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 The Map of Mathematics | R The Map of Mathematics http://qindex.info/d.php?c=4758#4834

 00 History | 17 BC 0800? Roman Numerals | R     BC 0570 - 0495 Pythagoras | R     BC 0500? Pythagorean Mathematicians | R     BC 0500? Hippasus | R     BC 0384 - 0322 Aristotle | R     BC 0300? Euclid | R     BC 0287 - 0212 Archimedes | R     08th century Hindu-Arabic numeral system | R     1202 Leonardo Fibonacci | R     1564 - 1642 Galileo Galilei | R     1571 - 1630 Johannes Kepler | R     1643 - 1727 Isaac Newton | R     1646 - 1716 Gottfried Wilhelm Leibniz | R     History of Mathematics | R     How Far Mathematical Foundations | R     Surfaces and Topology - Professor Raymond Flood | R     The evolution of geometric structures on 3-manifolds. | R

 10 Arithmatic | 46 01 Introduction to Mathematics | R     01 Place Value | R     02 Addition and Subtraction of Small Numbers | R     02 Decimal Place Value | R     03 Multiplication and Division of Small Numbers | R     03 What Is Arithmetic? | R     04 Fractions, Improper Fractions, and Mixed Numbers | R     04 Order Of Operations | R     05 Factoring | R     05 Large Whole Numbers: Place Values and Estimating | R     06 Decimals: Notation and Operations | R     06 Prime Factorization | R     07 Multi-Digit Addition | R     07 Working With Percentages | R     08 Converting Between Fractions, Decimals, and Percentages | R     08 Multi-Digit Subtraction | R     09 Addition and Subtraction of Large Numbers | R     09 Multi-Digit Multiplication Pt 1 | R     10 Multi-Digit Multiplication Pt 2 | R     10 The Distributive Property | R     11 Basic Division | R     11 Multiplication of Large Numbers | R     12 Division of Large Numbers | R     12 Long Division | R     13 Long Division with 2-Digit Divisors | R     13 Negative Numbers | R     14 Decimal Arithmetic | R     14 Understanding Exponents and Their Operations | R     15 Order of Arithmetic Operations: PEMDAS | R     15 The Distributive Property In Arithmetic | R     16 Divisibility, Prime Numbers, and Prime Factorization | R     16 Mean, Median and Mode | R     17 Least Common Multiple (LCM) | R     17 Negative Numbers | R     18 Adding & Subtracting Integers | R     18 Greatest Common Factor (GCF) | R     19 Addition and Subtraction of Fractions | R     19 Integer Multiplication & Division | R     20 Intro To Exponents (aka Indices) | R     20 Multiplication and Division of Fractions | R     21 Analyzing Sets of Data: Range, Mean, Median, and Mode | R     21 Exponents & Square Roots | R     22 Rounding | R     23 Basic Probability | R     Numbers, Numerals and Digits | R     Roman Numerals | R

 20 Geometry | 34 01 Introduction to Geometry | R     01 Points, Lines, & Planes | R     02 Angle Basics | R     02 Basic Euclidian Geometry: Points, Lines, and Planes | R     03 Angles & Degrees | R     03 Types of Angles and Angle Relationships | R     04 Polygons | R     04 Types of Triangles in Euclidian Geometry | R     05 Proving Triangle Congruence and Similarity | R     05 Triangles | R     06 Quadrilaterals | R     06 Special Lines in Triangles: Bisectors, Medians, and Altitudes | R     07 Perimeter | R     07 The Triangle Midsegment Theorem | R     08 Area | R     08 The Pythagorean Theorem | R     09 Circles, What Is PI? | R     09 Types of Quadrilaterals and Other Polygons | R     10 Calculating the Perimeter of Polygons | R     10 Circles, Circumference And Area | R     11 Circles: Radius, Diameter, Chords, Circumference, and Sectors | R     11 Volume | R     12 Calculating the Area of Shapes | R     12 The Pythagorean Theorem | R     13 Proving the Pythagorean Theorem | R     14 Three-Dimensional Shapes Part 1: Types, Calculating Surface Area | R     15 Three-Dimensional Shapes Part 2: Calculating Volume | R     Dimensions | R     The History of Non-Euclidian Geometry - A Most Terrible Possibility - Extra History - #4 | R     The History of Non-Euclidian Geometry - Sacred Geometry - Extra History - #1 | R     The History of Non-Euclidian Geometry - Squaring the Circle - Extra History - #3 | R     The History of Non-Euclidian Geometry - The Great Quest - Extra History - #2 | R     The History of Non-Euclidian Geometry - The World We Know - Extra History - #5 | R     Triangles - Equilateral, Isosceles and Scalene | R

