Topics on Mathematics

Topics on Mathematics have been divided into the following three sections:

(A) Level 0: Introduction to Probability and Statistics – Course Curricula -Probability & Statistics 5.6.2020

Sl no Name Module Topics
1 Introduction to Statistics 1 Introduction to Statistics
2 Data and Variable Types
3 Application areas – Polling, Customer Surveys, Drug Trials
4 Statistical Fallacies
2 Univariate Descriptive Statistics 1 Introduction
2 Measures of Location – Mean, Median, Mode, Partition Values
3 Measures of Dispersion – Measures of Variance and Shape
4 Freuquency tables and distributions
5 Diagrammatic Representation – Bar Diagrams, 2-D Diagrams, Pie Diagrams, Cartograms, and Pictograms
6 Graphical Presentations for – Frequency distributions, Time series, Stem-and-leaf display, and Box plot
7 Data Treatment – Transformations and Data Cleaning
3 Bivariate Descriptive Statistics 1 Introduction
2 Visualizations
3 Correlation
4 Analysing Categorical-Categorical Variables
4 Probability and Statistics 1 Why statistics + Data visualization
2 Summary statistics and probability
3 Probability distributions and central limit theorem (CLT)
4 Confidence intervals
5 Hypothesis testing – t test, z test
6 Hypothesis testing – chi square, ANOVA

(B) Machine Learning – Course Curricula -Machine Learning 19th-Oct-2020

Introduction to Machine Learning

 

Sl no Name Module Topics
1 Machine Learning: Level 01 1 Pre-requisite 1: R Programming
2 Pre-requisite 2: Python Programming
3 Mandatory 1: Hypothesis Testing
4 Mandatory 2: Exploratory Data Analysis
5 Mandatory 3: Feature Engineering
6 Mandatory 4: Forecasting

Machine Learning paradigms in detail

Sl no Name Module Topics
1 Time series forecasting 1 Time series forecasting
2 Regression: Level 01 1 Linear Regression
3 Regression: Level 02 1 Correlation and linear regression
2 GLMs and log-linear models
4 Regression: Level 03 1 Principal Component Regression (PCR)
2 Partial Least Square (PLS)
3 MARS, LARS and Quantile Regression
5 Classification: Level 01 1 Fundamentals of Classification and Introduction to Logistic Regression, Decision Trees, Random Forest, SVM, and XGBoost
6 Classification: Level 02 1 Logistic regression
2 Regularization in regression (Ridge, Lasso, Elastic Net)
3 K-Nearest Neighbor (KNN) and Naïve Bayes Classifier (NBC)
4 Model evaluation and diagnostic techniques
7 Decision Trees and Random Forests 1 Intro to decision tree and pruning the tree
2 Bagging and random forest
3 Boosting
8 Principal Component Analysis (PCA) 1 Dimensionality reduction using Principal Component Analysis (PCA)
9 Factor Analysis

 

 1 Beginner’s Guide
2 Math Behind Factor Analysis
3 Exploratory Factor Analysis
4 Confirmatory Factor Analysis
5 Implementation in R, Python, SPSS and PSPP
10 Clustering: Level 01 1 Clustering
11 Clustering: Level 02 1 Introduction to cluster analysis
2 K-means clustering
3 K-medoids clustering
4 Hierarchical clustering
5 Clustering validation and diagnostics
12 Model Validation: Level 01 1 Model Validation
13 Model Validation: Level 02 1 Introduction
2 Common Techniques
3 Clustering Validation
4 Classification Validation
5 Regression Validation
14 Advanced machine learning algorithms 1 Support Vector Machines (SVM)
2 Linear Discriminant Analysis (LDA)

(C) Deep Learning – Click to Download Course Curricula -Deep Learning 26.5.2020

Sl no Name Module Topics
1 Supervised Neutral Networks and Deep Learning 1 Abbreviations and python libraries
2 Introduction to Neural Networks and Deep Learning
3 Artificial Neural Networks (ANN)
4 Convolutio al Neural Networks (CNN)
5 Recurrent Neural Networks (RNN)
2 Unsupervised Neutral Networks and Deep Learning 1 Self-Organizaing Maps (SOM) or Kohonen Maps
2 Boltzmann Machines
3 Auto-Encoders
4 Appendix and further reading links
3 Reinforcement Learning: Level 01 1 Introduction to reinforcement learning
2 Nuances of Reinforcement learning
3 Q learning
4 Deep Q learning
5 Improvements in Deep Q learning
4 Reinforcement Learning: Level 02 1 Policy gradients with cartpole and doom
2 Advantage actor critic (A2C) methods
3 Proximal policy optimization (PPO)
4 Curiosity driven learning

D) Applied Math – Course Curricula -Applied Math 22.9.2020

Sl no Name Module Topics
1 Graph Theory: Level 01 1 General definitions and terminology
2 Problems
3 Self-assessment
4 Areas of application
5 Solving a problem
2

Graph Theory: Level 02

 1 Minimum Spanning Trees
2 Bellman–Ford algorithm
3 Borůvka’s algorithm
4 Breadth-first search
5 Depth-first search
6 Dijkstra’s algorithm
7 Edmonds–Karp algorithm
8 Floyd–Warshall algorithm
9 Ford–Fulkerson algorithm
10 Hopcroft–Karp algorithm
11 Hungarian algorithm
12 Kosaraju’s algorithm
13 Kruskal’s algorithm
14 Nearest neighbor algorithm
15 Network simplex algorithm
16 Planarity testing algorithms
17 Prim’s algorithm
18 Push–relabel maximum flow algorithm
19 Tarjan’s strongly connected components algorithm
20 Topological sorting

Further Reading

For queries/clarifications regarding the contents in this page, please contact: MSU_mulearn@mu-sigma.com