Top 100 mathematics keywords for Data Science – Part 1

Whoever is teaching you data science without teaching you Mathematics especially optimization is not teaching it right to you. That’s my biggest learning from Master of Data Science at IIT Gandhinagar – it will take you good 2 years to learn the related mathematics in all four major areas below. It’s not possible to learn this mathematics in few weeks even months, it will take a year or two. Here are the top 100 mathematical keywords commonly used in Data Science, Machine Learning, and AI (sourced from ChatGPT):


1. Probability & Statistics

  1. Probability
  2. Random Variable
  3. Expectation (Mean)
  4. Variance
  5. Standard Deviation
  6. Skewness
  7. Kurtosis
  8. Probability Density Function (PDF)
  9. Cumulative Distribution Function (CDF)
  10. Bayes’ Theorem
  11. Conditional Probability
  12. Joint Probability
  13. Likelihood
  14. Maximum Likelihood Estimation (MLE)
  15. Prior Probability
  16. Posterior Probability
  17. Hypothesis Testing
  18. Null Hypothesis (H0H_0)
  19. Alternative Hypothesis (HAH_A)
  20. p-value
  21. Confidence Interval
  22. T-test
  23. Chi-square Test
  24. ANOVA (Analysis of Variance)
  25. Z-score
  26. Central Limit Theorem (CLT)
  27. Law of Large Numbers
  28. Binomial Distribution
  29. Poisson Distribution
  30. Normal Distribution
  31. Gaussian Distribution
  32. Exponential Distribution
  33. Log-normal Distribution

2. Linear Algebra

  1. Vector
  2. Matrix
  3. Scalar
  4. Tensor
  5. Eigenvalues
  6. Eigenvectors
  7. Determinant
  8. Singular Value Decomposition (SVD)
  9. Principal Component Analysis (PCA)
  10. Covariance Matrix
  11. Orthogonality
  12. Dot Product
  13. Cross Product
  14. Matrix Multiplication
  15. Rank of a Matrix
  16. Trace of a Matrix
  17. Identity Matrix
  18. Inverse Matrix
  19. Transpose of a Matrix
  20. Diagonalization
  21. Gram-Schmidt Process

3. Calculus & Optimization

  1. Derivative
  2. Partial Derivative
  3. Gradient
  4. Hessian Matrix
  5. Jacobian Matrix
  6. Chain Rule
  7. Gradient Descent
  8. Stochastic Gradient Descent (SGD)
  9. Learning Rate
  10. Loss Function
  11. Cost Function
  12. Objective Function
  13. Convex Function
  14. Concave Function
  15. Local Minimum
  16. Global Minimum
  17. Local Maximum
  18. Global Maximum
  19. Lagrange Multipliers
  20. Optimization
  21. Regularization
  22. L1 Regularization (Lasso)
  23. L2 Regularization (Ridge)

4. Machine Learning Metrics & Functions

  1. Accuracy
  2. Precision
  3. Recall
  4. F1-score
  5. ROC Curve
  6. AUC (Area Under Curve)
  7. Confusion Matrix
  8. True Positive (TP)
  9. True Negative (TN)
  10. False Positive (FP)
  11. False Negative (FN)
  12. Logarithm (Log)
  13. Exponential Function
  14. Softmax Function
  15. Sigmoid Function
  16. Activation Function
  17. Cross-Entropy Loss
  18. Mean Squared Error (MSE)
  19. Mean Absolute Error (MAE)
  20. Hinge Loss
  21. Kullback-Leibler Divergence
  22. Entropy
  23. Information Gain

These 100 mathematical keywords form the foundation of Data Science, Machine Learning, and AI.

PartyRock.aws apps – Part 1

Here is a list of my experimentation with PartyRock@AWS since last 2 days. It seems like an amazing platform. Try out the 11 apps and do provide feedback. What is nice is that it creates apps with widgets and various flows using only one line of description.

https://partyrock.aws/u/neil-hsopc/8kdTd2eUX/ResearchMate

Welcome to the Research Methodology Assistant. This tool will help you explore and develop appropriate research methodologies for your field of study. Whether you’re working in natural sciences, mathematics, social sciences, or humanities, we’ll help you identify suitable approaches and discuss their implementation.

https://partyrock.aws/u/neil-hsopc/e3j8uV107/EngiChat

Welcome to the Engineering Explorer! This interactive tool helps you learn about and discuss various engineering disciplines, from civil to quantum engineering. Start by entering your engineering-related question or topic of interest, select a broad category, and receive detailed information followed by an interactive discussion.

