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 The Map of Mathematics

00 History
 BC 0800? Roman Numerals    BC 0570 - 0495 Pythagoras    BC 0500? Pythagorean Mathematicians    BC 0500? Hippasus    BC 0384 - 0322 Aristotle    BC 0300? Euclid    BC 0287 - 0212 Archimedes    08th century Hindu-Arabic numeral system    1202 Leonardo Fibonacci    1564 - 1642 Galileo Galilei    1571 - 1630 Johannes Kepler    1643 - 1727 Isaac Newton    1646 - 1716 Gottfried Wilhelm Leibniz    Crisis in the Foundation of Mathematics    History of Mathematics    How Far Mathematical Foundations  

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

20 Geometry
 01 Points, Lines, & Planes    02 Angle Basics    02 Basic Euclidian Geometry: Points, Lines, and Planes    03 Angles & Degrees    03 Types of Angles and Angle Relationships    04 Polygons    04 Types of Triangles in Euclidian Geometry    05 Proving Triangle Congruence and Similarity    05 Triangles    06 Quadrilaterals    06 Special Lines in Triangles: Bisectors, Medians, and Altitudes    07 Perimeter    07 The Triangle Midsegment Theorem    08 Area    08 The Pythagorean Theorem    09 Circles, What Is PI?    09 Types of Quadrilaterals and Other Polygons    10 Calculating the Perimeter of Polygons    10 Circles, Circumference And Area    11 Circles: Radius, Diameter, Chords, Circumference, and Sectors    11 Volume    12 Calculating the Area of Shapes    12 The Pythagorean Theorem    13 Proving the Pythagorean Theorem    14 Three-Dimensional Shapes Part 1: Types, Calculating Surface Area    15 Three-Dimensional Shapes Part 2: Calculating Volume   • Dave    Dimensions    Math 8 Lesson 23: Isometric Transformations (Simplifying Math)   • Matthew Salomone    Mysterium Cosmographicum    Symmetry and Transformations (Simplifying Math)    The History of Non-Euclidian Geometry - A Most Terrible Possibility - Extra History - #4    The History of Non-Euclidian Geometry - Sacred Geometry - Extra History - #1    The History of Non-Euclidian Geometry - Squaring the Circle - Extra History - #3    The History of Non-Euclidian Geometry - The Great Quest - Extra History - #2    The History of Non-Euclidian Geometry - The World We Know - Extra History - #5    Triangles  
 30 Algebra properties

30 Algebra
 01 Using Variables    01 What Is Algebra?    02 Basic Number Properties for Algebra    02 Solving Basic Equations Part 1    03 Algebraic Equations and Their Solutions    03 Solving Basic Equations Part 2    04 Algebraic Equations With Variables on Both Sides    04 Solving 2-Step Equations    05 Algebraic Word Problems    05 Exponents In Algebra    06 Solving Algebraic Inequalities    06 What Are Polynomials?    07 Simplifying Polynomials    07 Square Roots, Cube Roots, and Other Roots    08 Simplifying Expressions With Roots and Exponents    08 The Distributive Property    09 Graphing On The Coordinate Plane    09 Solving Algebraic Equations With Roots and Exponents    10 Functions    10 Introduction to Polynomials    11 Adding and Subtracting Polynomials    12 Multiplying Binomials by the FOIL Method    13 Solving Quadratics by Factoring    14 Solving Quadratics by Completing the Square    15 Solving Quadratics by Using the Quadratic Formula    16 Solving Higher Degree Polynomials by Synthetic Division and the Rational Roots Test    17 Manipulating Rational Expressions: Simplification and Operations    18 Graphing in Algebra: Ordered Pairs and the Coordinate Plane    19 Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts    20 Graphing Lines in Slope-Intercept Form (y = mx + b)    21 Graphing Lines in Standard Form (ax + by = c)    22 Graphing Parallel and Perpendicular Lines    23 Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination    24 Absolute Values: Defining, Calculating, and Graphing    25 What are the Types of Numbers?    30 Continuous, Discontinuous, and Piecewise Functions    33 Graphing Conic Sections Part 1: Circles    34 Graphing Conic Sections Part 2: Ellipses    35 Graphing Conic Sections Part 3: Parabolas in Standard Form    36 Graphing Conic Sections Part 4: Hyperbolas    37 Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros    38 Graphing Rational Functions and Their Asymptotes    39 Solving and Graphing Polynomial and Rational Inequalities    40 Evaluating and Graphing Exponential Functions    41 Logarithms Part 1    42 Logarithms Part 2    43 Logarithms Part 3    44 Solving Exponential and Logarithmic Equations    45 Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem    46 Set Theory: Types of Sets, Unions and Intersections    47 Sequences, Factorials, and Summation Notation    48 Theoretical Probability, Permutations and Combinations    Reflections of a Function - Nerdstudy    Why Computers are Bad at Algebra  
 31 Exponents, roots and logarithms

