Mathematics for Machine Learning and Data Science Specialization

machine-learning-calculus

week-1-derivatives-and-optimization

lesson-1-derivatives
course-introduction
machine-learning-motivation
motivation-to-derivatives-part-i
derivatives-and-tangents
slopes-maxima-and-minima
approximation-of-derivatives_instructions
derivatives-and-their-notation
some-common-derivatives-lines
some-common-derivatives-quadratics
some-common-derivatives-higher-degree-polynomials
some-common-derivatives-other-power-functions
the-inverse-function-and-its-derivative
derivative-of-trigonometric-functions
meaning-of-the-exponential-e
the-derivative-of-e-x
the-derivative-of-log-x
existence-of-the-derivative
properties-of-the-derivative-multiplication-by-scalars
properties-of-the-derivative-the-sum-rule
properties-of-the-derivative-the-product-rule
properties-of-the-derivative-the-chain-rule

ungraded-lab
optional-downloading-your-notebook-and-refreshing-your-workspace_instructions

lesson-2-optimization
introduction-to-optimization
optimization-of-squared-loss-the-one-powerline-problem
optimization-of-squared-loss-the-two-powerline-problem
optimization-of-squared-loss-the-three-powerline-problem
optimization-of-log-loss-part-1
optimization-of-log-loss-part-2
week-1-conclusion

programming-assignment-optimizing-functions-of-one-variable-cost-minimization
optional-assignment-troubleshooting-tips_instructions
optional-partial-grading-for-assignments_instructions

lecture-notes
week-1-slides_instructions

week-2-gradients-and-gradient-descent

lesson-1-gradients
introduction-to-tangent-planes
partial-derivatives-part-1
partial-derivatives-part-2
gradients
gradients-and-maxima-minima
optimization-with-gradients-an-example
optimization-using-gradients-analytical-method

lesson-2-gradient-descent
optimization-using-gradient-descent-in-one-variable-part-1
optimization-using-gradient-descent-in-one-variable-part-2
optimization-using-gradient-descent-in-one-variable-part-3
optimization-using-gradient-descent-in-two-variables-part-1
optimization-using-gradient-descent-in-two-variables-part-2
optimization-using-gradient-descent-least-squares
optimization-using-gradient-descent-least-squares-with-multiple-observations
week-2-conclusion

lecture-notes
week-2-slides_instructions

week-3-optimization-in-neural-networks-and-newtons-method

lesson-1-optimization-in-neural-networks
regression-with-a-perceptron
regression-with-a-perceptron-loss-function
regression-with-a-perceptron-gradient-descent
classification-with-perceptron
classification-with-perceptron-the-sigmoid-function
classification-with-perceptron-gradient-descent
classification-with-perceptron-calculating-the-derivatives
classification-with-a-neural-network
classification-with-a-neural-network-minimizing-log-loss
gradient-descent-and-backpropagation

lesson-2-newtons-method
newtons-method
newtons-method-an-example
the-second-derivative
the-hessian
hessians-and-concavity
newtons-method-for-two-variables
week-3-conclusion

acknowledgments-course-resources
acknowledgments_instructions
optional-opportunity-to-mentor-other-learners_instructions

lecture-notes
week-3-slides_instructions

machine-learning-linear-algebra

week-1-system-of-linear-equations

specialization-course-introduction
specialization-introduction
course-introduction
what-to-expect-and-how-to-succeed

system-of-linear-equations-2-variables
machine-learning-motivation
check-your-knowledge_instructions
system-of-sentences
system-of-equations
system-of-equations-as-lines
a-geometric-notion-of-singularity
singular-vs-nonsingular-matrices
linear-dependence-and-independence
the-determinant

ungraded-lab
optional-downloading-your-notebook-and-refreshing-your-workspace_instructions

system-of-linear-equations-3-variables
system-of-equations-3×3
singular-vs-non-singular-matrices-3×3
system-of-equations-as-planes-3×3
linear-dependence-and-independence-3×3
the-determinant-3×3
conclusion
matrices_exam

lecture-notes
week-1-slides_instructions

week-2-solving-system-of-linear-equations

solving-system-of-linear-equations-elimination
machine-learning-motivation
check-your-knowledge_instructions
solving-non-singular-system-of-linear-equations
solving-singular-systems-of-linear-equations
solving-systems-of-equations-with-more-variables
matrix-row-reduction
row-operations-that-preserve-singularity

solving-system-of-linear-equation-row-echelon-form-and-rank
the-rank-of-a-matrix
the-rank-of-a-matrix-in-general
row-echelon-form
row-echelon-form-in-general
reduced-row-echelon-form
conclusion
the-rank-of-a-matrix_exam

programming-assignment-system-of-linear-equations
optional-assignment-troubleshooting-tips_instructions
optional-partial-grading-for-assignments_instructions
system-of-linear-equations_instructions

lecture-notes
week-2-slides_instructions

week-3-vectors-and-linear-transformations

vector-algebra
machine-learning-motivation
check-your-knowledge_instructions
vectors-and-their-properties
sum-and-difference-of-vectors
distance-between-vectors
multiplying-a-vector-by-a-scalar
the-dot-product
geometric-dot-product
multiplying-a-matrix-by-a-vector

