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Omkar Nale Sir

Topics in Mathematics

list of some topics in Mathematics :

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List of Topics in Algebra-

  • Linear equations

  • Matrices

  • Matrix decompositions

  • Relations

  • Computations

  • Vector spaces

  • Structure

  • Multilinear algebra

  • Affine space and related topics

  • Projective space

Linear equations:

  • System of linear equations

  • Determinant

  • Minor

  • Cauchy–Binet formula

  • Cramer's rule

  • Gaussian elimination

  • Gauss–Jordan elimination

  • Strassen algorithm

Matrices

  • 2 × 2 real matrices

  • Matrix theory

  • Matrix addition

  • Matrix multiplication

  • Basis transformation matrix

  • Characteristic polynomial

  • Trace

  • Eigenvalue, eigenvector and eigenspace

  • Cayley–Hamilton theorem

  • Spread of a matrix

  • Jordan normal form

  • Weyr canonical form

  • Rank

  • Matrix inversion, invertible matrix

  • Pseudoinverse

  • Adjugate

  • Transpose

  • Dot product

  • Symmetric matrix

  • Orthogonal matrix

  • Skew-symmetric matrix

  • Conjugate transpose

  • Unitary matrix

  • Hermitian matrix, Antihermitian matrix

  • Positive-definite, positive-semidefinite matrix

  • Pfaffian

  • Projection

  • Spectral theorem

  • Perron–Frobenius theorem

  • List of matrices

  • Diagonal matrix, main diagonal

  • Diagonalizable matrix

  • Triangular matrix

  • Tridiagonal matrix

  • Block matrix

  • Sparse matrix

  • Hessenberg matrix

  • Hessian matrix

  • Vandermonde matrix

  • Stochastic matrix

  • Toeplitz matrix

  • Circulant matrix

  • Hankel matrix

  • (0,1)-matrix

Matrix decompositions:

  • Cholesky decomposition

  • LU decomposition

  • QR decomposition

  • Polar decomposition

  • Spectral theorem

  • Singular value decomposition

  • Higher-order singular value decomposition

  • Schur decomposition

  • Schur complement

  • Haynsworth inertia additivity formula

Relations

  • Matrix equivalence

  • Matrix congruence

  • Matrix similarity

  • Matrix consimilarity

  • Row equivalence

Computations

  • Elementary row operations

  • Householder transformation

  • Least squares, linear least squares

  • Gram–Schmidt process

  • Woodbury matrix identity

Vector spaces

  • Linear combination

  • Linear span

  • Linear independence

  • Scalar multiplication

  • Basis

  • Change of basis

  • Hamel basis

  • Cyclic decomposition theorem

  • Dimension theorem for vector spaces

  • Hamel dimension

  • Examples of examples spaces

  • Linear map

  • Shear mapping or Galilean transformation

  • Squeeze mapping or Lorentz transformation

  • Linear subspace

  • Row and column spaces

  • Column space

  • Row space

  • Cyclic subspace

  • Null space, nullity

  • Rank–nullity theorem

  • Nullity theorem

  • Dual space

  • Linear function

  • Linear functional

  • Category of vector spaces

Structures

  • Topological vector space

  • Normed vector space

  • Inner product space

  • Euclidean space

  • Orthogonality

  • Orthogonal complement

  • Orthogonal projection

  • Orthogonal group

  • Pseudo-Euclidean space

  • Null vector

  • Indefinite orthogonal group

  • Orientation (geometry)

  • Improper rotation

  • Symplectic structure

Multilinear algebra

  • Tensor

  • Classical treatment of tensors

  • Component-free treatment of tensors

  • Outer product

  • Tensor algebra

  • Exterior algebra

  • Symmetric algebra

  • Clifford algebra

  • Geometric algebra

Affine space and related topics

  • Affine transformation

  • Affine group

  • Affine geometry

  • Affine coordinate system

  • Flat (geometry)

  • Cartesian coordinate system

  • Euclidean group

  • Poincaré group

  • Galilean group

Projective space

  • Projective transformation

  • Projective geometry

  • Projective linear group

  • Quadric and conic section

Topics Releted to Geommetry :

Types, methodologies, and terminologies of geometry.