31 Exponents, roots and logarithms
 Graph of exponents, roots and logarithms    Summary of exponents, roots and logarithms    05 Exponents In Algebra    07 Square Roots, Cube Roots, and Other Roots    08 Simplifying Expressions With Roots and Exponents    09 Solving Algebraic Equations With Roots and Exponents    14 Understanding Exponents and Their Operations    40 Evaluating and Graphing Exponential Functions    41 Logarithms Part 1    42 Logarithms Part 2    43 Logarithms Part 3    44 Solving Exponential and Logarithmic Equations    Change of base    Exponential Functions    Logarithms    Saying Logarithm    Saying Logarithm    Triangle of Power  

32 Linear Algebra
 Summary of linear algebra    01 Vectors, what even are they?    02 Linear combinations, span and basis vectors    03 Linear transformations and matrices    04 Matrix multiplication as composition    07 How to organize, add and multiply matrices    12.1 Vectors in the Plane Part 1    12.1 Vectors in the Plane Part 2    12.2 Vectors in Three Dimensions    12.2 Vectors In Three Dimensions 12.2.75    12.3 Dot Product Part 1    12.3 Dot Product Part 2    12.4 Cross Product Part 1    12.4 Cross Product Part 2    12.5 Lines and Curves in Space Part 1    12.5 Lines and Curves in Space Part 2   • CBlissMath   • Dave    Linda Misener    Matrix   • Matthew Salomone   • Tensor    What is a Vector Space? (Abstract Algebra)  

35 Abstract Algebra
 Set Theory   • learnifyable   • MyWhyU   • Sacratica  
 40 Angles and coordinates around the unit circle
 40 Sin, cos, tan, csc, sec, cot
 40 Trigonometric laws and identities
 40 Sin, cos, tan, arcsin, arccos, arctan

40 Trigonometry
 01 Introduction to Trigonometry    02 Trigonometric Functions    03 The Easiest Way to Memorize the Trigonometric Unit Circle    04 Basic Trigonometric Identities    05 Graphing Trigonometric Functions    06 Inverse Trigonometric Functions    07 Verifying Trigonometric Identities    08 Formulas for Trigonometric Functions    09 Solving Trigonometric Equations    10 The Law of Sines    11 The Law of Cosines    Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses    Intro to Radians - Nerdstudy    Parametric Equations    Polar Coordinates and Graphing Polar Equations  

50 Limits & Continuity
 01 Limits and Continuity    Linda Misener    ε δ definition of limit    ε δ definition of limit  
 60 Calculus - derivatives and limits
 60 Calculus - integrals

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

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

90 Group Theory

99 Terms
 Congruence Modulo    Converse    Cross Product    Dot Product    Factorial, Permutation and Combination (Choose)    Iff    Integration    Limit    Line    Linear systems    Logarithms    Mathematical Induction    Mathematical Notation    Matrix    Partial derivative    Pascal's Triangle    Plane    Point    Point    Prime Factorization    Space    Transformation    Triangle classification    Trigonometric Functions    Vector  

 Glome in colors    Hollow Glome and Luffa    2018-10-30    3-sphere    A Breakthrough in Higher Dimensional Spheres    Cartesian product    Closed set    Compact space    Connected space    Contractible space    History of the Poincaré Conjecture    How Fast Is It - 01 - Preface    How Fast Is It - 02 - The Speed of Light    How Fast Is It - 03 - Special Relativity    How Fast Is It - 04 - General Relativity I - Geometry    How the Universe Works   • Images    Implicit Function    Implicit function theorem    Leonard Susskind    Loop    n-ball    n-sphere    Non-Euclidean Geometry    Path    Poincaré conjecture    Real coordinate space    Riemannian Curvature Tensor    Simply connected space    Simply connected space    Singularities Explained | Infinite Series    Space    The Poincare Conjecture    Thinking visually about higher dimensions    Three-torus    Tom Campbell    Topological manifold    volumes and surface areas of n-spheres     Zeno's Paradox   • Zeno's Paradox  
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