 30 Algebra | 46 Properties | R     01 Using Variables | R     01 What Is Algebra? | R     02 Basic Number Properties for Algebra | R     02 Solving Basic Equations Part 1 | R     03 Algebraic Equations and Their Solutions | R     03 Solving Basic Equations Part 2 | R     04 Algebraic Equations With Variables on Both Sides | R     04 Solving 2-Step Equations | R     05 Algebraic Word Problems | R     05 Exponents In Algebra | R     06 Solving Algebraic Inequalities | R     06 What Are Polynomials? | R     07 Simplifying Polynomials | R     07 Square Roots, Cube Roots, and Other Roots | R     08 Simplifying Expressions With Roots and Exponents | R     08 The Distributive Property | R     09 Graphing On The Coordinate Plane | R     09 Solving Algebraic Equations With Roots and Exponents | R     10 Functions | R     10 Introduction to Polynomials | R     11 Adding and Subtracting Polynomials | R     12 Multiplying Binomials by the FOIL Method | R     13 Solving Quadratics by Factoring | R     14 Solving Quadratics by Completing the Square | R     15 Solving Quadratics by Using the Quadratic Formula | R     16 Solving Higher Degree Polynomials by Synthetic Division and the Rational Roots Test | R     17 Manipulating Rational Expressions: Simplification and Operations | R     18 Graphing in Algebra: Ordered Pairs and the Coordinate Plane | R     19 Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts | R     20 Graphing Lines in Slope-Intercept Form (y = mx + b) | R     21 Graphing Lines in Standard Form (ax + by = c) | R     22 Graphing Parallel and Perpendicular Lines | R     23 Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination | R     24 Absolute Values: Defining, Calculating, and Graphing | R     25 What are the Types of Numbers? | R     30 Continuous, Discontinuous, and Piecewise Functions | R     33 Graphing Conic Sections Part 1: Circles | R     34 Graphing Conic Sections Part 2: Ellipses | R     35 Graphing Conic Sections Part 3: Parabolas in Standard Form | R     36 Graphing Conic Sections Part 4: Hyperbolas | R     Introduction to Exponential Functions - Nerdstudy | R     Logarithms Part 1 | R     Logarithms Part 2 | R     Logarithms Part 3 | R     Reflections of a Function - Nerdstudy | R

 31 Abstract Algebra | 8 Set Theory | R     01 Sets | R     02 Working with Sets | R     03 Definition of a Function | R     04 Injective Functions | R     05 Surjective Functions | R     06 Composition of Functions | R     Congruence Modulo n | R

 32 Linear Algebra | 22 01 Introduction to Vectors and Their Operations | R     01 Vectors, what even are they? | R     02 Linear combinations, span and basis vectors | R     02 The Vector Dot Product | R     03 Introduction to Linear Algebra | R     03 Linear transformations and matrices | R     04 Matrix multiplication as composition | R     04 Understanding Matrices and Matrix Notation | R     05 Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination | R     12.1 Vectors in the Plane Part 1 | R     12.1 Vectors in the Plane Part 2 | R     12.2 Vectors in Three Dimensions | R     12.2 Vectors In Three Dimensions 12.2.75 | R     12.3 Dot Product Part 1 | R     12.3 Dot Product Part 2 | R     12.4 Cross Product Part 1 | R     12.4 Cross Product Part 2 | R     12.5 Lines and Curves in Space Part 1 | R     12.5 Lines and Curves in Space Part 2 | R     How to organize, add and multiply matrices | R     Linda Misener | R     What is a Vector Space? (Abstract Algebra) | R