https://partyrock.aws/u/neil-hsopc/o19Ul0xtV/CodeTalk

Welcome to the Programming Languages Discussion Assistant! This tool helps you learn about different programming languages, get explanations of concepts, and see example code. Start by entering the programming language you want to discuss, then ask specific questions or request examples.

https://partyrock.aws/u/neil-hsopc/3bCf86mab/TechIntelligence-Nexus

Welcome to the AI Technology Explorer! This interactive assistant helps you explore and understand cutting-edge technologies in artificial intelligence, quantum computing, and cybersecurity. Simply select your area of interest and ask specific questions to begin an in-depth discussion.

https://partyrock.aws/u/neil-hsopc/hXEGkurZE/Globetrotter’s-Palette

Welcome to the Global Cultural Explorer! Here you can discover and learn about movies, music, places, and cultural traditions from around the world. Start by entering what interests you and selecting a category.

https://partyrock.aws/u/neil-hsopc/JnXSYu7VX/TechLeadChat

Welcome to the Tech & Management Discussion Assistant. This tool helps you explore and discuss topics related to technology and management. Start by entering your topic or question, select the primary focus area, and the AI will provide relevant context before engaging in a detailed discussion.

https://partyrock.aws/u/neil-hsopc/VZpGXXRo7/ScienceSync

Welcome to the Science Explorer! This interactive tool helps you learn about various scientific fields including Physics, Chemistry, and Biology. Choose your field of interest and ask specific questions to get detailed explanations. You can also engage in an interactive discussion about any scientific topic.

https://partyrock.aws/u/neil-hsopc/deJPerhon/TruthSift

Welcome to the Fact Checker Assistant. This tool helps you analyze claims and statements to determine their accuracy using reliable sources and AI-powered analysis. Start by entering a claim you’d like to fact-check, optionally upload supporting documents, and get a detailed analysis.

https://partyrock.aws/u/neil-hsopc/YDhulASn9/MathViz

Welcome to the Mathematics Visualization Assistant! This tool helps you explore mathematical concepts through discussion and visual representation. Enter your mathematical question or concept below, and I’ll help you understand it through explanations, discussions, and visual aids.

https://partyrock.aws/u/neil-hsopc/He7Rk5gJs/WikiGPT-Insights

Enter a topic to explore Wikipedia content and analyze it using AI. The assistant will help you understand the content better and answer any questions you have about the topic.

https://partyrock.aws/u/neil-hsopc/A-Tqrcto8/ForensiScan

Welcome to the Cyber Forensics Analysis Tool. This tool helps you analyze files for potential security threats, malware signatures, metadata anomalies, and hidden content. Upload your file and select the type of analysis you’d like to perform.

Major optimization techniques in Data Science categorized by constrained vs. unconstrained scenarios – Part 1

1. Unconstrained Optimization Methods

(Used when there are no explicit constraints on variables)

  • Gradient-Based Methods
  • Second-Order Methods
  • Heuristic & Meta-Heuristic Methods
  • Bayesian Optimization

2. Constrained Optimization Methods

(Used when optimization involves constraints on variables)

  • Convex Optimization Methods
  • Augmented Lagrangian Methods
  • Penalty Methods
  • Sequential Quadratic Programming (SQP)
  • Interior-Point Methods
  • Constraint-Specific Heuristic Approaches

Here are the Wikipedia references for each optimization method:

Unconstrained Optimization Methods

  1. Gradient Descent
  2. Stochastic Gradient Descent (SGD)
  3. Mini-Batch Gradient Descent
  4. Momentum
  5. Nesterov Accelerated Gradient (NAG)
  6. RMSprop
  7. AdaGrad
  8. Adam
  9. Adadelta
  10. Newton’s Method
  11. Quasi-Newton Methods (BFGS, L-BFGS)
  12. Conjugate Gradient Method
  13. Genetic Algorithms
  14. Simulated Annealing
  15. Particle Swarm Optimization (PSO)
  16. Bayesian Optimization

Constrained Optimization Methods

  1. Linear Programming (LP)
  2. Simplex Method
  3. Interior Point Methods
  4. Quadratic Programming (QP)
  5. Semidefinite Programming (SDP)
  6. Augmented Lagrangian Method
  7. Penalty Method (Quadratic Penalty)
  8. Barrier Methods (Log Barrier)
  9. Sequential Quadratic Programming (SQP)
  10. Interior-Point Method
  11. Genetic Algorithms with Constraints
  12. Constrained Particle Swarm Optimization (CPSO)