Study Plan
Cool Sites & Resources
Math Notation Cheatsheet
| Statistics | Probability | Calculus |
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Basics:
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Basics:
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Other: Miltivariate calculus |
Distributions:
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N/A
CNN Course on YouTube by Stanford
Essence of Calculus Course on YouTube by 3Blue1Brown
Math Notation & DS Skills Course on Coursera by Duke
Probability Course on Coursera by Uni Zurich
Probabilistic Graphical Models on Coursera by Stanford
2 ∈ A (two is an element of set A)
A = ∅ (set A is empty)
| A | = 5 (the ‘cardinality’ i.e. size of a set. There are 5 elements in set A) |
| ∅ | = 0 (the cardinality of the empty set is 0) |
vertical bar can also = absolute value = the distance a number is from zero.
| -1 | = 1 while | 3.1 | = 3.1. A definition of the set of real numbers between -1 and 1 = B = {x : | x | < 1 ^ x is a real number} |
A ∩ B (the intersection of set A and set B) (can also be noted by “circumflex agent” which looks like a “caret” ^)
| or | (colon or pipe means ‘such that’) |
f:x↦y means f is a function that takes the value x to the value y. (Think of a function as an operation that takes objects from one set and maps them to another set)
A ∪ B (the union of set A or set B) (all the elements in set A or B or both)
A ∪ B = {X: X ∈ A OR X ∈ B}
<=> means “if and only if e.g. A < b <=> b > A
« means “much, much less than”
[2, 4] = {x ∈ ℝ: 2 ≤ x ≤ 4} (square bracket means “closed interval”) (closed interval 2-4 where x is an element of the real numbers (ℝ) such that 2 is less than or equal to X and X is less than or equal to 4)
(2, 4) = {x ∈ ℝ: 2 < x < 4} (round bracket means “open interval”) (open interval 2-4 where x is an element of the real numbers (ℝ) such that 2 is less than but not equal to X and X is less than but not equal to 4)
(2, 4] = {x ∈ ℝ: 2 < x < 4} (one round bracket & one square bracket means “half open interval”) (half open interval 2-4 where x is an element of the real numbers (ℝ) such that 2 is less than but not equal to X and X is less than or equal to 4)
𝜇 (“mu” represents the mean value)
m Slope is often denoted by the letter m (m stands for multiple? e.g. Y is a multiple of x)
A popular form of a straight line is y= mx + c (this is called the slope-intercept form). Here c which is the intercept because when x = 0, y = c. m is the gradient because it makes y a multiple of x.
The slope “m” of the line is m (slope) = y subscript 2 - y subscript 1 (the change in y, aka delta y of dy) divided by x subscript 2 - x subscript 1 (the change/delta in x, aka delta x or dx)
If the slope m of a line and a point (x1,y1) on the line are both known, then the equation of the line can be found using the point-slope formula: y - y subscript 1 = m (x - x subscript 1)
α = the learning rate (in gradient descent)
Variance describes how “spread out” elements of a set are. The mean (𝜇) = E(x), [i.e. the mean is the “expected value” of X].
Variance is the average difference between X**2 and the mean.
Variation (σ) [aka Sigma] is calculated:
(Variation [sigma squared] = the mean of … the sum of the distances between x and the mean of the set … squared)
(Equation generated on hostmath.com \sigma_{(x)}{}^2 = \frac{1}{n} \left[ \sum_{i=1}^n (x_i - \mu_x)^2 \right])
Standard deviation =
Tilde “~” means “has a probability distribution of”. Picking from 2 boxes… P(A) = P(~A) = 1/2. (The probability of A occurring equals the probability distribution of A equals one of two)