 40 Trigonometry | 14 Identities | R     Laws | R     01 Introduction to Trigonometry | R     02 Trigonometric Functions | R     03 The Easiest Way to Memorize the Trigonometric Unit Circle | R     04 Basic Trigonometric Identities | R     05 Graphing Trigonometric Functions | R     06 Inverse Trigonometric Functions | R     07 Verifying Trigonometric Identities | R     08 Formulas for Trigonometric Functions | R     09 Solving Trigonometric Equations | R     10 The Law of Sines | R     11 The Law of Cosines | R     Intro to Radians - Nerdstudy | R

 45 Sequences and Series | 5 01 Sequences, Factorials and Summation Notation | R     02 Convergence and Divergence: The Return of Sequences and Series | R     2018-08-19 | R     Compound Interest - Nerdstudy | R     Recursive Formula - Nerdstudy | R

 50 Limits & Continuity | 5 01 Limits and Continuity | R     Linda Misener | R     PatricJMT | R     ε δ definition of limit | R     ε δ definition of limit | R

 60 Calculus | 49 Calculus 1 | R     Calculus 2 | R     Derivative | R     Integral 1 - A(x), The integral of f(x) | R     Integral 2 - The derivative of A(x) is f(x). | R     Integral 3 - Let F(x) be an antiderivative of f(x). | R     Integral 4, A(b) - A(a) = F(b) - F(a) | R     01 Essence of calculus | R     01 The Greeks, Newton and Leibniz | R     01 What Is a Derivative? | R     01 What is Calculus? | R     02 The paradox of the derivative | R     02 The Slope of a Tangent Line | R     02 The Tangent Line and the Derivative | R     03 Derivative formulas through geometry | R     03 Product Rule for Derivatives | R     03 Rates of Change | R     04 Limits and Limit Laws in Calculus | R     04 The Quotient Rule | R     04 Visualizing the chain rule and product rule | R     05 Derivatives of exponentials | R     05 What is a Derivative? | R     06 Derivatives of Polynomial Functions | R     06 Implicit differentiation, what's going on here? | R     07 Derivatives of Trigonometric Functions | R     07 Limits | R     08 Derivatives of Composite Functions: The Chain Rule | R     08 Integration and the fundamental theorem of calculus | R     09 Derivatives of Logarithmic and Exponential Functions | R     09 What does area have to do with slope? | R     10 Higher order derivatives | R     11 Taylor series | R     17 What is Integration? | R     18 The Fundamental Theorem of Calculus | R     19 Properties of Integrals and Evaluating Definite Integrals | R     20 Evaluating Indefinite Integrals | R     21 Evaluating Integrals With Trigonometric Functions | R     22 Integration Using The Substitution Rule | R     23 Integration By Parts | R     24 Integration by Trigonometric Substitution | R     25 Advanced Strategy for Integration in Calculus | R     26 Evaluating Improper Integrals | R     27 Finding the Area Between Two Curves by Integration | R     28 Calculating the Volume of a Solid of Revolution by Integration | R     29 Calculating Volume by Cylindrical Shells | R     30 The Mean Value Theorem For Integrals: Average Value of a Function | R     Taylor and Maclaurin Series | R     The fundamental theorem of calculus | R     What Is a Derivative? | R

