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Brilliant's wiki is no longer maintained. For the best place to learn math, programming, data, and more, check out Brilliant's interactive courses. For an archive of all previous wiki content, see below. Wiki pages by topic Algebra Expressions and Variables Simplifying Expressions Distributive Property Zero Product Property Contest Math I Solving Equations Setting Up Equations Simple Equations Solving Equations Verifying Solutions Multi-step Equations Isolating a Variable Balance Puzzles System of Linear Equations How are exponent towers evaluated? Does a square root have two values? Do Square Roots Always Multiply? Is 0.999... = 1? What is 0 to the power of 0? If AB=AC does B=C? Is (a/b)/c = a/(b/c)? Does sqrt(x²+y²) = x+y? Does cross multiply always work for inequalities? How does addition in the denominator work? Linear Equations Linear Equations Forms of Linear Equations Equations of Parallel and Perpendicular Lines Systems of Linear Equations Solving Linear Systems Using Matrices Absolute Value Absolute Value Absolute Value Equations Absolute Value Inequalities Linear Inequalities Linear Inequalities Absolute Value Linear Inequalities System of Inequalities Linear Programming Non-Linear Inequalities Polynomial Inequalities Classical Inequalities Absolute Value Inequalities (1 Quadratic Term) Exponential Inequalities Logarithmic Inequalities Quadratic Equations Factoring Quadratics Quadratic Equations Completing The Square Applications of Completing the Square Quadratic Discriminant Square Roots (Radicals) Simplifying Radicals Radical Equations Square Roots Cube Roots Rationalizing Denominators Arithmetic and Geometric Progressions Arithmetic Progressions Arithmetic Mean Harmonic Progression Harmonic Mean Geometric Progressions Geometric Mean Arithmetic and Geometric Progressions Problem Solving Arithmetic-Geometric Progression Functions Functions Evaluating Functions Function Composition Inverse Functions Function Terminology Relations Graphs of Functions Transforming Graphs of Functions Functional Equations Polynomials Polynomials Multiplying Polynomials Polynomial Division Synthetic Division Solving Identity Equations Difference Of Squares Applying the Perfect Square Identity Applying the Perfect Cube Identity Factoring Polynomials Factoring by Substitution Rational Expressions Simplifying Rational Expressions Factoring Compound Quadratics Factoring Cubic Polynomials Descartes' Rule of Signs Fundamental Theorem of Algebra Method of Undetermined Coefficients Remainder Factor Theorem Transforming Roots of Polynomials Rational Functions Intercepts of Rational Functions Rational Equations Asymptotes Graphing Rational Equations Partial Fractions (Linear Factors) Partial Fractions (Cover Up Rule) Partial Fractions (Irreducible Quadratics) Partial Fractions (Repeated Factors) Telescoping Series (Sum) Piecewise Functions Floor Function Ceiling Function Trailing Number of Zeros Fractional Part Function Hermite's Identity Exponents Rules of Exponents Simplifying Exponents Exponential Functions Rules of Exponents (Algebraic) Solving Exponential Equations Graphs of Exponential Functions Exponential Functions (Problem Solving) Interest Rate Leonhard Euler Logarithms Logarithms Solving Logarithmic Equations Polar Coordinates Converting Polar Coordinates to Cartesian Polar Coordinates Parametric Equations Parametric Equations Complex Numbers Complex Numbers Complex Conjugates Complex Numbers (Absolute Values) Complex Plane Complex Numbers in Geometry Gaussian Integers Discrete Fourier Transform Euler's Formula De Moivre's Theorem Roots of Unity Advanced Linear Algebra (Matrices) Linear Algebra Matrices Determinants Eigenvalues and Eigenvectors Kernel (Nullspace) Vector Space Rank Cayley-Hamilton Theorem Row And Column Spaces Spectral Theorem Fundamental Subspaces Change of Basis Basis Rank-Nullity Theorem Linear Transformations Linear Independence Jordan Canonical Form Affine Transformations Vieta Root Jumping Advanced Polynomials Algebraic Manipulation Algebraic Manipulation Identities Sum of n/n²/n³ Telescoping Series (Product) Nested Functions Cardano's Method Cubic Discriminant Gauss: The Prince