linear-transformations
matrices-as-linear-transformations
linear-transformations-as-matrices
matrix-multiplication
the-identity-matrix
matrix-inverse
which-matrices-have-an-inverse
neural-networks-and-matrices
conclusion
vector-and-matrix-operations-types-of-matrices_exam

programming-assignment-single-perceptron-neural-networks-for-linear-regression
single-perceptron-neural-networks-for-linear-regression_instructions

lecture-notes
week-3-slides_instructions

week-4-determinants-and-eigenvectors

determinants-in-depth
machine-learning-motivation
check-your-knowledge_instructions
singularity-and-rank-of-linear-transformations
determinant-as-an-area
determinant-of-a-product
determinants-of-inverses

eigenvalues-and-eigenvectors
bases-in-linear-algebra
span-in-linear-algebra
eigenbases
eigenvalues-and-eigenvectors
conclusion
eigenvalues-and-eigenvectors_exam
how-is-your-course-experience-so-far_instructions

lecture-notes
week-4-slides_instructions

programming-assignment-eigenvalues-and-eigenvectors
eigenvalues-and-eigenvectors_instructions

course-resources
reading-textbooks-and-resources_instructions
references_index
references_instructions
notations_instructions
acknowledgments_instructions

machine-learning-probability-and-statistics

week-1-introduction-to-probability-and-probability-distributions

lesson-1-introduction-to-probability
course-introduction
check-your-knowledge_instructions
what-is-probability
what-is-probability-dice-example
interactive-tool-repeated-experiments_instructions
complement-of-probability
sum-of-probabilities-disjoint-events
sum-of-probabilities-joint-events
independence
birthday-problem
conditional-probability-part-1
conditional-probability-part-2
bayes-theorem-intuition
bayes-theorem-mathematical-formula
bayes-theorem-spam-example
bayes-theorem-prior-and-posterior
bayes-theorem-the-naive-bayes-model
probability-in-machine-learning

lesson-2-probability-distributions
random-variables
probability-distributions-discrete
binomial-distribution
optional-binomial-coefficient
bernoulli-distribution
probability-distributions-continuous
probability-density-function
cumulative-distribution-function
interactive-tool-relationship-between-pmf-pdf-and-cdf-of-some-distributions_instructions
uniform-distribution
normal-distribution
optional-chi-squared-distribution
sampling-from-a-distribution
week-1-conclusion

programming-assingment-probability-distributions
optional-downloading-your-notebook-and-refreshing-your-workspace_instructions
optional-assignment-troubleshooting-tips_instructions
optional-partial-grading-for-assignments_instructions

week-2-describing-probability-distributions-and-probability-distributions-with

lesson-1-describing-distributions
measures-of-central-tendency
expected-value
expected-value-of-a-function
sum-of-expectations
variance
standard-deviation
sum-of-gaussians
standardizing-a-distribution
interactive-tool-mean-median-and-standard-deviation_instructions
skewness-and-kurtosis-moments-of-a-distribution
skewness-and-kurtosis-skewness
skewness-and-kurtosis-kurtosis
quantiles-and-box-plots
visualizing-data-box-plots
visualizing-data-kernel-density-estimation
visualizing-data-violin-plots
visualizing-data-qq-plots

lesson-2-probability-distributions-with-multiple-variables
joint-distribution-discrete-part-1
joint-distribution-discrete-part-2
joint-distribution-continuous
marginal-and-conditional-distribution
conditional-distribution
covariance-of-a-dataset
covariance-of-a-probability-distribution
covariance-matrix
correlation-coefficient
multivariate-gaussian-distribution
week-2-conclusion

week-3-sampling-and-point-estimation

lesson-1-population-and-sample
population-and-sample
sample-mean
sample-proportion
sample-variance
law-of-large-numbers
central-limit-theorem-discrete-random-variable
central-limit-theorem-continuous-random-variable

lesson-2-point-estimation
point-esimation
maximum-likelihood-estimation-motivation
mle-bernoulli-example
mle-gaussian-example
mle-for-gaussian-population_instructions
mle-linear-regression
interactive-tool-likelihood-functions_instructions
regularization
back-to-bayesics
frequentist-vs-bayesian-approach_instructions
relationship-between-map-mle-and-regularization
week-3-conclusion

week-4-confidence-intervals-and-hypothesis-testing

lesson-1-confidence-intervals
z-distribution
margin-of-error
interactive-tool-confidence-intervals_instructions
calculation-steps
confidence-interval-example
calculating-sample-size
difference-between-confidence-and-probability
unknown-standard-deviation
confidence-intervals-for-proportion

lesson-2-hypothesis-testing
defining-hypothesis
type-i-and-type-ii-errors
right-tailed-left-tailed-and-two-tailed-tests
p-value
critical-values
power-of-a-test
interpreting-results
t-distribution
t-tests
test-for-proportions_instructions
two-sample-t-test
two-sample-test-for-proportions_instructions
paired-t-test
ml-application-a-b-testing
week-4-conclusion

acknowledgments-course-resources
acknowledgments_instructions
optional-opportunity-to-mentor-other-learners_instructions
references_index
references_instructions