 70 Topology | 14 01 Definition of a Topological Space | R     02 Determine if T is a Topology on X | R     03 The Intersection of Topologies on X is a Topology on X Proof | R     04 Two Topologies on X whose Union is not a Topology on X | R     Bob Franzosa - Introduction to Topology | R     Mysterium Cosmographicum | R     Simplicial Complexes - Your Brain as Math Part 2 | Infinite Series | R     The Poincare Conjecture | R     Topology Riddles | R     What is a manifold? | R     What is a Manifold? Lesson 1: Point Set Topology and Topological Spaces | R     What is a Manifold? Lesson 2: Elementary Definitions | R     Who cares about topology? | R

 Crisis in the Foundation of Mathematics | R Infinite Series http://qindex.info/d.php?c=4758#4835

 Desmos | R Graphing http://qindex.info/d.php?c=4758#5071

 Exponents | 16 exponents, roots and logarithms | R     Summary | R     1 Repeated Multiplication | R     2 Inverse Operator, Root | R     3 Irrational Number | R     4 The power of 1 | R     5 The power of a fraction | R     6 The power of 0 | R     7 The power of a negative number | R     8 Inverse Operator, Logarithm | R     Logarithmic and exponential functions | R     Reading b^n | R     Saying Logarithm | R     Saying Logarithm | R     Triangle of Power | R

 Glome in colors | 56 Glome in colors | R     Hollow Glome | R     04 Limits and Limit Laws in Calculus | R     06 Derivatives of Polynomial Functions | R     2018-10-30 | R     3-sphere | R     A Breakthrough in Higher Dimensional Spheres | R     Basic Euclidian Geometry | R     Basic Euclidian Geometry | R     Closed set | R     Compact space | R     Connected space | R     Derivatives of Trigonometric Functions | R     Dimensions | R     Dot Product Part 1 | R     Dot Product Part 2 | R     Figure 7 | R     Formulas for Trigonometric Functions | R     History of the Poincaré Conjecture | R     How Fast Is It - 01 - Preface | R     How Fast Is It - 02 - The Speed of Light | R     How Fast Is It - 03 - Special Relativity | R     How Fast Is It - 04 - General Relativity I - Geometry | R     How the Universe Works | R     Integration Using The Substitution Rule | R     Leonard Susskind | R     Loop | R     n-ball | R     n-sphere | R     Non-Euclidean Geometry | R     Path | R     Real coordinate space | R     Riemannian Curvature Tensor | R     Simply connected space | R     Singularities Explained | Infinite Series | R     Space | R     The Poincare Conjecture | R     The Vector Dot Product | R     Thinking visually about higher dimensions | R     Tom Campbell | R     Topological manifold | R     volumes and surface areas of n-spheres  | R     Zeno's Paradox | R     Zeno's Paradox | 4

 Mathcha | R Online Math Editor http://qindex.info/d.php?c=4758#5327

 Number | 6 Are Prime Numbers Made Up? | Infinite Series | PBS Digital Studios | R     Pantographs and the Geometry of Complex Functions | R     Prime number | R     Prime Number Theorem | R     Visualizing the Riemann hypothesis and analytic continuation | R     What are quaternions, and how do you visualize them? A story of four dimensions. | R

 quiz | 5 A small circle rolling around a large circle | R     One Mile South, One Mile West, One Mile North | R     South Korean Geometry Problem | R     Triangles in a parallelogram | R     Triangles in a square | R

 Terms | 17 Calculus | R     Cross Product | R     Dot Product | R     Greek Alphabet | R     Isosceles triangle | R     Limit | R     Line | R     Logarithm | R     Logarithm | R     Logarithm | R     Partial derivative | R     Plane | R     Point | R     Scalene triangle | R     Space | R     Trigonometric Functions | R     ε δ definition of limit | R

 Theoretical Probability, Permutations and Combinations | R Theoretical Probability, Permutations and Combinations http://qindex.info/d.php?c=4758#5171

 Why Computers are Bad at Algebra | R Why Computers are Bad at Algebra | Infinite Series http://qindex.info/d.php?c=4758#5073
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