of Mathematics Srinivasa Ramanujan Binomial Coefficient Pascal's Triangle Binomial Theorem Negative Binomial Theorem Fractional Binomial Theorem Rational Root Theorem Vieta's Formula Newton's Identities Completing the Square (Multiple Variables) Algebraic Identities Factorization of Polynomials Sophie Germain Identity Algebraic Number Theory Fermat's Last Theorem Eisenstein's Irreducibility Criterion Group Theory Lagrange's Theorem Schwartz-Zippel Lemma Polynomial Interpolation by Remainder Factor Theorem Lagrange Interpolation Method of Differences Primitive Roots of Unity Symmetric Polynomials The uvw Method Chebyshev Polynomials (Definition and Properties) Advanced Inequalities Cauchy-Schwarz Inequality Titu's Lemma Rearrangement Inequality Chebyshev's Inequality Jensen's Inequality Holder's Inequality Young's Inequality Muirhead Inequality Reverse Rearrangement Inequality AM-GM Inequality Applying the AM-GM Inequality Power Mean Inequality (QAGH) Quadratic Mean Triangle Inequality RMO Math Contest Preparation INMO Math Contest Preparation Basic Mathematics Pattern Recognition Identifying Patterns Identifying Pattern Relationships What Comes Next? Finding Terms in a Sequence Recognizing Visual Patterns Arithmetic Estimation Irrelevant Information Trial and Error Checking Cases Counter-Examples SAT Logic SAT Reasoning Perfect Score Mental Math Tricks Subtracting Integers Division Remainder Exponents Rational Exponents Order of Operations Representation on the Real Line Natural Numbers Fractions Complex Fractions Componendo and Dividendo Continued Fractions Decimals Converting Decimals and Fractions Converting Fractions into Decimals Place Value Scientific Notation Percentages Converting Decimals and Percentages Converting Percentages and Fractions Ratio and Proportion Direct Variation Inverse Variation Speed Distance and Time Geometry Angles Parallel Lines Perimeter Area of a Triangle Area of a Rectangle Circles Composite Figures Length and Area Problem Solving Calculus Sequences and Limits Sequences Series Arithmetic Progressions Geometric Progressions Arithmetic-Geometric Progression Telescoping Series (Sum) Telescoping Series (Product) Convergence Tests Harmonic Number Absolutely Convergent Sums Of Divergent Series Limits of Sequences Infimum/Supremum Nested Functions Dedekind Cuts Limits of Functions Limits by Substitution Limits by Factoring Limits by Rationalization When Does A Limit Exist? Asymptotes Continuous Functions Epsilon-Delta Definition of a Limit Squeeze Theorem Extreme Value Theorem Intermediate Value Theorem Infinity Is infinity at the end of the real number line? If F(x) is the antiderivative... Do local extrema occur if and only if f'(x) = 0? Is Infinity / Infinity = 1? Is infinity times zero = zero? What is 1 divided by 0? If the limit of a sequence is 0 does the series converge? Differentiation Average and Instantaneous Rate of Change Tangent Line to a Curve Derivative by First Principle Derivatives of Polynomials Derivatives of Rational Functions Derivatives of Exponential Functions Derivatives of Logarithmic Functions Partial Derivatives Applying Differentiation Rules To Logarithmic Functions Power Rule Product Rule Quotient Rule Chain Rule Differentiation of Inverse Functions Applying Differentiation Rules to Trigonometric Functions Calculus With Inverse Trigonometric Functions Differentiation Rules Higher-order Derivatives Increasing / Decreasing Functions Inflection Points Implicit Differentiation Differentiable Function Mean Value Theorem Rolle's Theorem Applications of Differentiation Indeterminate Forms L'Hopital's Rule Related Rates of Change Extrema (Local and Absolute) Critical Points Second Derivative Test Optimization Lagrange Multipliers Vertical Asymptotes Average Velocity Instantaneous Velocity Taylor Series Maclaurin Series Taylor Series Approximation Taylor Series Manipulation Interval and Radius of Convergence Taylor Series (Error Bounds) Power Series Small-Angle Approximation Fourier Series Taylor's Theorem (with Lagrange Remainder) Analytic Continuation Integration Line Integral Integration Integration of Algebraic Functions Integration of Exponential Functions Integration of Trigonometric