###### Sage Math Tutoring

###### Making Math Easy and Fun

The following videos cover various sub-fields of Mathematics!

To build even more confidence through structured, consistent, and well-paced practice and guidance for your current or upcoming coursework, as well through sufficient practice regarding various mathematical concepts, do not hesitate to contact me for In-Home or Online tutoring. For more on my tutoring services, see the Math Tutoring Page!

Enjoy!

**Algebra: **Understanding Numbers, Working with Fractions, Expressions, Basic Equations, Introducing Linear Equations, Linear Equations, Linear Inequalities, Systems of Linear Equations and Inequalities, Polynomials, Factoring Polynomials, Working with Radicals, Quadratic Equations and Inequalities, High-Powered Equations, Introducing Functions, Graphing Functions, Rational Expressions, Rational Equations and Inequalities

**Algebra II****: **Going beyond Algebra I, Linear Equations, Quadratic Equations, Rational/Radicals/Negatives, Graphing, Functions, Quadratic Functions, Polynomials, Rational Functions, Exponential/Logarithmic Functions, Conic Sections, Systems of Linear Equations, Systems of Linear Inequalities, Simplifying Complex Numbers, Matrices, Sequences and Series, Sets

**Geometry:** Algebra skills you need, Vocabulary, Angle classifications, Lines and Angles, Polygons, Logic, Proofs, Proving Segment and Angle Relationships, Proving Relationships between Lines, Intro to Triangles, Congruent Triangles, Similar Triangles part I, Similar Triangles part II, Quadrilaterals, Proofs about Quadrilaterals, Intro to Circles, Segments and Angles, Circle Proofs, Surfaces and Solids, Transformations

**Pre-Calculus/Trigonometry:** Numbers and Arithmetic you need to know, Equations and Inequality concepts you need to know, Polynomial concepts you need to know, Rational Expression concepts you need to know, Function concepts you need to know, High Powered Functions and Equations, Logarithmic Functions, Exponential Functions, Trigonometry-Angles, Trigonometric Functions, Trigonometric Identities, Solving Trigonometric Equations, Oblique Triangle Theorems, Parabolas and Circles, Ellipses and Hyperbolas

**Calculus:** What is Calculus? Linear equations concepts you need to know, Exponential Rule concepts you need to know, Factoring Polynomial concepts you need to know, Quadratic Equation concepts you need to know, Function concepts you need to know, Functional Symmetry, Graphs to memorize, Constructing Inverse Functions, Parametric Equations, Periodic Functions, Trigonometric Function concepts you need to know, Unit Circle, Important Identities, Soving Trigonometric Equations, Limits, One-Sided Limits, "Existence" of Limits, Methods of evaluating Limits Numerically, Limis and Infinity, Special Limit Theorems, Continuity, Discontinuity, Intermediate Value Theorem, Diffference Quotient, Intro to Derivatives, Derivative techniques, Rates of Change, Trigonometric Derivatives, Common Differentiation Tasks, Using Derivatives to Graph, Derivatives and Motion, Common Derivative Applications (including L'Hopital's Rule), Approximating Area, Antiderivatives, The Power Rule, Integrating Trigonometric Functions, The Fundamental Theorem of Calculus, U-Substitution, Calculating the Area between two Curves, The Mean Value Theorem for Integration, Finding Distance Traveled, Accumulation Functions, Integration Tips-Seperation, Integration Tips-U-Substitution with Long Division, Integration Tips-Completing the Square, Integration Tips-Selecting the Correct Method, Integration by Parts, Integration by Partial Fractions, Improper Integrals, Volumes of Rotational Solids, Arch Length, Intro to Differential Equations, Visualizing Differential Equations, Sequences and Series, Infinite Series Convergence Testing, Special Series.

**Statistics:** Why Statistics?, Data, Displaying Descriptive Statistics, Mean/Median/Mode, Measures of Dispersion, Basic Probability Theory, Counting Principles/Probability Distributions, The Binomial Probability Distribution, The Poisson Probability Distribution, The Normal Probability Distribution, Intro to Sampling, Sampling Distributions, Confidence Intervals, Intro to Hypotheses Testing, Hypothesis Testing with One Sample, Hypothesis Testing with Two Samples, The Chi-Square Probability Distribution, Analysis of Variance, Correlation and Simple Regression

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**Set Theory:** Sets and Basic Operations on Sets, Sets and Elementary Properties of the Real Numbers, Relations, Functions, Further Theory of Sets and Functions, Cardinal Numbers, Ordered Sets and Lattices, Ordinal Numbers, Axiom of Choice, Zorn's Lemma, Well-Ordering Theorem, Logic and Propositional Calculus, Boolean Algebra

**Algebra Word Problems:** Numbers, __Rate/Time/Distance,__ Mixtures, Coins, Age, Levers, Finance, Work, Plane Geometric Figures, Digits, Solutions Using Two Unknowns, Quadratics

**How to do quick Mental Math:** Fundamentals of Mental Math, Addition, Subtraction, Multiplication, Division, Fractions/Mixed Numbers/Percentages

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**College-Level Advanced Geometry: **Euclid's Geometry, Logic and Incidence Geometry, Hilbert's Axioms, Neutral Geometry, History of the Parallel Postulate, Discovery of Non-Euclidean Geometry, Independence and the Parallel Postulate, Philosophical Implications, Geometric Transformations, Real Hyperbolic Geometries

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**Probability:** Probability in Everyday Life, Probability Terminology, Pictorial Representations (Venn Diagrams, Tree Diagrams, and Baye's Theorem), Contingency Tables, Combinations/Permutations, Probability in Gaming, Probability Distribution Basics, The Normal Distribution, Sampling Distributions and the Central Limit Theorem, Making Decisions with Probability, Poisson Distribution, Geometric Distribution, Negative Binomial Distribution, Hypergeometric Distribution, Continuous Uniform Distribution, The Exponential

**Number Theory:** Integers, Integer Representations and Operations, Primes and Greatest Common Divisors, Congruences, Applications of Congruences, Special Congruences, Multiplicative Functions, Cryptology, Primitive Roots, Applications of Primitive Roots, The Order of an Integer, Quadratic Residues, Decimal Fractions, Continued Fractions, Nonlinear Diophantine Equations, Gaussian Integers

**Proofs****:** Direct Proof, Related Statements, Proof by Contrapositive, Negation of a Statement, "If and only if", "Equivalence Theorems", Use of Counterexamples, Mathematical Induction, Existence Theorems, Uniqueness Theorems, Equality of Sets, Equality of Numbers, Composite Statements, Limits.

**Mind Challenges:** Easy...__1__, __2__, __3__, __4__, __5__, __6__, __7__, __8 __, __9__, __10__......Medium...1, 2, 3, 4, 5, 6, 7, 8 , 9, 10......Hard...1, 2, 3, 4, 5, 6, 7, 8 , 9, 10