in modeling1Discriminant analysis1Factor analysis1Optimization modeling1Duality in linear programming1Differential equation modeling1Common mistakes in mathematical modeling1Integer programming1Multi-objective optimization1Dynamic programming for modeling1Queueing model1Analytic hierarchy process1Poisson distribution1Zero-knowledge proofs1Simplex method1Yoneda lemma1Autocorrelation1Trigonometric identities1Logistic growth1Universal properties1Value at Risk1Proof by contradiction1Direct proof1Analysis of variance1Angles1Rigid motions1Well-posedness1Complete reducibility1Difference equation model1Sequence limit1Nash equilibrium1Brownian motion1Counterexamples1Linear regression1Verification and validation1Finite element method1Turing patterns1Weak convergence1Quadratic residues1Number theory1Analytic continuation1Compound interest1Absolute value1Almost everywhere1Lebesgue measure1Triangle congruence1Bipartite matching1Chain complexes1Trees1Fields1TOPSIS evaluation model1Compact operators1Bounded linear operators1Unique factorization domains1Binary operations1Differential forms1Isolated singularities1Laurent series1Schur's lemma1Area and volume1Matrix norms1Monotone convergence theorem1Mathematical induction1Transition matrices1Chi-squared distribution1Stochastic processes1Source coding1Gaussian curvature1Intermediate value theorem1Catalan numbers1Radians1Axiomatic systems1Non-Euclidean geometry1Reproduction number1Initial value problems1Prime number theorem1Discretization1Inclusion–exclusion1Stationary distributions1Chinese remainder theorem1Extreme value theorem1Solid geometry1Tangent function1Gradient descent1Poisson processes1Principal ideal domains1Finite fields1Singular value decomposition1Discrete dynamical systems1Problem formulation1Propositions1Dominated convergence theorem1Newton's method1Inequalities1Necessary and sufficient conditions1Characteristic equations1Logistic map1Percentages1Logistic regression1Orbits1Euler's totient1Stopping times1Convex optimization1Cosets and Lagrange's theorem1Subgroups1Cyclic groups1Galois theory1Field extensions1Noether's theorem1Sigma-algebras1Weights and roots1Lie algebras1Localization1Integral domains1Lyapunov exponents1Model risk1Wronskian1Chaotic dynamics1Fixed and periodic points1Graph Laplacian1Boundary value problems1Polynomial interpolation1Social choice1Law of cosines1Tensor products1Bootstrap1Law of 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Mathematical modeling·English

Number Theory | Euler's Totient Function: Definition and Basic Example

Michael Penn

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