Functions Integration of Rational Functions Integration of Logarithmic Functions Integration of Radical Functions Definite Integrals Riemann Sums Fundamental Theorem of Calculus Improper Integrals Multiple Integral u-Substitution Trigonometric Substitution in Integration Integration by Parts Differentiation Under the Integral Sign Integration Tricks Lebesgue Integration Stokes' Theorem Green's Theorem Area between curves Gamma Function Beta Function Digamma Function Riemann Zeta Function Cauchy Integral Formula Isolated Singularities and Residue Theorem Applications of Integration Disc Method Shell Method Arc Length Pappus's Centroid Theorems Parametric Equations Calculus Parametric Equations Polar Coordinates Converting Polar Coordinates to Cartesian Polar Curves Parametric Derivative Parametric Equations (Velocity and Acceleration) Polar Equations (Area) Differential Equations Differential Equations Separable Differential Equations Homogeneous Linear Differential Equations Euler's Method Euler's Method (Small Step Size) Logistic Differential Equations Bernoulli Equation Systems of Linear Differential Equations Chaos Theory Numerical Methods Root Approximation (Bisection) Newton Raphson Method Integral Approximation (Trapezium Rule) Integral Approximation (Simpson's Rule) Chebyshev's Formula Chemistry Fundamentals Chemistry in action Atoms/Molecules/Elements/Compounds Mixtures Dalton's Atomic Model Bohr's Model Periodic Table Atomic/Molecular Weights Mole Concept Concentration Terminology Nuclear Decay Balancing Chemical Reactions Limiting Reagents Laws of Chemical Combination Try It At Home Chemistry Experiments Chemistry Of Drugs Chemical Bonding Ionic Compounds Octet Rule Lewis Structure Hybridisation Valence Shell Electron Pair Repulsion Sigma and Pi Bonds Molecular Orbital Theory Coordinate Bonds Polarity Van der Waals Force Dipole Interactions Hydrogen Bonds Surface Tension Strength of Intermolecular Forces Chemistry of Diamonds Reaction Mechanics Chemical Equilibrium Basics of Statistical Mechanics Le Chatelier's Principle Acids and Bases Acid/Base Equilibrium Thermal Expansion Rate of Chemical Reactions Order of Chemical Reactions Activation Energy Chemistry of Fireworks Thermometry Electrolytic Cells Galvanic Cells Buffers Organic Chemistry Structural Representations IUPAC Nomenclature Structural Isomerism Geometric Isomerism Optical Isomerism Electrophiles and Nucleophiles Inductive/Electromeric/Resonance Effects Reactive Intermediates Common Types of Organic Reactions Grignard Reagent Alkanes/Alkenes/Alkynes Do objects gain protons to become positive? Chemistry Of Poisons Chemistry Of Nutrition Biology DNA Reverse Transcription Mutation and DNA repair CRISPR DNA Bricks Hemoglobin Viral Replication Zika Virus Computer Science Types and Data Structures Abstract Data Types Lists Array (ADT) Queues Double Ended Queues Stacks Associative Arrays Sets (ADT) Priority Queues Array (Data Structure) Disjoint-set Data Structure Dynamic Array Linked List Unrolled Linked List Skip List Hash Tables Bloom Filter Cuckoo Filter Merkle Tree Trees Recursive Backtracking Traversals Tries Treaps Fenwick Tree Binary Search Trees Red-Black Tree AVL Tree Scapegoat Tree Splay Tree Heaps Binary Heap Binomial Heap Fibonacci Heap Pairing Heap Graphs Graph implementation Adjacency Matrix Spanning Trees Social Networks Kruskal's Algorithm Strings Regular Expressions Algorithms Algorithms Divide and Conquer Greedy Algorithms Randomized Algorithms Complexity Theory Big O Notation Master Theorem Amortized Analysis Complexity Classes P versus NP Dynamic Programming Backpack Problem Egg Dropping Fast Fibonacci Transform Karatsuba Algorithm Sorting Algorithms Insertion Sort Bubble Sort Merge Sort Quick Sort Heap Sort Radix Sort Counting Sort Median-finding Algorithm Binary Search Depth-First Search Breadth-First Search A* Search Shortest Path Algorithms Dijkstra's Bellman-Ford Floyd-Warshall Johnson's Algorithm Matching (Graph Theory) Matching Algorithms Flow Network Max-flow Min-cut Ford-Fulkerson Edmonds-Karp Shunting Yard Algorithm Rabin-Karp Knuth-Morris-Pratt Basic Shapes/Polygons/Trigonometry Convex Hull Grids Finite State Machines Turing Machines Halting Problem