Mathematics for Data Science and Machine Learning using R

Explore foundational mathematics for data science with R, covering linear algebra, calculus, and vector spaces. Engage with brief lectures, lab exercises, and solution videos to reinforce learning and ask questions.

Demonstrates loading the tidyverse, creating and mutating data frames, computing means by class, and plotting highway versus city for 2008 models.

Explore vectors, matrices, and plotting in R: create vectors with c, colon, sequence, and rep; form matrices with matrix, rbind, and cbind; plot 2D and 3D with plot and plot3D.

Create a 3x4 matrix A in R filled row-wise with 1-12, verify A[2,4] equals 8, and plot vectors V1, V2 in 2D and V3 in 3D to illustrate vector operations.

Explore vector operations in R: plotting vectors in 2D and 3D, scalar multiplication, vector addition and subtraction, and visualizing vector sums with custom plotting functions.

Explore scalar multiplication, addition, subtraction, and true matrix multiplication in R. Identify dimension requirements, errors from nonconforming arrays, and the difference between element-wise and %*% matrix multiplication.

Learn to transpose matrices in R with t, including vector cases. Use solve for inverses of square matrices and verify that a times its inverse yields the identity.

Practice transposing a square matrix and finding its inverse by hand and in R, then multiply the matrix by its inverse to verify the identity.

Learn how linear regression models a dependent variable from one or more independent variables, using intercepts, coefficients, and an error term. Includes deterministic and stochastic examples.

Define and plot functions in R, then estimate the slope of a tangent line using secret lines and animation, with examples like x^2 and sqrt(x).

Learn how derivatives map inputs to tangent slopes and rates of change, from single-variable examples to partial derivatives like f_x and f_y in f(x,y)=x^2+y^2.

Explore derivatives in data science with R by plotting a function and its derivative, discovering the power rule. Learn to compute partial derivatives for two-variable functions.

Lab 2 demonstrates deriving derivatives for sqrt(x) and x, plotting functions with their derivatives to show tangent slopes, and practicing partial derivatives of x^3+y^3.

Explore linear regression with matrix calculus in r: define beta via X^T Y, verify derivatives, fit lm with weight and hp, and interpret residuals and mse for mpg.

Explore linear regression with weight and HP, derive beta, validate derivatives, fit the model, and evaluate residuals and model choice to discuss overfitting and predictive reliability.

Demonstrate gradient descent for linear regression by generating data, fitting with lm, and illustrating convergence of beta0 and beta1 to the intercept and the coefficient on x.

Use gradient descent to fit simple regression models predicting win percent from individual inputs—ops, homerun, and strikeouts—on baseball 2018 data set, and compare convergence to find the best predictor.