Mathematics for Machine Learning and Data Science Specialization

machine-learning-calculus

week-1-derivatives-and-optimization

lesson-1-derivatives
1 course-introduction
2 a-note-on-programming-experience
3 learning-python-recommended-resources_instructions
4 join-the-deeplearning-ai-forum-to-ask-questions-get-support-or-share-amazing_instructions
5 machine-learning-motivation
6 motivation-to-derivatives-part-i
7 derivatives-and-tangents
8 slopes-maxima-and-minima
9 approximation-of-derivatives_instructions
10 derivatives-and-their-notation
11 some-common-derivatives-lines
12 some-common-derivatives-quadratics
13 some-common-derivatives-higher-degree-polynomials
14 some-common-derivatives-other-power-functions
15 the-inverse-function-and-its-derivative
16 derivative-of-trigonometric-functions
17 meaning-of-the-exponential-e
18 the-derivative-of-e-x
19 the-derivative-of-log-x
20 existence-of-the-derivative
21 properties-of-the-derivative-multiplication-by-scalars
22 properties-of-the-derivative-the-sum-rule
23 properties-of-the-derivative-the-product-rule
24 properties-of-the-derivative-the-chain-rule

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

lesson-2-optimization
26 introduction-to-optimization
27 optimization-of-squared-loss-the-one-powerline-problem
28 optimization-of-squared-loss-the-two-powerline-problem
29 optimization-of-squared-loss-the-three-powerline-problem
30 optimization-of-log-loss-part-1
31 optimization-of-log-loss-part-2

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

week-1-wrap-up
34 week-1-conclusion
35 week-1-slides_instructions

week-2-gradients-and-gradient-descent

lesson-1-gradients
36 introduction-to-tangent-planes
37 partial-derivatives-part-1
38 partial-derivatives-part-2
39 gradients
40 gradients-and-maxima-minima
41 optimization-with-gradients-an-example
42 optimization-using-gradients-analytical-method

lesson-2-gradient-descent
43 optimization-using-gradient-descent-in-one-variable-part-1
44 optimization-using-gradient-descent-in-one-variable-part-2
45 optimization-using-gradient-descent-in-one-variable-part-3
46 optimization-using-gradient-descent-in-two-variables-part-1
47 optimization-using-gradient-descent-in-two-variables-part-2
48 optimization-using-gradient-descent-least-squares
49 optimization-using-gradient-descent-least-squares-with-multiple-observations

week-2-wrap-up
50 week-2-conclusion
51 week-2-slides_instructions

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

lesson-1-optimization-in-neural-networks
52 regression-with-a-perceptron
53 regression-with-a-perceptron-loss-function
54 regression-with-a-perceptron-gradient-descent
55 classification-with-perceptron
56 classification-with-perceptron-the-sigmoid-function
57 classification-with-perceptron-gradient-descent
58 classification-with-perceptron-calculating-the-derivatives
59 classification-with-a-neural-network
60 classification-with-a-neural-network-minimizing-log-loss
61 gradient-descent-and-backpropagation

lesson-2-newtons-method
62 newtons-method
63 newtons-method-an-example
64 the-second-derivative
65 the-hessian
66 hessians-and-concavity
67 newtons-method-for-two-variables
68 important-reminder-about-end-of-access-to-lab-notebooks_instructions

week-3-wrap-up
69 week-3-conclusion
70 week-3-slides_instructions

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

machine-learning-linear-algebra

week-1-systems-of-linear-equations

specialization-course-introduction
73 specialization-introduction
74 course-introduction
75 what-to-expect-and-how-to-succeed
76 join-the-deeplearning-ai-forum-to-ask-questions-get-support-or-share-amazing_instructions
77 a-note-on-programming-experience
78 notations_instructions
79 learning-python-recommended-resources_instructions

