Mathematical
Achievements throughout the Ages
(all
dates are approximate)
Math
before 400 CE Math
from 400-1400 CE Math
from 1400-1600 CE
Math
from 1600 CE to 1900 CE Math
from 1900 CE to present Definitions
Mathematics before
the year 400
1800 BCE-Egypt
Unit Fractions Linear Equations
Measurement of Circle
Lunar-Solar Calendar
Volume of a Pyramid
1700 BCE-Babylonia
Base 60 place value system
Systems of two linear equations
Measurement of Circle
Quadratic Equations and systems
Lunar-Solar Calendar
Square and Cube root tables
Square Root Calculations
Pythagorean Theorem
Pythagorean Triples
Volume of a Pyramid
500 BCE-India
Pythagorean Theorem
Measurement of Circle
Square Root Calculations
600-300
BCE-Greece
Proof of Theorems
Music and Number Theory
Theories Regarding Proportions The
Elements
Paradoxes of Motion
Logic of Syllogisms
Conic studies Mathematical Models, Area and
Volume
200 BCE-China
Counting Board in Base 10
Systems of up to five linear equations
Measurement of circle
Volume of a pyramid
Square and Cube Root Algorithms Pythagorean Theorem
Pythagorean Triples
Quadratic Equations and Systems
100-400
CE-Greece (Greek based algebra and Analysis)
Elementary Number Theory
Intermediate Equations
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300-600
CE-China/India
Math of Surveying
Remainder Problems
Sine Tables Mathematical
Methods
400-900
CE-Medieval Europe
Latin Versions of Greek Math Texts Arithmatic Problems
Counting Boards
700-900
CE-China/India
Indeterminate Equations
Tangent Tables
Algebra Problems
Combinatorial Problems
700-1000
CE-Islamic Countries
Algebra Practical
Geometry
Quadratic Equations
Algebra using Irrational Numbers
Centers of Gravity
Arabic Arithmetic
Theorems of Spherical Geometry
1000-1400
CE-Medieval Europe
Translation of Texts in Other Languages
Geometry Algebra
Trigonometry Induction
Combinatorics Proportions
Kinematics Exponentials
Graphs
1100-1300
CE-China/India
Pascal’s Triangle
Pell Equation
Algebraic Equations for Geometry Equation
Solving Techniques
Linear Congruence
Systems of Equations
1100-1300
CE-Islamic Countries
Inductive Logic
Irrational Numbers
Sums of Integral Powers
Trigonometry and Applications
Cubic Equations
Parallel Postulate
Decimals Polynomials
Binomial Theorem
Combinations and Permutations
Trigonometry Texts
Amicable Numbers
Proof of Combinatorial Results
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1400-1600 CE-Europe
Algebra evolves through the following specific areas
Abacus Cubic Equations
Roots Translation
improvements
Quartic Equations
Complex Numbers
Decimal Fractions
Equation Theory
Applied Mathematics evolves through the following specific areas
Perspective Trigonometry
Geometry of Perspective
Astronomy
Map Making Logarithms
Kinematics Applied
Geometry
Probability Analytic Geometry
Number Theory
Projective Geometry
Calculus evolves through the following areas
Power Series Maxima
Area Volumes
Areas under hyperbola
Normals
Extrema Tangents
Logarithms and Areas
Power series for logarithms
Algorithm for derivatives
Arc Lengths
Series Fundamental Theorem.
Celestial Mechanics
Differentials
Calculus of exponentials
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Mathematics
in the 17th-19th Centuries
Analysis’
progression throughout the 17th and 18th Centuries
Integration Problems
Partial Derivatives
Differential Equations
Taylor Series
Criticism of Calculus’s foundations Rules for Partial
Derivatives
Calculus Texts Written
Vibrating String Problems
Calculus through Power Series
Probability,
Algebra and Geometry in the 17th and 18th Centuries
Determinants Combinatorics and
Probability
Non-Euclidean Geometry
Cramer’s Rule
Probability Topology
Surveying Almanacs
Clockmaking Analytic and
Differential Geometry
Statistical Inference
Number Theory
Algebra
in the 19th Century
5th Degree Polynomial Equations
Number Theory
Permutations Determinants
Eigenvalues
Symbolical Algebra
Complex Numbers
Quaternions
Factorization Matrices
Logic Abstract Groups
Solution of Linear Systems
Vectors
Group Theory
Analysis
in the 19th Century
Surface integrals
Definition of Convergence
Geometric Representation of Complex Numbers
Analytic Probability
Least Squares
Fourier Series Complex
Variables
Normal Distribution
Continuity and Convergence
Complex Analysis
Normal Curves
Divergence Theorem
Vector Analysis
Regression and Correlation
Beginning of Topology
Statistical Methods
Partial Differential Equations
Geometry
of the 19th Century
Differential Geometry
Non-Euclidean Geometry
Geometry on Spheres
Projected Geometry
Geometry in N Dimensions
Surface of Negative Curvature
Postulates of Physical Space
Vector Space Axioms
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20th
Century Mathematics
Analytical Engine
Linear Associative Algebras
Computer Programming
Algebraic Topology
Set Theory Field Theory
Axioms for a Vector Space
Simplexes
Vector Spaces Homology Groups
Algebraic Topology
Category Theory
Linear Programming
Switching Circuits
Four Color Theorem
Independence of Axiom of Choice
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The above mathematical
terms and areas of specialty definitions and/or examples can be found at
the following websites:
http://www.matheducation.com/mdefinitions.htm
http://www.math.com/school/glossary/glossindex.html
http://www.pballew.net/etyindex.html
