# Mathematics ## Algebra ### Abstract Algebra #### Algebraic Structures - [[Field]] ### Boolean Algebra - **[[Boolean Algebra]]** - [[Conjunction]] - [[Disjunction]] - [[Exclusive Disjunction]] - [[Material Biconditional]] - [[Material Conditional]] - [[Negation]] #### Boolean Functions - **[[Boolean Function]]** - [[Minterms and Maxterms]] - [[Boole's Expansion Theorem]] #### Laws and Theorems - [[Boole's Expansion Theorem]] - [[De Morgan's Laws]] #### Visualisation - [[Karnaugh Map]] ### Elementary Algebra - [[Binomial Theorem]] - [[Partial Fraction Decomposition]] - [[Pascal's Triangle]] - [[Recurrence Relation]] ### Linear Algebra - [[Basis]] - [[Cross Product]] - [[Dot Product]] - **[[Linear Transformation]]** - **[[Matrix]]** - [[Matrix Multiplication]] - [[Square Matrix]] - [[Determinant]] - [[Scalar Projection]] - **[[Vector]]** - [[Pseudovector]] - [[Vector Space]] ### Relations - **[[Relation]]** - [[Antisymmetric Relation]] - [[Connected Relation]] - [[Equivalence Relation]] - [[Partial Order Relation]] - [[Reflexive Relation]] - [[Symmetric Relation]] - [[Total Order Relation]] - [[Transitive Relation]] ****** ## Analysis - **[[Analytic Function]]** ### Complex Analysis - [[Contour Integral]] - [[Euler's Formula]] #### Complex Functions - [[Cauchy's Integral Formula]] - [[Cauchy's Integral Theorem]] - [[Cauchy-Riemann Equations]] - [[Complex Logarithm]] - [[Holomorphic Function]] #### Complex Numbers - **[[Complex Number]]** - [[Complex Conjugate]] - [[De Moivre's Formula]] - [[Fundamental Theorem of Algebra]] - [[Root of Unity]] ### Harmonic Analysis - [[Fourier Series]] - [[Fourier Transform]] - [[Harmonic Function]] - [[Laplace Transform]] - [[Comparison of the Laplace and Fourier Transform]] ### Real Analysis #### Functions - [[Big O Notation]] - [[Bijective Function]] - [[Convolution]] - [[Discontinuity]] - [[Even and Odd Function]] - **[[Function]]** - [[Codomain]] - [[Domain]] - [[Image]] - [[Implicit Function]] - [[Injective Function]] - [[Involution]] - [[Periodic Function]] - [[Phase]] - [[Sinusoid]] - [[Surjective Function]] > [!List of named functions]- > - [[Dirac Delta Function]] > - [[Exponential Function]] > - [[Floor and Ceiling Function]] > - [[Natural Logarithm]] > - [[Trigonometric Functions]] > - [[Unit Step Function]] *** ## Calculus - **[[Fundamental Theorem of Calculus]]** - [[Squeeze Theorem]] ### Differential Calculus - **[[Derivative]]** - [[Implicit Differentiation]] > [!List of differentiation rules]- > - [[Chain Rule]] > - [[Inverse Function Rule]] > - [[Power Rule]] > - [[Product Rule]] > - [[Quotient Rule]] > - [[Reciprocal Rule]] ### Integral Calculus - [[Antiderivative]] - [[Cauchy Principal Value]] - [[Lebesgue Integral]] - **[[Integral]]** - [[Improper Integral]] - [[Riemann Integral]] ### Multivariable Calculus - [[Jacobian Matrix]] - [[Line Integral]] - [[Multiple Integral]] - [[Partial Derivative]] - [[Surface Integral]] - [[Total Derivative]] ### Series - [[Taylor Series]] ### Vector Calculus - [[Curl]] - [[Directional Derivative]] - [[Divergence]] - [[Divergence Theorem]] - [[Gradient]] - [[Normal]] - **[[Vector Field]]** *** ## Discrete Mathematics ### Combinatorics - **[[Combination]]** - [[Permutation]] ### Graph Theory - [[Cut]] - [[Cycle]] - **[[Graph]]** - [[Bipartite Graph]] - [[Complete Graph]] - [[Connected Graph]] - [[Directed Acyclic Graph]] - [[Flow Network]] - [[Planar Graph]] - [[Tree, graph theory|Tree]] - [[Graph Condensation]] - [[Maximum Flow Problem]] - [[Ford-Fulkerson Algorithm]] - [[Edmonds-Karp Algorithm]] - [[Path]] - [[Eulerian Path]] - [[Hamiltonian Path]] - [[Shortest Path Problem]] - [[Strongly Connected Component]] - [[Topological Sorting]] ## Geometry - [[Face]] - [[Schlegel Diagram]] ### Coordinate systems - [[Cartesian Coordinate System]] #### Two-dimensional #### Three-dimensional ### Trigonometry - [[Cosine Rule]] - **[[Trigonometric Functions]]** - [[List of Trigonometric Identities]] *** ## Number Theory - [[Bézout’s Identity]] - [[Division Theorem]] - [[Euclidean Algorithm]] - [[Fermat's Little Theorem]] - **[[Fundamental Theorem of Arithmetic]]** - [[Greatest Common Divisor]] - [[Least Common Multiple]] - [[Modular Arithmetic]] - [[Triangular Number]] ### Arithmetic - [[Exponentiation]] - [[Logarithm]] ### Numeral systems - [[Base Conversion]] - [[Radix Complement]] #### Binary - [[Binary Multiplication]] - [[Signed Binary Number]] - [[Unsigned Binary Subtraction]] *** ## Set Theory - [[Cardinality]] - [[Countable Set]] - [[De Morgan's Laws]] - [[Disjoint Sets]] - [[Inclusion-Exclusion Principle]] - **[[Set]]** - [[Set Algebra]] - [[Cartesian Product]] - [[Complement]] - [[Intersection]] - [[Union]] - [[Set Difference]] - [[Symmetric Difference]] - [[Subset]] - [[Power Set]] - [[Partition]] *** ## Topology - [[Euler Characteristic]] - [[Homotopy]] - [[Interior]] - [[Neighbourhood]] - [[Simply Connected Space]] *** ## Reference - [[Boolean Algebra#Laws|Boolean algebra laws]] - [[Greek alphabet]] - [[Exponentiation#Index laws|Index laws]] - [[List of trigonometric identities]] - [[Logarithm#Logarithm laws|Log laws]] - [[Set Algebra#Laws|Set algebra laws]] ### Mathematical constants - [[e]]