systems-of-equations
80 linear-algebra-applied-i
81 linear-algebra-applied-ii
82 check-your-knowledge_instructions
83 system-of-sentences
84 system-of-equations
85 system-of-equations-as-lines-and-planes
86 interactive-tool-graphical-representation-of-linear-systems-with-2-variables_instructions
87 interactive-tool-system-of-equations-as-planes-3x3_instructions
88 a-geometric-notion-of-singularity
89 singular-vs-non-singular-matrices
90 linear-dependence-and-independence
91 the-determinant
92 optional-downloading-your-notebook-and-refreshing-your-workspace_instructions

week-1-wrap-up
93 conclusion
94 week-1-slides_instructions

week-2-solving-systems-of-linear-equations

solving-systems-of-linear-equations-elimination
95 check-your-knowledge_instructions
96 solving-non-singular-system-of-linear-equations
97 solving-singular-system-of-linear-equations
98 solving-system-of-equations-with-more-variables
99 interactive-tool-graphical-representation-of-linear-systems-with-3-variables_instructions
100 matrix-row-reduction
101 row-operations-that-preserve-singularity

solving-system-of-linear-equations-row-echelon-form-and-rank
102 the-rank-of-a-matrix
103 the-rank-of-a-matrix-in-general
104 row-echelon-form
105 row-echelon-form-in-general
106 reduced-row-echelon-form
107 the-gaussian-elimination-algorithm

programming-assignment-gaussian-elimination
108 optional-assignment-troubleshooting-tips_instructions
109 optional-partial-grading-for-assignments_instructions

week-2-wrap-up
110 conclusion
111 week-2-slides_instructions

week-3-vectors-and-linear-transformations

vector-algebra
112 machine-learning-motivation
113 check-your-knowledge_instructions
114 vectors-and-their-properties
115 vector-operations
116 the-dot-product
117 geometric-dot-product
118 multiplying-a-matrix-by-a-vector

linear-transformations
119 matrices-as-linear-transformations
120 linear-transformations-as-matrices
121 interactive-tool-linear-transformations_instructions
122 matrix-multiplication
123 the-identity-matrix
124 matrix-inverse
125 which-matrices-have-an-inverse
126 neural-networks-and-matrices

week-3-wrap-up
127 conclusion
128 week-3-slides_instructions

week-4-determinants-and-eigenvectors

determinants-in-depth
129 week-4-introduction
130 check-your-knowledge_instructions
131 singularity-and-rank-of-linear-transformations
132 determinant-as-an-area
133 determinant-of-a-product
134 determinants-of-inverses

eigenvalues-and-eigenvectors
135 bases-in-linear-algebra
136 span-in-linear-algebra
137 interactive-tool-linear-span_instructions
138 eigenbases
139 eigenvalues-and-eigenvectors
140 calculating-eigenvalues-and-eigenvectors
141 on-the-number-of-eigenvectors
142 dimensionality-reduction-and-projection
143 motivating-pca
144 variance-and-covariance
145 covariance-matrix
146 pca-overview
147 pca-why-it-works
148 pca-mathematical-formulation
149 discrete-dynamical-systems

week-4-wrap-up
150 conclusion
151 week-4-slides_instructions
152 how-is-your-course-experience-so-far_instructions

course-resources
153 reading-textbooks-and-resources_instructions
154 references_index
155 references_instructions
156 acknowledgments_instructions

machine-learning-probability-and-statistics

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

lesson-1-introduction-to-probability
157 course-introduction
158 join-the-deeplearning-ai-forum-to-ask-questions-get-support-or-share-amazing_instructions
159 check-your-knowledge_instructions
160 a-note-on-programming-experience
161 learning-python-recommended-resources_instructions
162 what-is-probability
163 what-is-probability-dice-example
164 interactive-tool-repeated-experiments_instructions
165 complement-of-probability
166 sum-of-probabilities-disjoint-events
167 sum-of-probabilities-joint-events
168 independence
169 birthday-problem
170 conditional-probability-part-1
171 conditional-probability-part-2
172 bayes-theorem-intuition
173 bayes-theorem-mathematical-formula
174 bayes-theorem-spam-example
175 bayes-theorem-prior-and-posterior
176 bayes-theorem-the-naive-bayes-model
177 probability-in-machine-learning