Kolmogorov Complexity Traveling Salesperson Problem Pushdown Automata Regular Languages Context Free Grammars Context Free Languages Signals and Systems Linear Time Invariant Systems Predicting System Behavior Programming Languages Subroutines List comprehension While For Primality Testing Pattern matching Logic Gates Control Flow Statements Object-Oriented Programming Objects Classes Methods Map Foldlist Filter Cryptography and Simulations Caesar Cipher Vigenere Cipher RSA Encryption Enigma Machine Diffie-Hellman Knapsack Cryptosystem Secure Hash Algorithms Entropy (Information Theory) Huffman Code Error correcting codes Symmetric Ciphers Inverse Transform Sampling Monte-Carlo Simulation Annealing Genetic Algorithms Programming Blackjack Machine Learning Machine Learning Supervised Learning Unsupervised Learning Feature Vector Naive Bayes Classifier K-nearest Neighbors Perceptron Support Vector Machines Principal Component Analysis Ridge Regression k-Means Clustering Markov Chains Hidden Markov Models Gaussian Mixture Model Collaborative Filtering Artificial Neural Network Feedforward Neural Networks Backpropagation Recurrent Neural Network Discrete Mathematics Counting Rule of Sum Counting Integers in a Range Rule of Product Rule of Sum and Product Problem Solving Counting Shapes Discrete Mathematics Set Complement Permutations Permutations with Repetition Permutations With Restriction Combinatorics Combinations Rectangular Grid Walk Sets and Partitions Set Theory Set Sets (Elements) Sets (Subsets) Classical Sets Cardinality Partially Ordered Sets ZFC Ordinal Numbers Venn Diagram Union and Intersection Principle of Inclusion and Exclusion Double Counting Derangements Bijection Injection and Surjection Bijective Functions Burnside's Lemma Pigeonhole Principle Ramsey Theory Dilworth's Theorem Distinct Objects into Distinct Bins Distinct Objects into Identical Bins Identical Objects into Distinct Bins Identical Objects into Identical Bins Partition of an Integer Data Mean Interquartile Range Understanding Data (Problem Solving) Data Presentation (Tables) Data Presentation (Bar Charts) Data Presentation (Pie Charts) Data Presentation (Dot Diagram) Data Presentation (Histogram) Data Presentation (Stem-leaf plot) Probability Probability Uniform Probability Probability (Rule of Sum) Probability (Rule of Product) Probability (By Complement) Probability (Problem Solving) Math of Poker (Basics) Conditional Probability Probability (Independent events) Probabilistic PIE Bayes' Theorem Conditional Probability Distribution Monty Hall Problem Bayesian Theory Poker Strategy Expected Value Linearity of Expectation Law of Iterated Expectation Coupon Collector Problem Variance Standard Deviation Covariance Geometric Probability Random Variables Discrete Random Variables - Definition Discrete Random Variables - Probability Density Function (PDF) Discrete Random Variables - Cumulative Distribution Function Discrete Random Variables - Joint Probability Distribution Discrete Random Variables - Indicator Variables Continuous Random Variables - Definition Continuous Random Variables - Probability Density Function (PDF) Continuous Random Variables - Cumulative Distribution Function Continuous Random Variables - Joint Probability Distribution Bernoulli Distribution Binomial Distribution Geometric Distribution Poisson Distribution Hypergeometric Distribution Uniform Distribution (Continuous) Normal Distribution Exponential Distribution Log-normal Distribution Multivariate Normal Distribution Statistics Sampling Chi-Squared Test Maximum Likelihood Estimation Inverse Transform Sampling Statistical Significance Markov Chains Stationary Distributions Transience and Recurrence Ergodic Markov Chains Absorbing Markov Chains Binomial Theorem Binomial Coefficient Pascal's Triangle Binomial Theorem Negative Binomial Theorem Fractional Binomial Theorem Multinomial Coefficients Multinomial Theorem Recurrence Relations Recursion Recurrence Relations Fractals Minkowski Dimension Fibonacci Sequence Linear Recurrence Relations Advanced Topics Combinatorial Games (Definition) Combinatorial Games (Winning Positions) Sprague Grundy Theorem Nim Dots and Boxes Fair Division Axiom of Determinacy