DDMA Level II
Mathematical Concepts in Data Science cheat sheet
Every chapter's key points, formulas and definitions on one page, for the last week before the exam. Each heading links to the chapter that explains it.
Linear algebra
- A linear equation relates unknowns to constants through addition, subtraction and multiplication only, and a straight line can be written in general, slope-intercept, point-slope, intercept or two-point form.
- In slope-intercept form, y = mx + c, m is the slope and c is the y-intercept.
- A system of two linear equations in two unknowns is solved by substitution or elimination, and the answer is checked by substituting it back.
- Vectors are added, subtracted and multiplied by a scalar component by component.
- A unit vector has magnitude 1: divide a vector by its own magnitude and it keeps the same direction.
Key terms
- General form
- Ax + By + C = 0, the most flexible form.
- Slope-intercept form
- y = mx + c, where m is the slope and c is the y-intercept, the most common form for quick graphing.
- Point-slope form
- y - y1 = m(x - x1), useful when a point on the line and its slope are known.
- Intercept form
- x/a + y/b = 1, where a and b are the x- and y-intercepts.
- Two-point form
- (y - y1)/(y2 - y1) = (x - x1)/(x2 - x1), useful when two points on the line are known.
- Vector addition
- Add corresponding components of two vectors: (a1, a2) + (b1, b2) = (a1+b1, a2+b2).
- Vector subtraction
- Subtract corresponding components: (a1, a2) - (b1, b2) = (a1-b1, a2-b2).
- Scalar multiplication
- Multiply every component of a vector by a single number.
- Properties of vector addition and scalar multiplication
- Addition is commutative and associative; scalar multiplication distributes over vector addition, the same algebraic rules ordinary numbers follow.
- Unit vector
- A vector with magnitude 1, found by dividing a vector by its own magnitude, pointing in the same direction as the original.
The rest of the sheet covers
- Calculus
- Probability theory
- Statistical methods
- Worked examples
- Exam technique and revision
- Glossary