Curriculum

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====== Math ======

  * [[Arithmetic]]
    * add, subtract
    * multiply, divide
    * exponent, logarithm
    * fractions, decimals
  * [[Algebra]]: the study of generalizations of arithmetic operations  
    * [[Gallery of Curves]]
    * [[Spirals]]
    * [[Polynomial]]
    * [[Linear]]
    * [[Quadratic]]
    * [[Conic Section]]
    * [[Factoring]]
    * [[Equations and Functions]]
    * [[Exponent]]
    * [[Logarithm]]
  * [[Geometry]]: the study of shape  
  * [[Trigonometry]]: the study of the triangle 
  * [[Miscellaneous Concepts]]
    * [[Sets]] - set theory
    * [[Classifications]] - real, integer, whole, rational, etc.
    * [[Dimensions]] - 2D, 3D, 4D, nD
    * [[Logic]] - if then else
    * [[Functions]]
    * [[Linear, non-linear, curve, curvilinear]]
      * [[Nonlinear Programming]]
    * [[Number Systems]] - base-10, base-2, etc.
    * Number theory - prime numbers
    * [[Scale]]
  * [[Linear Algebra]]  
    * [[Matrix Math]]
    * [[Matrix Multiplication]]
  * [[Calculus]]: the mathematical study of continuous change  
    * [[Differential Calculus]]: rates of change and slopes of curves  
    * [[Integral Calculus]]: accumulation of quantities and the areas under and between curves  
  * [[Statistics and Probability]]
    * [[Statistics]]
    * [[Probability]]
  * [[Linear Regression]]
    * Analysis, modeling
    * Simple Linear Regression 
    * Multiple Linear Regression  
    * Multi-Variate Linear Regression
    * [[Non-Linear Regression]]
    * [[Logistic Regression]]
  * [[Neural Network]]
    * NN Variations
    * Deep Learning

Gil Strang's course 18.065
  * Linear Algebra (Matrix Math)
  * Statistics and Probability
  * Optimization (Calculus)
  * Deep Learning (Neural Network)

project-based. no tests.  "that's how people learn"

[[Notes on Gilbert Strang Deep Learning]]

==== Timeline ====
  * 2000 BC, Babylon, algebra in use
  * 10th century BCE, in China, ancient texts describe the use of _arrays_ to solve simultaneous equations, including the concept of determinants.  
  * 6th century BCE, in Greece, Pythagoras...
  * 4th century BCE, in India, the Hindu numerals 1-9 and 0 are in use.
  * 3rd century BCE, in Greece, Euclid and Archimedes...
  * 300 BC, School of Athens, classical Greece, Euclid, Geometry, shapes, circles, triangles
  * 300 BC, Greece, diaphantus 
  * 5th century CE, in India, first use of decimal places.
  * 600 AD, India, Brahmagupta
  * 780-850 CE, in Bahgdad, the Hindu numerals spread to the Islamic world thanks to Persian mathematician al-Khwarizmi, who also coins the word _al-jabr_, or in english, _algebra_.
  * 1250 CE, in Europe, the Hindu numerals and decimal system arrived in the works of al-Khwarizmi, brought back from the holy lands by the crusaders, replacing the Greek and Roman numeral systems.
  * 1545-1850 CE, in Europe and Japan, _array_ methods arrive from China, and the word _matrix_ is coined to replace the word _array_.
  * 1600 Decartes, 32 youngers than Galileo , Cartesian Coordinate System  connection between algebra and geometry
  * 1600 galileo
  * 1700 Isaac Newton, Gottfried Leibnez, Euler, another guy, in Europe, invented calculus among other things.
  * Niels bohr, goes beyond Newton in subparticle and interplanetary physics.  
  * Hermann Minkowski 4d space time 1908

  * Pythagoras Euclid Archimedes  
  * Classical Hellenic Hellenistic  
  * Copernicus  

==== Miscellaneous Topics ====

== Euler's Number ==

== Euler's Formula ==

== Power Function ==

== Exponentiation ==

== Exponential Function ==

==== Notes ====

[W,s,v] = svd((repmat(sum(x.*x,1),size(x,1),1).*x)*x');

in week 1 > parameter learning > gradient descent for linear regression

batch gradient descent

use lsode to solve multiple equations using calculus

https://www.gnu.org/software/octave/doc/v4.0.1/Ordinary-Differential-Equations.html

==== References ====
  * Cheat Sheets: <http://tutorial.math.lamar.edu/>  

== Unicode Characters Used in Equations ==
  * http://xahlee.info/comp/unicode_math_operators.html  
  * http://math.typeit.org/  
  * http://sites.psu.edu/symbolcodes/accents/math/mathchart/  
  * http://www.fileformat.info/info/unicode/category/Sm/list.htm  
  * http://azuliadesigns.com/html-character-codes-ascii-entity-unicode-symbols/  
  * http://samantha.voyc.com/doc/script/python/mathsymbols.html