Casework Conjectures Construction Extremal Principle Invariant Principle Vandermonde's Identity Hockey Stick Identity Graph Theory Eulerian Path Hamiltonian Path Four Color Theorem Graph Coloring and Chromatic Numbers Hall's Marriage Theorem Applications of Hall's Marriage Theorem Art Gallery Problem Combinatorial Optimization Group actions Generating Functions Manipulating Generating Functions Coloring (Parity Arguments) Knots Electricity and Magnetism Electrostatics Charge and Electric Fields Standard Model Spin Superposition of Electric Fields Electrostatics Electric Potential Electric Dipoles Energy of an electric field Electric Flux Gauss's law Conductors Poynting Vector Circuits Simple Circuits Heat Dissipated by Resistors Transformation of Resistances Ohm's Law Capacitors Energy Stored in a Capacitor Using Gauss' law to find E-field and capacitance Transformers Series and Parallel Capacitors RC Circuits RLC Circuits Impedance Phasor Diagrams Resonant circuits Magnetism Magnetic Field Lines Lorentz Force Law Biot-Savart Law Energy of a magnetic field Magnetic vector potential Ampere's Law Magnetic Flux and Faraday's Law Lenz's Law Magnetic Moment Magnetic Effects of Current Is a perfect transparent material black? Semiconductors Electrodynamics Maxwell's Equations Geometry Geometric Measurement Angles Parallel Lines Area of a Triangle Area of a Rectangle Circles Length and Area Problem Solving Composite Figures Volume of a Cuboid Volume of a Cylinder Volume of a Sphere Volume of a Pyramid Volume Problem Solving Calculating the Size of Earth Sphere Packing Surface Area Surface Area of a Cuboid Surface Area of a Sphere Surface Area of a Cylinder Triangles Triangles Pythagorean Theorem Triangle Inequality Symmedian Classification of Triangles Properties of Equilateral Triangles Properties of Isosceles Triangles Congruent and Similar Triangles Heron's Formula Pascal's Theorem Centroid of a Triangle Circumcenter Incenter Orthocenter Euler Line Ceva's Theorem Apollonius's Theorem Polygons Quadrilateral Classification Properties of Squares Properties of Rectangles Properties of Parallelograms Properties of Trapezoids Similar Figures Regular Polygons Perimeter Basic Composite Figures Pick's Theorem Irregular Polygons Area of a Polygon Circles Pi Tangent (Perpendicular to Radius) Alternate Segment Theorem Two Secants Tangent-Secant Incircle of Triangle Incircles and Excircles Cyclic Quadrilaterals Steiner Ellipse Coordinate Geometry Linear Equations Equations of Parallel and Perpendicular Lines Midpoint of a Line Segment Distance Formula Distance between Point and Line Section Formula Equation of Locus Determining Coordinates Coordinate Geometry (Angle Bisector) Conic Sections Equation of a Circle Parabola Ellipse Hyperbola Discriminant of a Conic Section 3D Coordinate Geometry (Distance) 3D Coordinate Geometry (Equation of a Line) 3D Coordinate Geometry (Skew Lines) 3D Coordinate Geometry (Equation of a Plane) 3D Coordinate Geometry (Parallel Planes) 3D Coordinate Geometry (Perpendicular Planes) 3D Coordinate Geometry (Intersection of Planes) Trigonometry Trigonometry Converting Degrees and Radians Basic Trigonometric Functions Reciprocal Trigonometric Functions Inverse Trigonometric Functions Bearing (Word Problems) Hyperbolic Trigonometric Functions Local Linearization Sine and Cosine Graphs Tangent and Cotangent Graphs Cosecant and Secant Graphs Inverse Trigonometric Graphs Symmetry in Trigonometric Graphs Trigonometric Graphs (Amplitude and Periodicity) Graphical Transformation of Trigonometric Functions Graphs of Trigonometric Functions (Problem Solving) Trigonometric Equations Trigonometric Equations (Double Angle Formula) Lengths in Right Triangles Sine Rule (Law of Sines) Cosine Rule (Law of Cosines) Solving Triangles Trigonometric Identities Pythagorean Identities Ratio of Trigonometric Functions Trigonometric Even-odd Functions Trigonometric Periodicity Identities Trigonometric Co-function Identities Trigonometric R method Fundamental Trigonometric Identities Double Angle Identities Sum and Difference Formulas Triple Angle Identities Expansions of sin(nx) and cos(nx) Half Angle Tangent Substitution Trigonometric Power Reduction