  • Absolute geometry

  • Affine geometry

  • Algebraic geometry

  • Analytic geometry

  • Archimedes' use of infinitesimals

  • Birational geometry

  • Complex geometry

  • Combinatorial geometry

  • Computational geometry

  • Conformal geometry

  • Constructive solid geometry

  • Contact geometry

  • Convex geometry

  • Descriptive geometry

  • Differential geometry

  • Digital geometry

  • Discrete geometry

  • Distance geometry

  • Elliptic geometry

  • Enumerative geometry

  • Epipolar geometry

  • Finite geometry

  • Fractal geometry

  • Geometry of numbers

  • Hyperbolic geometry

  • Incidence geometry

  • Information geometry

  • Integral geometry

  • Inversive geometry

  • Inversive ring geometry

  • Klein geometry

  • Lie sphere geometry

  • Non-Euclidean geometry

  • Numerical geometry

  • Ordered geometry

  • Parabolic geometry

  • Plane geometry

  • Projective geometry

  • Quantum geometry

  • Reticular geometry

  • Riemannian geometry

  • Ruppeiner geometry

  • Spherical geometry

  • Symplectic geometry

  • Synthetic geometry

  • Systolic geometry

  • Taxicab geometry

  • Toric geometry

  • Transformation geometry

  • Tropical geometry

Euclidean geometry, foundations

  • Hilbert's axioms

  • Point

  • Locus

  • Line

  • Parallel

  • Angle

  • Concurrent lines

  • Adjacent angles

  • Central angle

  • Complementary angles

  • Inscribed angle

  • Internal angle

  • Supplementary angles

  • Angle trisection

  • Congruence

  • Reflection

  • Rotation

  • Coordinate rotations and reflections

  • Translation

  • Glide reflection

  • Similarity

  • Similarity transformation

  • Homothety

  • Shear mapping

Euclidean plane geometry (plane geometry)

  • 2D computer graphics

  • 2D geometric model

  • Altitude

  • Brahmagupta's formula

  • Bretschneider's formula

  • Compass and straightedge constructions

  • Squaring the circle

  • Complex geometry

  • Conic section

  • Focus

  • Circle

  • List of circle topics

  • Thales' theorem

  • Circumcircle

  • Concyclic

  • Incircle and excircles of a triangle

  • Orthocentric system

  • Monge's theorem

  • Power center

  • Nine-point circle

  • Circle points segments proof

  • Mrs. Miniver's problem

  • Isoperimetric theorem

  • Annulus

  • Ptolemaios' theorem

  • Steiner chain

  • Eccentricity

  • Ellipse

  • Semi-major axis

  • Hyperbola

  • Parabola

  • Matrix representation of conic sections

  • Dandelin spheres

  • Curve of constant width

  • Reuleaux triangle

  • Frieze group

  • Golden angle

  • Holditch's theorem

  • Interactive geometry software

  • Parallel postulate

  • Polygon

  • Star polygon

  • Pick's theorem

  • Shape dissection

  • Bolyai–Gerwien theorem

  • Poncelet–Steiner theorem

  • Polygon triangulation

  • Pons asinorum

  • Quadrilateral

  • Bicentric quadrilateral

  • Cyclic quadrilateral

  • Equidiagonal quadrilateral

  • Kite (geometry)

  • Orthodiagonal quadrilateral

  • Rhombus

  • Rectangle

  • Square

  • Tangential quadrilateral

  • Trapezoid

  • Isosceles trapezoid

  • Sangaku

  • Straightedge

  • Symmedian

  • Tessellation

  • Prototile

  • Aperiodic tiling

  • Wang tile

  • Penrose tiling

  • Trapezoid (trapezium)

  • Isosceles trapezoid

  • Triangle

  • Acute and obtuse triangles

  • Equilateral triangle

  • Euler's line

  • Heron's formula

  • Integer triangle

  • Heronian triangle

  • Isosceles triangle

  • List of triangle inequalities

  • List of triangle topics

  • Pedal triangle

  • Pedoe's inequality

  • Pythagorean theorem

  • Pythagorean triangle

  • Right triangle

  • Triangle inequality

  • Trigonometry

  • List of trigonometry topics

  • Wallpaper group

3-dimensional Euclidean geometry (solid geometry)