lesson-2-probability-distributions
178 random-variables
179 probability-distributions-discrete
180 binomial-distribution
181 optional-binomial-coefficient
182 bernoulli-distribution
183 probability-distributions-continuous
184 probability-density-function
185 cumulative-distribution-function
186 interactive-tool-relationship-between-pmf-pdf-and-cdf-of-some-distributions_instructions
187 uniform-distribution
188 normal-distribution
189 optional-chi-squared-distribution
190 sampling-from-a-distribution

programming-assignment-probability-distributions
191 optional-common-coursera-labs-operations_instructions
192 optional-assignment-troubleshooting-tips_instructions
193 optional-partial-grading-for-assignments_instructions

week-1-wrap-up
194 week-1-conclusion
195 week-1-slides_instructions

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

lesson-1-describing-distributions
196 expected-value
197 other-measures-of-central-tendency-median-and-mode
198 expected-value-of-a-function
199 sum-of-expectations
200 variance
201 standard-deviation
202 sum-of-gaussians
203 standardizing-a-distribution
204 interactive-tool-mean-median-and-standard-deviation_instructions
205 skewness-and-kurtosis-moments-of-a-distribution
206 skewness-and-kurtosis-skewness
207 skewness-and-kurtosis-kurtosis
208 quantiles-and-box-plots
209 visualizing-data-box-plots
210 visualizing-data-kernel-density-estimation
211 visualizing-data-violin-plots
212 visualizing-data-qq-plots

lesson-2-probability-distributions-with-multiple-variables
213 joint-distribution-discrete-part-1
214 joint-distribution-discrete-part-2
215 joint-distribution-continuous
216 marginal-and-conditional-distribution
217 conditional-distribution
218 covariance-of-a-dataset
219 covariance-of-a-probability-distribution
220 covariance-matrix
221 correlation-coefficient
222 multivariate-gaussian-distribution

week-2-wrap-up
223 week-2-conclusion
224 week-2-slides_instructions

week-3-sampling-and-point-estimation

lesson-1-population-and-sample
225 population-and-sample
226 sample-mean
227 sample-proportion
228 sample-variance
229 law-of-large-numbers
230 central-limit-theorem-discrete-random-variable
231 central-limit-theorem-continuous-random-variable

lesson-2-point-estimation
232 point-estimation
233 maximum-likelihood-estimation-motivation
234 mle-bernoulli-example
235 mle-gaussian-example
236 mle-for-gaussian-population_instructions
237 interactive-tool-likelihood-functions_instructions
238 mle-linear-regression
239 regularization
240 back-to-bayesics
241 bayesian-statistics-frequentist-vs-bayesian
242 bayesian-statistics-map
243 bayesian-statistics-updating-priors
244 bayesian-statistics-full-worked-example
245 relationship-between-map-mle-and-regularization

week-3-wrap-up
246 week-3-conclusion
247 week-3-slides_instructions

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

lesson-1-confidence-intervals
248 confidence-intervals-overview
249 confidence-intervals-changing-the-interval
250 confidence-intervals-margin-of-error
251 interactive-tool-confidence-intervals_instructions
252 confidence-intervals-calculation-steps
253 confidence-intervals-example
254 calculating-sample-size
255 difference-between-confidence-and-probability
256 unknown-standard-deviation
257 confidence-intervals-for-proportion

lesson-2-hypothesis-testing
258 defining-hypotheses
259 type-i-and-type-ii-errors
260 right-tailed-left-tailed-and-two-tailed-tests
261 p-value
262 critical-values
263 power-of-a-test
264 interpreting-results
265 t-distribution
266 t-tests
267 test-for-proportions_instructions
268 two-sample-t-test
269 two-sample-test-for-proportions_instructions
270 paired-t-test
271 ml-application-a-b-testing

end-of-access-to-lab-notebooks
272 important-reminder-about-end-of-access-to-lab-notebooks_instructions

week-4-wrap-up
273 week-4-conclusion
274 week-4-slides_instructions

acknowledgments-course-resources
275 acknowledgments_instructions
276 optional-opportunity-to-mentor-other-learners_instructions
277 references_index
278 references_instructions