Identities Product-to-Sum Trigonometric Formulas Sum to Product Trigonometric Identities Proving Trigonometric Identities Chebyshev Polynomials (Definition and Properties) Vectors Vectors Vector Addition Vector Decomposition Unit Vectors Dot Product Cross Product 3D Geometry Regular Polyhedra Euclidean Geometry Isosceles Triangle Theorem Angle Bisector Theorem Menelaus' Theorem Stewart's Theorem Orthic Triangle Nine-point Circle Routh's Theorem Pedal Triangle Projective Geometry Brahmagupta's Formula Power of a Point Radical Axis of 2 Circles Ptolemy's Theorem Pitot's Theorem Descartes' Circle Theorem Geometric Transformations Symmetry Reflection Affine Transformations Does 1 square meter equal 100 square centimeters? Can a triangle have an angle of 0 degrees? Mobius Strips Klein Bottle Spherical Geometry Hyperbolic Geometry Topology Topology Metric Space Homeomorphism Dense Set Cantor Set Stone-Weierstrass Theorem Brouwer Fixed Point Theorem Ham Sandwich Theorem Hilbert Space Banach Tarski Paradox Axiom Of Choice Converse Of Intermediate Value Theorem Connected Space Open Sets Closed Sets Compact Space Subsequences Mechanics Dynamics Newton's Laws of Motion Identifying Action-Reaction Forces Lagrangian Mechanics Fluid Mechanics Continuity Equation Bernoulli's Principle Pressure Density Free Body Diagrams Solving for Equilibrium Friction 1D Dynamics Problem Solving Motion Along Inclined Planes Centripetal acceleration Calculating impulse Conservation of Momentum Analyzing inelastic collisions Is force a necessary condition to persist a motion? Do heavier objects fall faster than lighter objects? If an object is moving then a net force must be acting on it Since every action has an equal and opposite reaction nothing will be moved Is acceleration the rate of change of speed? Is the acceleration of an object at rest zero? Does a rolling ball follow Newton's first law of motion? Is there gravity in the Space Station? Is heat the same as temperature? Are Photons Massless? Does an object accelerate under uniform circular motion? Kinematics Introduction to Kinematics Motion Under Constant Velocity Motion under Constant Acceleration Equations Of Motion 1D Kinematics Problem Solving Hyperloop Different Representations of Vectors Adding velocity vectors Physics of Traffic Jams Projectile Motion Position-Time Graph Uniform Circular Motion Conservation Laws Conservation of Energy Kinetic energy Determining Kinetic Energy Lost in Inelastic Collisions Work Rocket Physics Conservative vs. Non-conservative Forces Gravitational Potential Energy Analyzing Elastic Collisions Conservative Forces Units and Measurements SI Multiplier Prefixes SI Divisor Prefixes SI Length SI Fluid Measure Converting Units Dimensional Analysis Fermi Estimate Rotational Motion Converting Degrees and Radians Angular Kinematics Calculating Torque as a Cross Product Torque (Equilibrium) Torque (Dynamical Behavior) Rotational Form of Newton's Second Law Moment of Inertia Rotational Kinetic Energy (Translational) Rotational Kinetic Energy (Work-Kinetic Theorem) Rotational Kinetic Energy (Conservation of Energy) Rotational Kinetic Energy (Problem Solving) Oscillation and Waves Periodic Motion Hooke's Law Understanding Basic Traveling Waves Waves Amplitude/Frequency/Wave Number/Phase Shift Doppler Effect Snell's Law Power of a Wave Applying Boundary Conditions to Standing Waves Wave Equation Sound Deriving Exponential Decay from Damping Forces Using Exponential Decay to Explain Amplitude Decreases Damped Harmonic Oscillators Damped Oscillators (Problem Solving) Geometrical Optics Lenses Mirrors Dispersion and Scattering Gravity and Space Black Holes Dark Matter Isaac Newton Deriving Kepler's Laws Applying Kepler's Laws Characteristics of Circular Orbits Modern Physics Entropy Intensive and Extensive Properties Microstates and macrostates Configurational entropy (qualitative) Configurational entropy (quantitative) Zeroth law of thermodynamics First Law of Thermodynamics Second Law of Thermodynamics Equilibrium Ideal Gas Law Specific Heat Phase Changes Quantum Mechanics Wave-Particle Duality Schrodinger Equation Wavefunctions and Measurement Heisenberg Uncertainty Principle Quantum Harmonic