Math 380: Mathematical Foundations of Data Science - Revision history

Ls5: /* Courses for which this course is prerequisite */

2024-10-02T15:15:00Z

‎Courses for which this course is prerequisite

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Ls5: Created page with "== Catalog Information == === Title === Mathematical Foundations of Data Science === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === Contact Department..."

2024-03-14T17:48:37Z

Created page with "== Catalog Information == === Title === Mathematical Foundations of Data Science === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === Contact Department..."

New page

== Catalog Information ==

=== Title ===
Mathematical Foundations of Data Science

=== (Credit Hours:Lecture Hours:Lab Hours) ===
(3:3:0)

=== Offered ===
Contact Department

=== Prerequisite ===
[[Math 112]]

=== Description ===
Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.

== Desired Learning Outcomes ==

=== Minimal learning outcomes ===

=== Textbooks ===

=== Additional topics ===

=== Courses for which this course is prerequisite ===

← Older revision		Revision as of 15:15, 2 October 2024
Line 51:		Line 51:

	=== Courses for which this course is prerequisite ===		=== Courses for which this course is prerequisite ===
		+	[[Category:Courses\|380]]

@@ Line 19: / Line 19: @@
 === Minimal learning outcomes ===
 # Geometry and linear algebra in high-dimensional space
 #* Working in high-dimensional space
@@ Line 45: / Line 44: @@
 #** Prediction
 #** Anomaly detection
 === Textbooks ===

@@ Line 42: / Line 42: @@
 #* MLE is an optimization problem that usually cannot be solved analytically
 #* Use modeling and optimization skills to solve an interesting problem:
-##* Clustering
+#** Clustering
-##* Prediction
+#** Prediction
-##* Anomaly detection
+#** Anomaly detection
 </div>

@@ Line 21: / Line 21: @@
 <div style="-moz-column-count:2; column-count:2;">
 # Geometry and linear algebra in high-dimensional space
-** Working in high-dimensional space
+#* Working in high-dimensional space
-** Intro to dimension reduction (including for visualization and computational necessity)
+#* Intro to dimension reduction (including for visualization and computational necessity)
 #* Johnson-Lindenstrauss
 #* SVD
-##* For dimension reduction
+#** For dimension reduction
-##* For data compression
+#** For data compression
-##* PCA
+#** PCA
-##* Use to solve the normal equation of OLS, even with collinearity
+#** Use to solve the normal equation of OLS, even with collinearity
 #* More about eigenvalues and eigenvectors and their uses
 #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups

@@ Line 21: / Line 21: @@
 <div style="-moz-column-count:2; column-count:2;">
 # Geometry and linear algebra in high-dimensional space
-## Working in high-dimensional space
+** Working in high-dimensional space
-#* Intro to dimension reduction (including for visualization and computational necessity)
+** Intro to dimension reduction (including for visualization and computational necessity)
 #* Johnson-Lindenstrauss
 #* SVD

← Older revision		Revision as of 15:01, 2 October 2024
Line 19:		Line 19:

	=== Minimal learning outcomes ===		=== Minimal learning outcomes ===
		+	<div style="-moz-column-count:2; column-count:2;">
		+	# Geometry and linear algebra in high-dimensional space
		+	#* Working in high-dimensional space
		+	#* Intro to dimension reduction (including for visualization and computational necessity)
		+	#* Johnson-Lindenstrauss
		+	#* SVD
		+	##* For dimension reduction
		+	##* For data compression
		+	##* PCA
		+	##* Use to solve the normal equation of OLS, even with collinearity
		+	#* More about eigenvalues and eigenvectors and their uses
		+	#* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups
		+	# Optimization
		+	#* Motivation: Overview of Machine Learning—it’s all just optimization and sampling
		+	#* Gradients and Hessians and what they tell us about the loss landscape
		+	#* Symbolic and automatic differentiation (sympy and autograd)
		+	#* Gradient descent
		+	#* Newton and Quasi-Newton
		+	#* Regularization
		+	# Probabilistic Modeling
		+	#* Basic distributions, both discrete and continuous
		+	#* MLE is an optimization problem that usually cannot be solved analytically
		+	#* Use modeling and optimization skills to solve an interesting problem:
		+	##* Clustering
		+	##* Prediction
		+	##* Anomaly detection
		+
		+	</div>

	=== Textbooks ===		=== Textbooks ===