Basic Math Tutoring: Operations on Whole Numbers, Addition and Subtraction Using Fractional Notation, Addition and Subtraction Using Decimal Notation, Multiplication and Division Using Fractional Notation, Multiplication and Division Using Decimal Notation, Ratio and Proportion, Percent Notation, The Real Number System, Dimensional analysis, Number Systems Other than Base 10, Order of Operations, Exponents, Set Operations, Venn diagrams, Logic; Truth tables, Conditionals and Bi-conditionals.
Algebra Tutoring: Linear equations; Applications, Absolute value - Inequalities;Linear, Absolute value, Non linear - Functions / Graphs; Function notation, Linear,Polynomials, Translations / Shifting / Reflecting graphs, Composition, Inverse functions - Roots of polynomials; Quadratic, Factoring, Complete square, Quadratic formula,Complex Numbers, Higher Degree, Factoring special cases, Synthetic division - Exponentials and Logs; Graphs, Properties, Solving equations - Systems of linear equations; 2 equations 2 unknowns, Matrix algebra, Gaussian elimination, Inverses, Determinates - Conics - Mathematics of finance; Simple/compound interest, Annuities, Amortization - Linear programming; Geometric approach, simplex method.
Trigonometric functions: Angles and their measure, Right Triangle trigonometry,Functions of Any Angle, Applications - Graphs of Trigonometric Functions; Inverse Trig functions - Analytic Trigonometry, Solving equations, Verifying Identities,Formulas -Law of Sins, Law of Cosines - Complex numbers - Vectors - Analytic Geometry;Conics, Polar equations.
Calculus Tutoring: Limits; Definition, Limit Theorems, L'Hospital's Rule - Continuity;Intermediate Value Theorem - Derivatives; Chain Rule, Implicit Differentiation -Applications of Derivatives; Analysis of Graphs, Mean Value Theorem, Max/Min, Related Rates - Integrals; Definition, Definite Integrals, Fundamental Theorem of Calculus - Integration Techniques; Polynomials, Exponential and Logs, Trigonometric, Substitution,Trig substitution, Parts, Partial Fractions - Applications of Integrals; Length of Curves, Work, Volume, Surface Area - Parametric equations - Polar coordinates - Sequences and Series; Convergence test, Power series.
Statistics Tutoring: Descriptive Statistics, Data Analysis (Graphic Representations,Measures of Central Tendency, Dispersion, Position, Regression and Correlation);Probability (Combinatorics, Random Variables, Probability Distributions for Discrete and Continuous Random Variables; Inferential Statistics (Sampling and Sampling Distributions,Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Inference Concerning Correlation and Regression); Analysis of Variance (Categorical Data Analysis; Chi-square;Contingency Tables; Homogeneity tests; Decision Theory); Process and Quality Control(Control Charts)
Advanced Statistics Tutoring
Basic Review: Box plots, histograms, bar charts, pie charts, counting principles;descriptive statistics, mean, median, mode, five-number summary, standard deviation,range, IQR, Probability distributions.
Estimation Theory: Estimates by method of moments, their properties; Maximum likelihood estimates & their properties, Fisher information, Rao-Cramer inequality, efficient estimates; Bayes estimates, prior and posterior distributions, conjugate priors;Sufficient and jointly sufficient statistics, Neyman-Fisher factorization criterion,Rao-Blackwell theorem; Estimates for parameters of normal distribution, their properties; Chi-square, Fisher and Student distributions; Sampling distributions; Confidence intervals (For sampling distribution and for parameters of normal distribution).
Hypotheses Testing: Testing simple hypotheses, Bayes decision rules, types of error,most powerful tests, likelihood ratio tests, randomized tests; Composite hypotheses, power function, monotone likelihood ratio and uniformly most powerful tests; t-tests and F-tests; Goodness-of-fit tests, chi-square tests, tests of independence and homogeneity, Kolmogorov-Smirnov test, Effect Sizes; Two independent samples, paired sample t-tests; Test for equality of variance.
Regression and Classification: Simple linear regression, least-squares fit, statistical inference in simple linear regression, confidence intervals, prediction intervals;Classification problem, boosting algorithm; Multiple linear regression; Correlation;Normal probability plots and other assumption checking techniques; Effect Sizes; Logistic regression; Correlation and regression techniques for quantitative and qualitative data analysis; nominal scales, interactions; other related multivariate methods.
eTutorIcon's well-balanced Mathematics Online tutoring program for all students
An effective Mathematics Online Tutoring program balances three important components of mathematics conceptual understanding (making sense of mathematics), procedural proficiency (skills, facts, and procedures),and problem solving and mathematical processes (using mathematics to reason, think, and apply mathematical knowledge).These standards make clear the importance of all three of these components, purposefully interwoven to support students development as increasingly sophisticated mathematical thinkers. The standards of eTutorIcon's Mathematics Online Tutoring programs are to support the development of students so that they know and understand mathematics.
Mathematics and statistics tutors are available 24/7.
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