Oscillator Quantum Tunneling Double-slit Experiment Schrodinger's Cat Hydrogen Atom Blackbody Radiation Quantum Entanglement Bell's Theorem Quantum Teleportation Quantum Computing Spacetime Special Relativity General Relativity Gravitational Waves Cosmology Albert Einstein Quantum Mechanical Model Energy Level and Transition of Electrons Orbitals and Quantum Numbers Electron Configurations Spherical Harmonics Green's Functions String Theory Number Theory Integers Even and Odd Numbers Divisibility Rules Remainder Prime Numbers Infinitely Many Primes Distribution of Primes Mersenne Prime Prime Factorization Perfect Squares/Cubes/Powers Factors Perfect Numbers Fundamental Theorem of Arithmetic Greatest Common Divisor Lowest Common Multiple Division Algorithm Euclidean Algorithm Bezout's Identity Extended Euclidean Algorithm Decimal Expansion Binary Numbers Hexadecimal Numbers Number Base Fractional and Non-Integer Number Bases Negative Integer Number Base Factorials Stirling's Formula Double Factorials and Multifactorials Trailing Number of Zeros Rightmost Non-zero Digit of n! Wilson's Theorem Fibonacci Sequence Tribonacci Sequence Catalan Numbers Is 0 even odd or neither? Is 0 a prime number? Is 1 prime? Is 2 prime? Modular Arithmetic Misconceptions Converting Decimals and Fractions Converting Fractions into Decimals Converting Repeating Decimals into Fractions Rational Numbers Irrational Numbers History of Irrational Numbers Real Numbers Transcendental Numbers Modular Arithmetic Modular Arithmetic Parity of Integers Number Theory Chinese Remainder Theorem Fermat's Little Theorem Lucas' Theorem Sum of Squares Theorems Euler's Totient Function Euler's Theorem Finding the Last Digit of a Power Order of an Element Primitive Roots Lifting The Exponent Carmichael's Lambda Function Arithmetic Function Multiplicative Function Mobius Function Dirichlet Convolution Dirichlet Series Riemann Zeta Function Prime Zeta Function Cyclotomic Polynomials Quadratic Residues Legendre Symbol Jacobi Symbol Law of Quadratic Reciprocity Euler's Criterion Public-Key Cryptography Diffie-Hellman RSA Encryption Diophantine Equations Linear Diophantine Equations System of Linear Diophantine Equations Postage Stamp Problem / Chicken McNugget Theorem Integer Equations (Stars and Bars) Finding The Number of Digits Diophantine Equations (Solve by Factoring) Diophantine Equations (Modular Arithmetic Considerations) Fermat's Method of Infinite Descent Pell's Equation Hensel's Lemma Vieta Root Jumping General Diophantine Equations (Problem Solving) Quantitative Finance Fixed Income Types of Fixed Income Securities Time value of money Bond Valuation Bond Yield Macaulay Duration Modified Duration Fixed Income Glossary Bond issuers (Treasury) Bond issuers (Municipals) Interest Rate Derivatives Forward contract Futures contract Pricing Forward and Futures Call and Put Options American and European Options Option value Put Call Parity Efficient Market Hypothesis Option Greeks (Delta) Option Greeks (Gamma) Option Greeks (Vega) Straddle/Strangle Straddle Approximation Formula Call and Put Spreads Butterfly/Condor Mathematics Prerequisites Rule of Sum and Product Problem Solving Permutations Combinations Principle of Inclusion and Exclusion Understanding Data (Problem Solving) Data Presentation (Tables) Data Presentation (Bar Charts) Data Presentation (Pie Charts) Data Presentation (Dot Diagram) Data Presentation (Histogram) Data Presentation (Stem-leaf plot) Probability (Problem Solving) Expected Value Central Limit Theorem Markov Chains Limits of Sequences Limits of Functions Differentiation Rules Implicit Differentiation Integration u-Substitution Integration by Parts Eigenvalues and Eigenvectors Matrix Exponentiation Subspace Linear Regression Hypothesis Testing Confidence Intervals Root Approximation (Bisection) Newton Raphson Method Fermi Estimate Computer Science Concepts For Subroutines Pattern matching Big O Notation Stacks Graphs Backpack Problem Recursive Backtracking Monte-Carlo Simulation Logical Reasoning Induction Proof by Contradiction Bijection/Injection/Surjection Symmetry Modular Arithmetic Telescoping Series (Sum)

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