  • 3D projection

  • 3D computer graphics

  • Binary space partitioning

  • Ray tracing

  • Graham scan

  • Borromean rings

  • Cavalieri's principle

  • Cross section

  • Crystal

  • Cuisenaire rods

  • Desargues' theorem

  • Right circular cone

  • Hyperboloid

  • Napkin ring problem

  • Pappus's centroid theorem

  • Paraboloid

  • Polyhedron

  • Defect

  • Dihedral angle

  • Prism

  • Prismatoid

  • Honeycomb

  • Pyramid

  • Parallelepiped

  • Tetrahedron

  • Heronian tetrahedron

  • Platonic solid

  • Archimedean solid

  • Kepler-Poinsot polyhedra

  • Johnson solid

  • Uniform polyhedron

  • Polyhedral compound

  • Hilbert's third problem

  • Deltahedron

  • Surface normal

  • 3-sphere, spheroid, ellipsoid

  • Parabolic microphone

  • Parabolic reflector

  • Soddy's hexlet

  • Sphericon

  • Stereographic projection

  • Stereometry

n-dimensional Euclidean geometry

  • Ball

  • Convex

  • Convex hull

  • Coxeter group

  • Euclidean distance

  • Homothetic center

  • Hyperplane

  • Lattice

  • Ehrhart polynomial

  • Leech lattice

  • Minkowski's theorem

  • Packing

  • Sphere packing

  • Kepler conjecture

  • Kissing number problem

  • Honeycomb

  • Andreini tessellation

  • Uniform tessellation

  • Voronoi tessellation

  • Delaunay triangulation

  • Quasicrystal

  • Parallelogram law

  • Polytope

  • Schläfli symbol

  • Regular polytope

  • Regular Polytopes

  • Sphere

  • Quadric

  • Hypersphere, sphere

  • Spheroid

  • Ellipsoid

  • Hyperboloid

  • Paraboloid

  • Cone

  • Torus

  • Root system

  • Similarity

  • Zonotope

Other geometries (not Euclidean)

  • Projective geometry

  • Arc (projective geometry)

  • Desargues' theorem

  • Girard Desargues

  • Desarguesian plane

  • Line at infinity

  • Point at infinity

  • Plane at infinity

  • Hyperplane at infinity

  • Projective line

  • Projective plane

  • Oval (projective plane)

  • Roman surface

  • Projective space

  • Complex projective line

  • Complex projective plane

  • Fundamental theorem of projective geometry

  • Projective transformation

  • Möbius transformation

  • Cross-ratio

  • Duality

  • Homogeneous coordinates

  • Pappus's hexagon theorem

  • Incidence

  • Pascal's theorem

  • Affine geometry

  • Affine space

  • Affine transformation

  • Finite geometry

  • Differential geometry

  • Contact geometry

  • Riemannian geometry

  • Symplectic geometry

  • Non-Euclidean plane geometry

  • Angle excess

  • Hyperbolic geometry

  • Pseudosphere

  • Tractricoid

  • Elliptic geometry

  • Spherical geometry

  • Minkowski space

  • Thurston's conjecture

Numerical geometry

  • Curve interpolation

  • Parametric curve

  • Bézier curve

  • Spline

  • Hermite spline

  • Beta spline

  • B-spline

  • Higher-order spline

  • NURBS

  • Parametric surface

  • Parametric patch

Geometric algorithms

  • Convex hull construction

  • Euclidean shortest path

  • Point in polygon

  • Point location

  • Hidden line removal

Mathematical morphology

  • Minkowski addition

Generalizations

  • Noncommutative geometry

  • Topology

Various

  • Coordinate-free treatment

  • Chirality

  • Handedness

  • Relative direction

  • Mirror image

  • Erlangen program

  • Four-dimensional space

  • Group action, invariant

  • Hadwiger's theorem

  • Infinitesimal transformation

  • Pi

  • Polar sine

  • Symmetry, shape, pattern

  • Crystal system

  • Frieze group

  • Isometry

  • Lattice

  • Point group

  • Point groups in two dimensions

  • Point groups in three dimensions

  • Space group

  • Symmetry group

  • Translational symmetry

  • Wallpaper group

  • Mathematics and fiber arts

  • Van Hiele model

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